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  • 1995-1999  (160,909)
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  • Books  (111)
  • Articles  (299,440)
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  • 1
    Electronic Resource
    Electronic Resource
    Nonextensive Bose–Einstein condensation model (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1268-1279 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The imperfect Boson gas supplemented with a gentle repulsive interaction is completely solved. In particular, it is proved that it has nonextensive Bose–Einstein condensation, i.e., there is condensation without macroscopic occupation of the ground (k=0) state level. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532800
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  • 2
    Electronic Resource
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    Dynamical semigroups for interacting quantum and classical systems (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1300-1316 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A mathematical framework for the completely positive semigroup coupling between classical and quantum systems is proposed. The coupling ensures a flow of information from the quantum system to the classical one and the influence of the classics on the dynamics of the quantum system in a dissipative way. The classical evolution on average is modified by the expectation value of some quantum operator. Examples of a classical particle moving along a geodesic line in a curved space interacting with the quantum system, and the coupling of a two state quantum system to all pure states, are discussed. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532803
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  • 3
    Electronic Resource
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    Toward quantum mathematics. I. From quantum set theory to universal quantum mechanics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1344-1358 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We develop the old idea of von Neumann of a set theory with an internal quantum logic in a modern categorical guise [i.e., taking the objects of the category H of (pre-)Hilbert spaces and linear maps as the sets of the basic level]. We will see that in this way it is possible to clarify the relationship between categorification and quantization and besides this to understand that in some sense a categorificational approach to quantization is a discretized version of the one taken by noncommutative geometry. The tower of higher categorifications will appear as the analog of the von Neumann hierarchy of classical set theory (where by classical set theory, we will understand the usual Zermelo–Fraenkel system). Finally, we make a suggestion of how to understand all the different categorifications as different realizations of one and the same abstract structure by viewing quantum mechanics as universal in the sense of category theory. This gives the possibility to view extended topological quantum field theories purely as involving an abstract notion of quantum mechanics plus representation theory without the need to enlarge the class of kinematic structures of quantum systems on each step of categorification. In a future part of the work we will apply the language developed here to deal especially with the question of a categorification of the manifold notion. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532806
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  • 4
    Electronic Resource
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    Extended Jordanian twists for Lie algebras (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4569-4586 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Jordanian quantizations of Lie algebras are studied using the factorizable twists. For a restricted Borel subalgebra B∨ of sl(N) the explicit expressions are obtained for the twist element F, universal R-matrix and the corresponding canonical element T. It is shown that the twisted Hopf algebra UF(B∨) is self-dual. The cohomological properties of the involved Lie bialgebras are studied to justify the existence of a contraction from the Dinfeld–Jimbo quantization to the Jordanian one. The construction of the twist is generalized to a certain type of inhomogenious Lie algebras. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532987
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  • 5
    Electronic Resource
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    Operator representations of a q-deformed Heisenberg algebra (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4596-4605 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A class of well-behaved * -representations of a q-deformed Heisenberg algebra previously introduced [Phys. Lett. B 291, 273 (1992); Z. Phys. C 64, 335 (1994)] is studied and classified. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532989
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  • 6
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    On the root mean square quantitative chirality and quantitative symmetry measures (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4587-4595 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The properties of the root mean square chiral index of a d-dimensional set of n points, previously investigated for planar sets, are examined for spatial sets. The properties of the root mean squares direct symmetry index, defined as the normalized minimized sum of the n squared distances between the vertices of the d-set and the permuted d-set, are compared to the properties of the chiral index. Some most dissymetric figures are analytically computed. They differ from the most chiral figures, but the most dissymetric 3-tuples and the most chiral 3-tuples have a common remarkable geometric property: the squared lengths of the sides are each equal to three times a squared distance vertex to the mean point. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532988
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  • 7
    Electronic Resource
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    Asymptotics of the scattering coefficients for a generalized Schrödinger equation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3701-3709 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The generalized Schrödinger equation d2ψ/dx2+F(k)ψ=[ikP(x)+Q(x)]ψ is considered, where P and Q are integrable potentials with finite first moments and F satisfies certain conditions. The behavior of the scattering coefficients near zeros of F is analyzed. It is shown that in the so-called exceptional case, the values of the scattering coefficients at a zero of F may be affected by P(x). The location of the k-values in the complex plane where the exceptional case can occur is studied. Some examples are provided to illustrate the theory. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532920
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  • 8
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    On the dynamics of the Holstein model from the anticontinuous limit (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3710-3717 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider the Holstein model describing an electron interacting with a lattice of identical oscillators. We remark that the on site system (i.e., the system in which the interaction between the different sites of the lattice vanishes) is integrable and anisocronous. This allows us to apply some recent Nekhoroshev-type results to show that corresponding to the majority of initial data in which the electron probability is concentrated on a finite number of sites, the electron probability distribution is approximatively constant for times growing exponentially with the inverse of the coupling parameter. Moreover, for the same times, the total energy of the oscillator system is approximatively constant. © 1999 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532921
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  • 9
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    Generalized Lamé functions. I. The elliptic case (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1595-1626 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We present and study a class of functions associated with the two-particle quantum relativistic Calogero–Moser system with elliptic interactions. The functions may be viewed as joint eigenfunctions of two independent commuting analytic difference operators, one of which is the defining quantum dynamics; The second one is obtained by interchanging the step size and the imaginary period. The functions depend on parameters that are dense in the natural parameter domain. In essence, they consist of products of Weierstrass σ-functions and plane waves. The zeros of the σ-functions satisfy a constraint system encoding both Schrödinger equations at once. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532822
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  • 10
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    A reverse log-Sobolev inequality in the Segal-Bargmann space (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1677-1695 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This article is based on recent results of the author on the properties of the reproducing kernel of the Segal-Bargmann space. Those results are used here to demonstrate a family of energy-entropy inequalities in the Segal-Bargmann space. In some cases this is a log-Sobolev inequality while in other cases this is actually a reverse log-Sobolev inequality, which means that the energy term is bounded above by the entropy term, plus a norm term. This implies that in the Segal-Bargmann space the entropy is finite if and only if the energy is finite. Applications of this result to the Segal-Bargmann transform are given as well as a discussion of its possible relation with reverse hypercontractivity. It should be noted that all of the results of this article are proved without using hypercontractivity estimates. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532825
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  • 11
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    The Eikonal equation in asymptotically flat space–times (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1041-1056 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In an arbitrary Lorentzian manifold we provide a description for the construction of null surfaces and their associated singularities, via solutions of the Eikonal equation. In particular, we study the singularities of the past light-cones from points on null infinity, the future light-cones from arbitrary interior points and the intersection of these with null infinity and unifying relationships between the different singularities. The starting point for this work is the assumption of a known family of solutions to the Eikonal equation. The work is based on the standard theory of singularities of smooth maps by Arnold and his colleagues. Though the work is intended to stand on its own, it can be thought of as being closely related to the recently developed null surface reformulation of GR. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532705
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  • 12
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    Characteristic surface data for the eikonal equation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1093-1102 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A method of solving the eikonal equation, in either flat or curved space–times, with arbitrary Cauchy data, is extended to the case of data given on a characteristic surface. We find a beautiful relationship between the Cauchy and characteristic data for the same solution, namely they are related by a Legendre transformation. From the resulting solutions, we study and describe the wave-front singularities that are associated with their level surfaces (the characteristic surfaces or "big wave fronts"). © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532708
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  • 13
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    Erratum: "On the dynamics of characteristic surfaces" [J. Math. Phys. 36, 6397–6416 (1995)] (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1113-1113 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.532702
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  • 14
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    Erratum: "GR via characteristic surfaces" [J. Math. Phys. 36, 4984–5004 (1995)] (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1115-1115 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
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    URL: http://dx.doi.org/10.1063/1.532700
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  • 15
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    Functional versus canonical quantization of a nonlocal massive vector-gauge theory (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 585-600 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It has been shown in literature that a possible mechanism of mass generation for gauge fields is through a topological coupling of vector and tensor fields. After integrating over the tensor degrees of freedom, one arrives at an effective massive theory that, although gauge invariant, is nonlocal. Here we quantize this nonlocal resulting theory both by path integral and canonical procedures. This system can be considered as equivalent to one with an infinite number of time derivatives and consequently an infinite number of momenta. This means that the use of the canonical formalism deserves some care. We show the consistency of the formalism we use in the canonical procedure by showing that the obtained propagators are the same as those of the (Lagrangian) path integral approach. The problem of nonlocality appears in the obtainment of the spectrum of the theory. This fact becomes very transparent when we list the infinite number of commutators involving the fields and their velocities. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532677
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  • 16
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    The osp(1,2)-covariant Lagrangian quantization of irreducible massive gauge theories (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 674-698 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The osp(1,2)-covariant Lagrangian quantization of general gauge theories is formulated which applies also to massive fields. The formalism generalizes the Sp(2)-covariant Batalin–Lavrov–Tyutin (BLT) approach and guarantees symplectic invariance of the quantized action. The dependence of the generating functional of Green's functions on the choice of gauge in the massive case disappears in the limit m→0. Ward identities related to osp(1,2) symmetry are derived. Massive gauge theories with closed algebra are studied as an example. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532681
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  • 17
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    Bethe ansatz solution of a closed spin 1 XXZ Heisenberg chain with quantum algebra symmetry (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 726-735 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A quantum algebra invariant integrable closed spin 1 chain is introduced and analyzed in detail. The Bethe ansatz equations as well as the energy eigenvalues of the model are obtained. The highest weight property of the Bethe vectors with respect to Uq(sl(2)) is proved. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532701
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  • 18
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    On rotational coherent states in molecular quantum dynamics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 766-786 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Coherent states suitable for the description of molecular rotations are developed and their connection to similar coherent states in the literature are explored. In particular their quasiclassical properties are developed. The use of such coherent states in time-dependent electron nuclear dynamics studies of molecular collision processes is discussed. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532684
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  • 19
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    Reduction of constrained systems with symmetries (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 795-820 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general model is proposed for constrained dynamical systems on a symplectic manifold which covers, among others, the description of Lagrangian and Hamiltonian systems with nonholonomic constraints and the canonical description of mechanical systems with a singular Lagrangian. The reduction properties of these systems in the presence of symmetry are investigated within this general framework. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532686
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  • 20
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    The Camassa–Holm equation as a geodesic flow on the diffeomorphism group (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 857-868 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Misiolek [J. Geom. Phys. 24, 203–208 (1998)] has shown that the Camassa–Holm equation is a geodesic flow on the Bott–Virasoro group. In this paper it is shown that the Camassa–Holm equation for the case κ=0 is the geodesic spray of the weak Riemannian metric on the diffeomorphism group of the line or the circle obtained by right translating the H1 inner product over the entire group. This paper uses the right-trivialization technique to rigorously verify that the Euler–Poincaré theory for Lie groups can be applied to diffeomorphism groups. The observation made in this paper has led to physically meaningful generalizations of the CH-equation to higher dimensional manifolds. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532690
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  • 21
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    Similarity reduction for a class of algebraically special perfect fluids (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 897-908 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For a class of perfect fluids first considered by Wainwright [Int. J. Theor. Phys. 10, 39 (1974)], a complete symmetry analysis of the field equations is performed. The results are used for a symmetry reduction of the field equations and the construction of (new) similarity solutions. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532693
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  • 22
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    Nonlinear realizations of the diffeomorphism group in metric-affine gauge theory of gravity (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 939-954 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The action of diffeomorphisms on coupled metric and spinor fields on a world manifold X is interpreted in terms of nonlinear realizations of the group GL&dbigwig;+(4,R), the universal twofold covering group of the general linear group GL+(4,R), on the quotient manifold (GL&dbigwig;+(4,R)×V)/SL(2,C), where SL(2,C) is the spin group and V is the spinor space. By using nonlinear realizations the connection of a metric-affine world manifold couples naturally to standard spinor fields. This enables us not to exceed the scope of usual spinor models as in the case in which infinite-dimensional representations of GL&dbigwig;+(4,R) are considered. As an application, by starting from the familiar Lagrangian for spin-1/2 models and using the nonlinear realization method, a Lagrangian density for spinor fields which has GL&dbigwig;+(4,R) as invariance group is constructed. The total Lagrangian density is obtained by adding the Lagrangian of the metric-affine gravity. The energy-momentum current associated with every vector field on the world manifold X is calculated explicitly. It turns out that spinor fields do not contribute to the corresponding superpotential, which takes a form similar to that obtained by Komar. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532696
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  • 23
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    Singularities at the tip of a plane angular sector (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1087-1092 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Solutions of the Helmholtz and Laplace equations in three dimensions which vanish, or have vanishing normal derivative on an angular sector of opening angle β, are considered. The solutions are required to be functions of distance from the tip of the sector multiplied by functions of the angular coordinates. The angular functions are eigenfunctions of the Laplace–Beltrami operator on the unit sphere, which vanish or have vanishing normal derivative, on a great circle arc of length β. It is shown that the Dirichlet eigenvalues are nondecreasing functions of β, and the Neumann eigenvalues are nonincreasing. Furthermore, each Dirichlet eigenvalue of a sector of angle β is a Neumann eigenvalue of a sector of angle 2π−β and conversely. The eigenvalues for β=0, π, and 2π are found explicitly. These results lead to a qualitative description of the eigenvalues as functions of β. The eigenvalues determine the singular behavior of the solutions at the tip. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532707
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    Application of geometric probability techniques to the evaluation of interaction energies arising from a general radial potential (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1103-1112 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A formalism is developed for using geometric probability techniques to evaluate interaction energies arising from a general radial potential V(r12), where r12=|r2−r1|. The integrals that arise in calculating these energies can be separated into a radial piece that depends on r12 and a nonradial piece that describes the geometry of the system, including the density distribution. We show that all geometric information can be encoded into a "radial density function" G(r12;ρ1,ρ2), which depends on r12 and the densities ρ1 and ρ2 of two interacting regions. G(r12;ρ1,ρ2) is calculated explicitly for several geometries and is then used to evaluate interaction energies for several cases of interest. Our results find application in elementary particle, nuclear, and atomic physics. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532709
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    Wigner–Weyl correspondence and semiclassical quantization in spherical coordinates (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6302-6318 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Wigner–Weyl quantum-to-classical correspondence rule is nonunique with respect to coordinate choice. This ambiguity can be exploited to improve the accuracy of semiclassical approximations. For instance, the well-known Langer modification was recently derived by applying a coordinate transformation to the radial Schrödinger equation prior to using the Wigner–Weyl rule—albeit only by presuming exact quantum solutions for all nonradial degrees of freedom [J. J. Morehead, J. Math. Phys. 36, 5431 (1995)]. In this paper, the full classical Hamiltonian is derived in all degrees of freedom, using a (hyper)spherical coordinate Wigner–Weyl correspondence with a Langer-like modification of polar angles. For central force Hamiltonians, the new result is radially equivalent to that of Langer, and to the standard Cartesian form. The new correspondence is superior with respect to all angular momentum operators however, in that the resultant semiclassical eigenvalues are exact—a desirable goal, evidently achieved here for the first time. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.533094
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  • 26
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    SU(N) skyrmions and harmonic maps (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6353-6365 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Harmonic maps from S2 to CPN−1 are introduced to construct low-energy configurations of the SU(N) Skyrme model. We show that one of such maps gives an exact, topologically trivial, solution of the SU(3) model. We study various properties of these maps and show that, in general, their energies are only a little higher than the energies of the corresponding SU(2) embeddings. Moreover, we show that the baryon and energy densities of the SU(3) configurations with baryon number B=3−6 are more symmetrical than their SU(2) analogs, thus suggesting that there exist solutions of the model with these symmetries. We also show that any SU(2) solution embedded into the SU(4) Skyrme model becomes a topologically trivial solution of this model. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.533097
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  • 27
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    Quasilinearization method and its verification on exactly solvable models in quantum mechanics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6266-6291 
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    Topics: Mathematics , Physics
    Notes: The proof of the convergence of the quasilinearization method of Bellman and Kalaba, whose origin lies in the theory of linear programming, is extended to large and infinite domains and to singular functionals in order to enable the application of the method to physical problems. This powerful method approximates solution of nonlinear differential equations by treating the nonlinear terms as a perturbation about the linear ones, and is not based, unlike perturbation theories, on existence of some kind of small parameter. The general properties of the method, particularly its uniform and quadratic convergence, which often also is monotonic, are analyzed and verified on exactly solvable models in quantum mechanics. Namely, application of the method to scattering length calculations in the variable phase method shows that each approximation of the method sums many orders of the perturbation theory and that the method reproduces properly the singular structure of the exact solutions. The method provides final and reasonable answers for infinite values of the coupling constant and is able to handle even super singular potentials for which each term of the perturbation theory is infinite and the perturbation expansion does not exist. © 1999 American Institute of Physics.
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    Picard–Fuchs equations and Whitham hierarchy in N=2 supersymmetric SU(r+1) Yang–Mills theory (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6292-6301 
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    Topics: Mathematics , Physics
    Notes: In general, Whitham dynamics involves infinitely many parameters called Whitham times, but in the context of N=2 supersymmetric Yang–Mills theory it can be regarded as a finite system by restricting the number of Whitham times appropriately. For example, in the case of SU(r+1) gauge theory without hypermultiplets, there are r Whitham times and they play an essential role in the theory. In this situation, the generating meromorphic one-form of the Whitham hierarchy on the Seiberg–Witten curve is represented by a finite linear combination of meromorphic one-forms associated with these Whitham times, but it turns out that there are various differential relations among these differentials. Since these relations can be written only in terms of the Seiberg–Witten one-form, their consistency conditions are found to give the Picard–Fuchs equations for the Seiberg–Witten periods. © 1999 American Institute of Physics.
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    Geodesic completeness of orthogonally transitive cylindrical space–times (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4028-4034 
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    Notes: In this paper a theorem is derived in order to provide a wide sufficient condition for an orthogonally transitive cylindrical space–time to be singularity free. The applicability of the theorem is tested on examples provided by the literature that are known to have regular curvature invariants. © 1999 American Institute of Physics.
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    Zeros of the Jimbo, Miwa, Ueno tau function (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6638-6681 
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    Notes: We introduce a family of local deformations for meromorphic connections on P1 in the neighborhood of a higher rank (simple) singularity. Following the scheme in Malgrange [Mathematique et Physique, Progress in Mathematics (Birkhäuser, Boston, 1983), Vol. 37, pp. 381–400, ibid., pp. 401–426; ibid., pp. 427–438] we use these local models to prove that the zeros of the tau function, introduced by Jimbo, Miwa, and Ueno in their pioneering work on "Birkhoff" deformations at irregular singular points [Physica D 2, 306–352; 2, 407–448 (1981); 4, 26–46 (1983); Publ. RIMS Kyoto Univ. 17-2, 703–721 (1981)], occur at precisely those points in the deformation space at which a certain Birkhoff–Riemann–Hilbert problem fails to have a solution. © 1999 American Institute of Physics.
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    Invariance groups of transformations of basic hypergeometric series (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6692-6700 
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    Notes: We show that certain two-term transformation formulas between basic hypergeometric series can easily be described by means of invariance groups. For the transformations of nonterminating 3φ2 series, and those of terminating balanced 4φ3 series, these invariance groups are symmetric groups. For transformations of 2φ1 series the invariance group is the dihedral group of order 12. Transformations of terminating 3φ2 series are described by means of some subgroup of S6, and finally the invariance group of transformations of very-well-poised nonterminating 8φ7 series is shown to be isomorphic to the Weyl group of a root system of type D5. © 1999 American Institute of Physics.
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    On the Schrödinger equation with steplike potentials (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5289-5305 
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    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: The one-dimensional Schrödinger equation is considered when the potential is asymptotic to a positive constant on the right half line in a certain sense. The zero-energy limits of the scattering coefficients are obtained under weaker assumptions than used elsewhere, and the continuity of the scattering coefficients from the left are established. The scattering coefficients for the potential are expressed in terms of the corresponding coefficients for the pieces of the potential on the positive and negative half lines. The number of bound states for the whole potential is related to the number of bound states for the two pieces. Finally, an improved result is given on the small-energy asymptotics of reflection coefficients for potentials supported on a half line. © 1999 American Institute of Physics.
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    Separation of variables for soliton equations via their binary constrained flows (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6526-6557 
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    Notes: Binary constrained flows of soliton equations admitting 2×2 Lax matrices have 2N degrees of freedom, which is twice as many degrees of freedom than in the case of monoconstrained flows. By using the normal method, their Lax matrices directly give rise to first N pairs of canonical separated variables for their separation of variables. We propose a new method to introduce the other N pairs of canonical separated variables and additional separated equations. The Jacobi inversion problems for binary constrained flows are established. Finally, the factorization of soliton equations by two commuting binary constrained flows and the separability of binary constrained flows enable us to construct the Jacobi inversion problems for some soliton hierarchies. © 1999 American Institute of Physics.
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    On the limiting power of the set of knots generated by 1+1- and 2+1-braids (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6598-6608 
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    Notes: We estimate from above the set of knots, Ω(n,μ), generated by closure of the n-string 1+1- and 2+1-dimensional braids of irreducible length μ(μ(very-much-greater-than)1) in the limit n(very-much-greater-than)1. © 1999 American Institute of Physics.
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    The osp(1,2)-covariant Lagrangian quantization of reducible massive gauge theories (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6189-6208 
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    Notes: The osp(1,2)-covariant Lagrangian quantization of irreducible gauge theories is generalized to L-stage reducible theories. The dependence of the generating functional of Green's functions on the choice of gauge in the massive case is discussed and Ward identities related to osp(1,2) symmetry are given. Massive first-stage theories with closed gauge algebra are studied in detail. The generalization of the Chapline–Manton model and topological Yang–Mills theory to the case of massive fields are considered as examples. © 1999 American Institute of Physics.
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    Casimir energy of a ball and cylinder in the zeta function technique (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 6254-6265 
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    Notes: A simple method is proposed to construct the spectral zeta functions required for calculating the electromagnetic vacuum energy with boundary conditions given on a sphere or on an infinite cylinder. When calculating the Casimir energy in this approach no exact divergencies appear and no renormalization is needed. The starting point of the consideration is the representation of the zeta functions in terms of contour integral, further the uniform asymptotic expansion of the Bessel function is essentially used. After the analytic continuation, needed for calculating the Casimir energy, the zeta functions are presented as infinite series containing the Riemann zeta function with rapidly falling down terms. The spectral zeta functions are constructed exactly for a material ball and infinite cylinder placed in a uniform endless medium under the condition that the velocity of light does not change when crossing the interface. As a special case, perfectly conducting spherical and cylindrical shells are also considered in the same line. In this approach one succeeds, specifically, in justifying, in mathematically rigorous way, the appearance of the contribution to the Casimir energy for cylinder which is proportional to ln(2π). © 1999 American Institute of Physics.
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    A generalization of Wigner's unitary–antiunitary theorem to Hilbert modules (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5544-5554 
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    Notes: Let H be a Hilbert C*-module over a matrix algebra A. It is proved that any function T:H→H which preserves the absolute value of the (generalized) inner product is of the form Tf=cursive-phi(f )Uf (f∈H), where cursive-phi is a phase-function and U is an A-linear isometry. The result gives a natural extension of Wigner's classical unitary–antiunitary theorem for Hilbert modules. © 1999 American Institute of Physics.
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    The spectrum of the Liouville–von Neumann operator in the Hilbert–Schmidt space (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4106-4118 
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    Notes: The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian. © 1999 American Institute of Physics.
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    Anomalies and analytic torsion on hyperbolic manifolds (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4119-4133 
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    Notes: The global additive and multiplicative properties of the Laplacian on j-forms and related zeta functions are analyzed. The explicit form of zeta functions on a product of closed oriented hyperbolic manifolds Γ(backward-slash)Hd and of the multiplicative anomaly are derived. We also calculate in an explicit form the analytic torsion associated with a connected sum of such manifolds.© 1999 American Institute of Physics.
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    On Lie algebras all nilpotent subalgebras of which are Abelian (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4151-4156 
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    Notes: By Kirillov's theorem, every non-Abelian nilpotent Lie algebra contains the three-dimensional Heisenberg algebra H(3) as a subalgebra. [R. Schimming, Arch. Math. 24, 65–74 (1988)]. Here we are interested in a sufficient condition for a non-nilpotent Lie algebra to contain a subalgebra isomorphic to H(3). Explicitly, we show: Every indecomposable non-nilpotent Lie algebra L of dimension dim L≥3 with a nonvanishing center Z(L)≠{0} contains a non-Abelian nilpotent subalgebra and hence a copy of H(3). © 1999 American Institute of Physics.
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    Matrix representation of octonions and generalizations (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4134-4150 
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    Notes: We define a special matrix multiplication among a special subset of 2N×2N matrices, and study the resulting (nonassociative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative nonassociative, and when they become associative. In particular, these algebras yield special matrix representations of octonions and complex numbers; they naturally lead to the Cayley–Dickson doubling process. Our matrix representation of octonions also yields elegant insights into Dirac's equation for a free particle. A few other results and remarks arise as byproducts. © 1999 American Institute of Physics.
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    Conservation laws for linear equations on braided linear spaces (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4165-4176 
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    Notes: The properties of linear equations on braided linear spaces are investigated and conservation laws for them are derived. The conserved currents are given in the explicit form. The procedure is then applied to scalar wave equations on a quantum plane and on q-Minkowski space. © 1999 American Institute of Physics.
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    Bose–Einstein condensation in an external potential at zero temperature: Solitary-wave theory (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5522-5543 
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    Notes: For a trapped, dilute atomic gas of short-range, repulsive interactions at extremely low temperatures, when Bose–Einstein condensation is nearly complete, some special forms of the time-dependent condensate wave function and the pair-excitation function, the latter being responsible for phonon creation, are investigated. Specifically, (i) a class of external potentials Ve(r,t) that allow for localized, shape-preserving solutions to the nonlinear Schrödinger equation for the condensate wave function, each recognized as a solitary wave moving along an arbitrary trajectory, is derived and analyzed in any number of space dimensions; and (ii) for any such external potential and condensate wave function, the nonlinear integro-differential equation for the pair-excitation function is shown to admit solutions of the same nature. Approximate analytical results are presented for a sufficiently slowly varying trapping potential. Numerical results are obtained for the condensate wave function when Ve is a time-independent, spherically symmetric harmonic potential. © 1999 American Institute of Physics.
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    Estimates for the spectral shift function of the polyharmonic operator (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5578-5592 
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    Notes: The Lifshits–Krein spectral shift function is considered for the pair of operators H0=(−Δ)l, l〉0 and H=H0+V in L2(Rd), d≥1; here V is a multiplication operator. The estimates for this spectral shift function ξ(λ;H,H0) are obtained in terms of the spectral parameter λ〉0 and the integral norms of V. These estimates are in a good agreement with the ones predicted by the classical phase space volume considerations. © 1999 American Institute of Physics.
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    The action operator for continuous-time histories (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5657-5674 
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    Notes: We define the action operator for the consistent histories formalism, as the quantum analog of the classical action functional, for the simple harmonic oscillator case. We conclude that the action operator is the generator of time transformations, and is associated with the two types of time evolution of the standard quantum theory: the wave-packet reduction and the unitary time evolution. We construct the corresponding classical histories and demonstrate the relevance with the quantum histories. Finally, we show the relation of the action operator to the decoherence functional. © 1999 American Institute of Physics.
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    Bethe Ansatz and thermodynamic limit of affine quantum group invariant extensions of the t–J model (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5687-5701 
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    Notes: We have constructed a one-dimensional exactly solvable model, which is based on the t–J model of strongly correlated electrons, but which has additional quantum group symmetry, ensuring the degeneration of states. We use Bethe Ansatz technique to investigate this model. The thermodynamic limit of the model is considered and equations for different density functions written down. These equations demonstrate that the additional color degrees of freedom of the model behave as in a gauge theory, namely, an arbitrary distribution of color indices over particles leave invariant the energy of the ground state and the excitations. The S-matrix of the model is shown to be the product of the ordinary t–J model S-matrix and the unity matrix in the color space. © 1999 American Institute of Physics.
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    Connections and metrics respecting purification of quantum states (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3246-3267 
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    Notes: Standard purification interlaces Hermitian and Riemannian metrics on the space of density operators with metrics and connections on the purifying Hilbert–Schmidt space. We discuss connections and metrics which are well adopted to purification, and present a selected set of relations between them. A connection, as well as a metric on state space, can be obtained from a metric on the purification space. We include a condition, with which this correspondence becomes one to one. Our methods are borrowed from elementary *-representation and fiber space theory. We lift, as an example, solutions of a von Neumann equation, write down holonomy invariants for cyclic ones, and "add noise" to a curve of pure states. © 1999 American Institute of Physics.
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    Lifetimes of impurity states in crossed magnetic and electric fields (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3275-3282 
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    Notes: We study the quantum dynamics of localized impurity states created by a point interaction for an electron moving in two dimensions under the influence of a perpendicular magnetic field and an in-plane weak electric field. All impurity states are unstable in presence of the electric field. Their lifetimes are computed and shown to grow in a Gaussian way as the electric field tends to zero. © 1999 American Institute of Physics.
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    On form-preserving transformations for the time-dependent Schrödinger equation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3268-3274 
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    Notes: In this paper we point out a close connection between the Darboux transformation and the group of point transformations which preserve the form of the time-dependent Schrödinger equation (TDSE). In our main result, we prove that any pair of time-dependent real potentials related by a Darboux transformation for the TDSE may be transformed by a suitable point transformation into a pair of time-independent potentials related by a usual Darboux transformation for the stationary Schrödinger equation. Thus, any (real) potential solvable via a time-dependent Darboux transformation can alternatively be solved by applying an appropriate form-preserving point transformation of the TDSE to a time-independent potential. The pre-eminent role of the latter type of transformations in the solution of the TDSE is illustrated with a family of quasi-exactly solvable time-dependent anharmonic potentials. © 1999 American Institute of Physics.
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    Optimal cloning of pure states, testing single clones (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3283-3299 
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    Notes: We consider quantum devices for turning a finite number N of d-level quantum systems in the same unknown pure state σ into M〉N systems of the same kind, in an approximation of the M-fold tensor product of the state σ. In a previous paper it was shown that this problem has a unique optimal solution, when the quality of the output is judged by arbitrary measurements, involving also the correlations between the clones. We show in this paper, that if the quality judgment is based solely on measurements of single output clones, there is again a unique optimal cloning device, which coincides with the one found previously. © 1999 American Institute of Physics.
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    Tunneling of a massless field through a 3D Gaussian barrier (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3300-3310 
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    Notes: We propose a method for the approximate computation of the Green function of a scalar massless field φ subjected to potential barriers of given size and shape in space–time. This technique is applied to the case of a 3D Gaussian ellipsoidlike barrier, placed on the axis between two pointlike sources of the field. Instead of the Green function we compute its temporal integral, that gives the static potential energy of the interaction of the two sources. Such interaction takes place in part by tunneling of the quanta of φ across the barrier. We evaluate numerically the correction to the potential in dependence on the barrier size and on the barrier-sources distance. © 1999 American Institute of Physics.
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    The semispin groups in string theory (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4699-4712 
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    Notes: In string theory, an important role is played by certain Lie groups which are locally isomorphic to SO(4m), m≤8. It has long been known that these groups are actually isomorphic not to SO(4m) but rather to the groups for which the half-spin representations are faithful, which we propose to call Semispin(4m). (They are known in the physics literature by the ambiguous name of "Spin(4m)/Z2.") Recent work on string duality has shown that the distinction between SO(4m) and Semispin(4m) can have a definite physical significance. This work is a survey of the relevant properties of Semispin(4m) and its subgroups. © 1999 American Institute of Physics.
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    Generalized adiabatic product expansion: A nonperturbative method of solving the time-dependent Schrödinger equation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3311-3326 
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    Topics: Mathematics , Physics
    Notes: We outline a method based on successive canonical transformations which yields a product expansion for the evolution operator of a general (possibly non-Hermitian) Hamiltonian. For a class of such Hamiltonians this expansion involves a finite number of terms, and our method gives the exact solution of the corresponding time-dependent Schrödinger equation. We apply this method to study the dynamics of a general nondegenerate two-level quantum system, a time-dependent classical harmonic oscillator, and a degenerate system consisting of a spin 1 particle interacting with a time-dependent electric field E(vector)(t) through the Stark Hamiltonian H=λ(J(vector)⋅E(vector))2. © 1999 American Institute of Physics.
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    Extended gauge theories starting from the matter field Lagrangian (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4609-4615 
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    Topics: Mathematics , Physics
    Notes: We obtain an extended gauge theory by imposing that the matter field Lagrangian is invariant under a local gauge transformation that also contains a vector parameter besides the usual scalar one. © 1999 American Institute of Physics.
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    On the number of particles that a curved quantum waveguide can bind (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4630-4638 
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    Topics: Mathematics , Physics
    Notes: We discuss the discrete spectrum of N particles in a curved planar waveguide. If they are neutral fermions, the maximum number of particles that the waveguide can bind is given by a one-particle Birman–Schwinger bound in combination with the Pauli principle. On the other hand, if they are charged, e.g., electrons in a bent quantum wire, the Coulomb repulsion plays a crucial role. We prove a sufficient condition under which the discrete spectrum of such a system is empty. © 1999 American Institute of Physics.
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    Covariant phase observables in quantum mechanics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4688-4698 
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    Notes: In this paper we characterize all the phase shift covariant normalized positive operator measures, i.e., phase observables, and we investigate some of their examples. We also characterize those phase observables which arise from the phase space observables as their polar coordinate angle margins. © 1999 American Institute of Physics.
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    Grassmann algebra and fermions at finite temperature (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4944-4955 
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    Notes: For any d-dimensional self-interacting fermionic model, all coefficients in the high-temperature expansion of its grand canonical partition function can be put in terms of multivariable Grassmann integrals. A new approach to calculate such coefficients, based on direct exploitation of the Grassmannian nature of fermionic operators, is presented. We apply the method to the soluble Hatsugai–Kohmoto model, reobtaining well-known results. © 1999 American Institute of Physics.
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    The stationary KdV hierarchy and so(2,1) as a spectrum generating algebra (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 4995-5003 
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    Topics: Mathematics , Physics
    Notes: The family FLκ of all potentials V(x) for which the Hamiltonian H=−d2/dx2+V(x) in one space dimension possesses a high-order Lie symmetry is determined. A subfamily FSGA(2) of FLκ, which contains a class of potentials allowing a realization of so(2,1) as spectrum generating algebra of H through differential operators of finite order, is identified. Furthermore and surprisingly, the families FSGA(2) and FLκ are shown to be related to the stationary KdV hierarchy. Hence, the "harmless" Hamiltonian H connects different mathematical objects: high-order Lie symmetry, the realization of so(2,1)-spectrum generating algebra and families of nonlinear differential equations. We describe in a physical context the interplay between these objects. © 1999 American Institute of Physics.
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    Algebraic exact solvability of trigonometric-type Hamiltonians associated to root systems (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5004-5013 
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    Notes: In this article, we study and settle several structural questions concerning the exact solvability of the Olshanetsky–Perelomov quantum Hamiltonians corresponding to an arbitrary root system. We show that these operators can be written as linear combinations of certain basic operators admitting infinite flags of invariant subspaces, namely the Laplacian and the logarithmic gradient of invariant factors of the Weyl denominator. The coefficients of the constituent linear combination become the coupling constants of the final model. We also demonstrate the L2 completeness of the eigenfunctions obtained by this procedure, and describe a straightforward recursive procedure based on the Freudenthal multiplicity formula for constructing the eigenfunctions explicitly. © 1999 American Institute of Physics.
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    Degenerate Frobenius manifolds and the bi-Hamiltonian structure of rational Lax equations (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5058-5079 
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    Notes: The bi-Hamiltonian structure of certain multicomponent integrable systems, generalizations of the dispersionless Toda hierarchy, is studied for systems derived from a rational Lax function. One consequence of having a rational rather than a polynomial Lax function is that the corresponding bi-Hamiltonian structures are degenerate, i.e., the metric that defines the Hamiltonian structure has a vanishing determinant. Frobenius manifolds provide a natural setting in which to study the bi-Hamiltonian structure of certain classes of hydrodynamic systems. Some ideas on how this structure may be extended to include degenerate bi-Hamiltonian structures, such as those given in the first part of the paper, is given. © 1999 American Institute of Physics.
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    Simultaneous Beltrami conditions in coupled vortex dynamics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5080-5091 
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    Notes: The two-fluid model of a plasma describes the strong coupling between the magnetic and the fluid aspects of the plasma. The Beltrami condition that demands alignment of vortices and flows becomes a system of simultaneous equations in the magnetic field and the flow velocity. Combining these equations yields the double curl Beltrami equation. General solvability of the equation has been proved using the spectral theory of the curl operator. The set of solutions contains field configurations that can be qualitatively different from the conventional constant-α-Beltrami fields (which are naturally included in the set). The larger new set may help us understand a variety of structures generated in plasmas. © 1999 American Institute of Physics.
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    On the differentiability of Cauchy horizons (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5138-5142 
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    Notes: Chrus´ciel and Galloway constructed a Cauchy horizon that is nondifferentiable on a dense set. We prove that in a certain class of Cauchy horizons densely nondifferentiable Cauchy horizons form a dense set. We show that our class of densely nondifferentiable Cauchy horizons implies the existence of densely nondifferentiable Cauchy horizons arising from partial Cauchy surfaces and also the existence of densely nondifferentiable black hole event horizons. © 1999 American Institute of Physics.
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    Well-posed forms of the 3+1 conformally-decomposed Einstein equations (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5143-5156 
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    Notes: We show that well-posed, conformally-decomposed formulations of the 3+1 Einstein equations can be obtained by densitizing the lapse and by combining the constraints with the evolution equations. We compute the characteristics structure and verify the constraint propagation of these new well-posed formulations. In these formulations, the trace of the extrinsic curvature and the determinant of the 3-metric are singled out from the rest of the dynamical variables, but are evolved as part of the well-posed evolution system. The only free functions are the lapse density and the shift vector. We find that there is a 3-parameter freedom in formulating these equations in a well-posed manner, and that part of the parameter space found consists of formulations with causal characteristics, namely, characteristics that lie only within the lightcone. In particular there is a 1-parameter family of systems whose characteristics are either normal to the slicing or lie along the lightcone of the evolving metric. © 1999 American Institute of Physics.
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    A new perturbative technique for solving integro-partial differential equations (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5224-5239 
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    Notes: Integro-partial differential equations occur in many contexts in mathematical physics. Typical examples include time-dependent diffusion equations containing a parameter (e.g., the temperature) that depends on integrals of the unknown distribution function. The standard approach to solving the resulting nonlinear partial differential equation involves the use of predictor–corrector algorithms, which often require many iterations to achieve an acceptable level of convergence. In this paper we present an alternative procedure that allows us to separate a family of integro-partial differential equations into two related problems, namely (i) a perturbation equation for the temperature, and (ii) a linear partial differential equation for the distribution function. We demonstrate that the variation of the temperature can be determined by solving the perturbation equation before solving for the distribution function. Convergent results for the temperature are obtained by recasting the divergent perturbation expansion as a continued fraction. Once the temperature variation is determined, the self-consistent solution for the distribution function is obtained by solving the remaining, linear partial differential equation using standard techniques. The validity of the approach is confirmed by comparing the (input) continued-fraction temperature profile with the (output) temperature computed by integrating the resulting distribution function. © 1999 American Institute of Physics.
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    Quasi-Hopf superalgebras and elliptic quantum supergroups (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5264-5282 
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    Notes: We introduce the quasi-Hopf superalgebras which are Z2-graded versions of Drinfeld's quasi-Hopf algebras. We describe the realization of elliptic quantum supergroups as quasi-triangular quasi-Hopf superalgebras obtained from twisting the normal quantum supergroups by twistors which satisfy the graded shifted cocycle condition, thus generalizing the quasi-Hopf twisting procedure to the supersymmetric case. Two types of elliptic quantum supergroups are defined, that is, the face type Bq,λ(G) and the vertex type Aq,p[sl(n|&dbgcaret;n)] (and Aq,p[gl(n|&dbgcaret;n)]), where G is any Kac–Moody superalgebra with symmetrizable generalized Cartan matrix. It appears that the vertex type twistor can be constructed only for Uq[sl(n|&dbgcaret;n) in a nonstandard system of simple roots, all of which are fermionic. © 1999 American Institute of Physics.
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    Response to "Comment on ‘Exact periodic solutions of the complex Ginzburg–Landau equation' " [J. Math. Phys. 40, 5283 (1999)] (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 5284-5284 
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    Notes: © 1999 American Institute of Physics.
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    Isolated versus nonisolated periodic orbits in variants of the two-dimensional square and circular billiards (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 101-122 
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    Notes: Square and circular infinite wells are among the simplest two-dimensional potentials which can completely solved in both classical and quantum mechanics. Using the methods of periodic orbit theory, we study several variants of these planar billiard systems which admit both singular isolated and continuous classes of nonisolated periodic orbits. (In this context, isolated orbits are defined as those which are not members of a continuous family of paths whose orbits are all of the same length.) Examples include (i) various "folded" versions of the standard infinite wells (i.e., potentials whose geometrical shapes or "footprints" can be obtained by repeated folding of the basic square and circular shapes) and (ii) a square well with an infinite-strength repulsive δ-function "core," which is a special case of a Sinai billiard. In each variant case considered, new isolated orbits are introduced and their connections to the changes in the quantum mechanical energy spectrum are explored. Finally, we also speculate about the connections between the periodic orbit structure of supersymmetric partner potentials, using the two-dimensional square well and it superpartner potential as a specific example. © 1999 American Institute of Physics.
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    Lattice electromagnetic theory from a topological viewpoint (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 169-187 
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    Notes: The language of differential forms and topological concepts are applied to study classical electromagnetic theory on a lattice. It is shown that differential forms and their discrete counterparts (cochains) provide a natural bridge between the continuum and the lattice versions of the theory, allowing for a natural factorization of the field equations into topological field equations (i.e., invariant under homeomorphisms) and metric field equations. The various potential sources of inconsistency in the discretization process are identified, distinguished, and discussed. A rationale for a consistent extension of the lattice theory to more general situations, such as to irregular lattices, is considered. © 1999 American Institute of Physics.
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    Pseudo-orthogonal groups and integrable dynamical systems in two dimensions (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 188-209 
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    Notes: Integrable systems in low dimensions, constructed through the symmetry reduction method, are studied using phase portrait and variable separation techniques. In particular, invariant quantities and explicit periodic solutions are determined. Widely applied models in Physics are shown to appear as particular cases of the method. © 1999 American Institute of Physics.
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    The Eikonal equation in flat space: Null surfaces and their singularities. I (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 383-407 
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    Notes: The level surfaces of solutions to the eikonal equation define null or characteristic surfaces. In this paper we study, in Minkowski space, properties of these surfaces. In particular, we are interested both in the singularities of these "surfaces" (which can, in general, self-intersect and be only piecewise smooth) and in the decomposition of the null surfaces into a one-parameter family of two-dimensional wavefronts which can also have self-intersections and singularities. We first review a beautiful method for constructing the general solution to the flat-space eikonal equation; it allows for solutions either from arbitrary Cauchy data or for time-independent (stationary) solutions of the form S=t−S0(x,y,z). We then apply this method to obtain global, asymptotically spherical, null surfaces that are associated with shearing ("bad") two-dimensional cuts of null infinity; the surfaces are defined from the normal rays to the cut. This is followed by a study of the caustics and singularities of these surfaces and those of their associated wavefronts. We then treat the same set of issues from an alternative point of view, namely from Arnold's theory of generating families. This treatment allows one to deal (parametrically) with the regions of self-intersection and nonsmoothness of the null surfaces, regions which are difficult to treat otherwise. Finally, we generalize the analysis of the singularities to the case of families of characteristic surfaces. © 1999 American Institute of Physics.
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    Lie subalgebras of real and complex orthogonal groups in dimension four (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 449-453 
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    Notes: We give an explicit description of all Lie subalgebras of the Lie algebras so4R and so4C of the orthogonal groups O(4,R) and O(4,C). © 1999 American Institute of Physics.
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    Gauge transformations in quantum mechanics and the unification of nonlinear Schrödinger equations (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 49-63 
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    Notes: Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum theories physically equivalent to linear quantum mechanics through nonlinear gauge transformations. We show that under two physically motivated assumptions, these transformations are uniquely determined: they are exactly the group of time-dependent, nonlinear gauge transformations introduced previously for a family of nonlinear Schrödinger equations. The general equation in this family, including terms considered by Kostin, by Bialynicki-Birula and Mycielski, and by Doebner and Goldin, with time-dependent coefficients, can be obtained from the linear Schrödinger equation through gauge transformation and a subsequent process we call gauge generalization. We thus unify, on fundamental grounds, a rather diverse set of nonlinear time evolutions in quantum mechanics. © 1999 American Institute of Physics.
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    Second-order mixtures in relativistic Schrödinger theory (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 71-92 
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    Topics: Mathematics , Physics
    Notes: In relativistic Schrödinger theory the mixtures and pure states can be treated from a unified point of view such that a pure state merely emerges as a special case of a mixture. Here the concept of mixture is of purely local nature and therefore the mixture character (degree of order) can change over space and time. Although the general dynamics does not forbid the transitions from mixtures to pure states (and vice versa), the considered models do admit these transitions only in an asymptotic sense. The general concepts and results are demonstrated by considering the four-component Dirac theory for spinning matter over the Robertson–Walker universes. A detailed study is made for a specific subclass of second-order mixtures sharing many of their properties with the pure states (i.e., wave functions). © 1999 American Institute of Physics.
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    A special irreducible matrix representation of the real Clifford algebra C(3,1) (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3616-3631 
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    Topics: Mathematics , Physics
    Notes: 4×4 Dirac (gamma) matrices [irreducible matrix representations of the Clifford algebras C(3,1), C(1,3), C(4,0)] are an essential part of many calculations in quantum physics. Although the final physical results do not depend on the applied representation of the Dirac matrices (e.g., due to the invariance of traces of products of Dirac matrices), the appropriate choice of the representation used may facilitate the analysis. The present paper introduces a particularly symmetric real representation of 4×4 Dirac matrices (Majorana representation) which may prove useful in the future. As a by-product, a compact formula for (transformed) Pauli matrices is found. The consideration is based on the role played by isoclinic 2-planes in the geometry of the real Clifford algebra C(3,0) which provide an invariant geometric frame for it. It can be generalized to larger Clifford algebras. © 1999 American Institute of Physics.
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    Congruences and canonical forms for a positive matrix: Application to the Schweinler–Wigner extremum principle (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3632-3642 
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    Topics: Mathematics , Physics
    Notes: It is shown that a N×N real symmetric [complex Hermitian] positive definite matrix V is congruent to a diagonal matrix modulo a pseudo-orthogonal [pseudo-unitary] matrix in SO(m,n)[SU(m,n)], for any choice of partition N=m+n. It is further shown that the method of proof in this context can easily be adapted to obtain a rather simple proof of Williamson's theorem which states that if N is even then V is congruent also to a diagonal matrix modulo a symplectic matrix in Sp(N,R)[Sp(N,C)]. Applications of these results considered include a generalization of the Schweinler–Wigner method of "orthogonalization based on an extremum principle" to construct pseudo-orthogonal and symplectic bases from a given set of linearly independent vectors. © 1999 American Institute of Physics.
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    Superintegrability of the Calogero–Moser system: Constants of motion, master symmetries, and time-dependent symmetries (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 236-247 
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    Notes: The classical n-dimensional Calogero–Moser system is a maximally superintegrable system endowed with a rich variety of symmetries and constants of motion. In the first part of the article some properties related with the existence of several families of constants of motion are analyzed. In the second part, the master symmetries and the time-dependent symmetries of this system are studied. © 1999 American Institute of Physics.
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    A rigorous path integral for quantum spin using flat-space Wiener regularization (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2549-2559 
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    Notes: Adapting ideas of Daubechies and Klauder [J. Math. Phys. 26, 2239 (1985)] we derive a rigorous continuum path-integral formula for the semigroup generated by a spin Hamiltonian. More precisely, we use spin coherent vectors parametrized by complex numbers to relate the coherent representation of this semigroup to a suitable Schrödinger semigroup on the Hilbert space L2(R2) of Lebesgue square-integrable functions on the Euclidean plane R2. The path-integral formula emerges from the standard Feynman–Kac–Itô formula for the Schrödinger semigroup in the ultradiffusive limit of the underlying Brownian bridge on R2. In a similar vein, a path-integral formula can be constructed for the coherent representation of the unitary time evolution generated by the spin Hamiltonian. © 1999 American Institute of Physics.
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    A new type of loop independence and SU(N) quantum Yang–Mills theory in two dimensions (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2584-2610 
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    Notes: The expectation values of Wilson loop products for the pure Euclidean Yang–Mills theory on R×R given by Ashtekar et al. in the article "SU(N) Quantum Yang–Mills Theory in Two Dimensions: A Complete Solution" [J. Math. Phys. 38, 5453 (1997)] are determined directly for all piecewise analytic loops. For that purpose we enlarge their calculations from quadratic lattices to general floating lattices introducing a new kind of loop independence and slightly modifying the regularization scheme. © 1999 American Institute of Physics.
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    Quantization of massive vector fields in curved space–time (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2611-2626 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We develop a cannonical quantization for massive vector fields on a globally hyperbolic Lorentzian manifold. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532718
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    The geometry of coherent states (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2568-2583 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We examine the geometry of the state space of a relativistic quantum field. The mathematical tools used involve complex algebraic geometry and Hilbert space theory. We consider the Kähler geometry of the state space of any quantum field theory based on a linear classical field equation. The state space is viewed as an infinite-dimensional complex projective space. In the case of boson fields, a special role is played by the coherent states, the totality of which constitutes a nonlinear submanifold C of the projective Fock space PF. We derive the metric on C induced from the ambient Fubini–Study metric on PF. Arguments from differential geometric, algebraic, and Kählerian points of view are presented, leading to the result that the induced metric is flat, and that the intrinsic geometry of C is Euclidean. The coordinates for the single-particle Hilbert space of solutions are shown to be complex Euclidean coordinates for C. A transversal intersection property of complex projective lines in PF with C is derived, and it is shown that the intrinsic geodesic distance between any two coherent states is strictly greater than the corresponding geodesic distance in the ambient Fubini–Study geometry. The functional metric norm of a difference field is shown to give the intrinsic geodesic distance between two coherent states, and the metric overlap expression is shown to measure the angle subtended by two coherent states at the vacuum, which acts as a preferred origin in the Euclidean geometry of C. Using the flatness of C we demonstrate the relationship between the manifold complex structure on PF and the quantum complex structure viewed as an active transformation on the single-particle Hilbert space. These properties of C hold independently of the specific details of the single-particle Hilbert space. We show how C arises as the affine part of its compactification obtained by setting the vacuum part of the state vector to zero. We discuss the relationship between unitary orbits and geodesics on C and on PF. We show that for a Fock space in which the expectation of the total number operator is bounded above, the coherent state submanifold is Kähler and has finite conformal curvature. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532716
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    Dissipative canonical flows in classical and quantum mechanics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2805-2815 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A theory of stochastic flows over the algebra of observables of a dynamical system is presented in which the main objective is to ensure that the overall canonical/symplectic structure on the algebra is preserved. We study both classical and quantum systems and the importance of physical interpretation in the Stratonovich interpretation is stressed. We find the natural formulation of quantum dissipative systems to be given in terms of quantum stochastic calculus. This treatment allows for a physically meaningful treatment of both constant and nonlinear dissipation. As an application, we quantize a mechanical system with the same nonlinear damping mechanism as the van der Pol oscillator. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532729
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    Finite-band solutions of the classical Boussinesq–Burgers equations (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2971-2982 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The classical Boussinesq–Burgers hierarchy is decomposed into two systems of solvable ordinary differential equations with the help of the Lax representations of stationary evolution equations, from which the finite-band solutions of the higher-order classical Boussinesq–Burgers equations are obtained. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532739
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    The nonlinear Schrödinger equation on the half line (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2949-2970 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The nonlinear Schrödinger equation on the half line with mixed boundary condition is investigated. After a brief introduction to the corresponding classical boundary value problem, the exact second quantized solution of the system is constructed. The construction is based on a new algebraic structure, which is called in what follows boundary algebra and which substitutes, in the presence of boundaries, the familiar Zamolodchikov–Faddeev algebra. The fundamental quantum field theory properties of the solution are established and discussed in detail. The relative scattering operator is derived in the Haag–Ruelle framework, suitably generalized to the case of broken translation invariance in space. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532738
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    New direct linearizations for KdV and solutions of the other Cauchy problem (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2983-3020 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The author showed previously that there are several equations that "directly linearize" the Korteweg de Vries equation. They may give different classes of solutions and they correspond either to generalized Gelfand Levitan or generalized Marchenko inversion equations. The idea is developed here with a precise goal: solving by linear methods the "other Cauchy problem" for KdV, i.e., the boundary value problem where the solution is known at fixed x, together with its two first derivatives. After several new direct linearization equations are given and analyzed, the one that solves the problem is eventually obtained. It also corresponds to a new inverse spectral problem, whose scalar equations are fourth order, and that is first studied in the Gelfand Levitan form, and then studied and completely solved in the Marchenko form. The methods given here can be extended probably to most nonlinear integrable equations, and suggest several new problems. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532740
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    Hamiltonian structures of generalized Manin–Radul super-KdV and constrained super KP hierarchies (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3021-3034 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A study of Hamiltonian structures associated with supersymmetric Lax operators is presented. Following a constructive approach, the Hamiltonian structures of Inami–Kanno super-KdV hierarchy and constrained modified super-KP hierarchy are investigated from the reduced supersymmetric Gelfand–Dickey brackets. By applying a gauge transformation on the Hamiltonian structures associated with these two nonstandard super-Lax hierarchies, we obtain the Hamiltonian structures of generalized Manin–Radul super-KdV and constrained super-KP hierarchies. We also work out a few examples and compare them with the known results. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532741
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    Random walk with memory (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3072-3083 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A reinforced random walk on the d-dimensional lattice is considered. It is shown that this walk is equivalent to an iterated function system (IFS). Criteria for the existence of limit cycles are given. Numerical results and conjectures about the quantitative behavior of the walk are stated. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532745
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    Variational and conformal structure of nonlinear metric-connection gravitational Lagrangians (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3063-3071 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We examine the variational and conformal structures of higher-order theories of gravity that are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first-order formalism when applied to these theories may lead consistently to a new method of reduction of order of the associated field equations. We show that the similarity of the field equations that are derived from appropriate actions via this formalism to those produced by Hilbert varying purely metric Lagrangians is not merely formal but is implied by the diffeomorphism covariant property of the associated Lagrangians. We prove that the conformal equivalence theorem of these theories with general relativity plus a scalar field, holds in the extended framework of Weyl geometry with the same forms of field and self-interacting potential but, in addition, there is a new "source term" that plays the role of a stress. We point out how these results may be further exploited and address a number of new issues that arise from this analysis. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532744
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    Center and universal R-matrix for quantized Borcherds superalgebras (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3123-3145 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We construct a nondegenerate symmetric bilinear form on quantized enveloping algebras associated to Borcherds superalgebras. With this, we study its center and its universal R matrix. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532750
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    Geometry and representations of the quantum supergroup OSPq(1|2n) (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3175-3190 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quantum supergroup OSPq(1|2n) is studied systematically. A Haar functional is constructed, and an algebraic version of the Peter–Weyl theory is extended to this quantum supergroup. Quantum homogeneous superspaces and quantum homogeneous supervector bundles are defined following the strategy of Connes' theory. Parabolic induction is developed by employing the quantum homogeneous supervector bundles. Quantum Frobenius reciprocity and a generalized Borel–Weil theorem are established for the induced representations. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532882
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    Toroidal and level 0 Uq′(sln+1&dbgcaret;) actions on Uq(gln+1&dbgcaret;) modules (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3191-3210 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: (1) Utilizing a braid group action on a completion of Uq(sln+1&dbgcaret;), an algebra homomorphism from the toroidal algebra Uq(sln+1,tor) (n≥2) to a completion of Uq(gln+1&dbgcaret;) is obtained. (2) The toroidal actions by Saito induces a level 0 Uq′(sln+1&dbgcaret;) action on level 1 integrable highest weight modules of Uq(sln+1&dbgcaret;). Another level 0 Uq′(sln+1&dbgcaret;) action was defined by Jimbo et al., in the case n=1. Using the fact that the intertwiners of Uq(sln+1&dbgcaret;) modules are intertwiners of toroidal modules for an appropriate comultiplication, the relation between these two level 0 Uq′(sln+1&dbgcaret;) actions is clarified. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.533078
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    On the signature of certain intersection forms (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 3227-3234 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We prove a conjecture of Zuber on the signature of intersection forms associated with affine algebras of type A, which is based on connections between N=2 integrable models in two dimensions and certain class of graphs. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532754
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    Nonunitary representations of the SU(2) algebra in the Dirac equation with a Coulomb potential (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2324-2336 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that allow the factorization of the problem. An extra phase is needed as a new variable in order to define the algebra. We take advantage of the operators to solve the Dirac equation using algebraic methods. A similar path to the one used in the angular momentum case is used; hence, the radial eigenfunctions so calculated comprise nonunitary representations of the algebra. One of the interesting properties of such nonunitary representations is that they are not labeled by integer nor by half-integer numbers, as occurs in the usual angular momentum representation. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532867
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    Physical properties of quantum field theory measures (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2337-2353 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Well known methods of measure theory on infinite dimensional spaces are used to study physical properties of measures relevant to quantum field theory. The difference of typical configurations of free massive scalar field theories with different masses is studied. We apply the same methods to study the Ashtekar–Lewandowski (AL) measure on spaces of connections. In particular we prove that the diffeomorphism group acts ergodically, with respect to the AL measure, on the Ashtekar–Isham space of quantum connections modulo gauge transformations. We also prove that a typical, with respect to the AL measure, quantum connection restricted to a (piecewise analytic) curve leads to a parallel transport discontinuous at every point of the curve. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532868
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    New approach to semiclassical analysis in mechanics (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1699-1718 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new method is proposed for constructing approximate solutions to the Schrödinger equation. In place of the wave function, its Gaussian-windowed Fourier transform is used as the fundamental entity. This allows an intuitively attractive connection to be made with a family of classical trajectories and, at all times, the wave function is inferred from the present state of these trajectories. The fact that the connection between the wave function and the classical trajectories is consistently constructed in phase space allows this method to be free of the limitations of other methods. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532829
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    Gauge symmetries of the master action in the Batalin–Vilkovisky formalism (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1792-1806 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the geometry of the Lagrangian Batalin–Vilkovisky (BV) theory on an antisymplectic manifold. We show that gauge symmetries of the BV theory are essentially the symmetries of an even symplectic structure on the stationary surface of the master action. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532835
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    Two-particle scattering theory for anyons (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1831-1869 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider potential scattering theory of a nonrelativistic quantum mechanical 2-particle system in R2 with anyon statistics. Sufficient conditions are given which guarantee the existence of Møller operators and the unitarity of the S-matrix. As examples the rotationally invariant potential well and the δ-function potential are discussed in detail. In case of a general rotationally invariant potential the angular momentum decomposition leads to a theory of Jost functions. The anyon statistics parameter gives rise to an interpolation for angular momenta analogous to the Regge trajectories for complex angular momenta. Levinson's theorem is adapted to the present context. In particular we find that in case of a zero energy resonance the statistics parameter can be determined from the scattering phase. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532837
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    Poisson brackets of normal-ordered Wilson loops (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1870-1890 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We formulate Yang–Mills theory in terms of the large-N limit, viewed as a classical limit, of gauge-invariant dynamical variables, which are closely related to Wilson loops, via deformation quantization. We obtain a Poisson algebra of these dynamical variables corresponding to normal-ordered quantum (at a finite value of (h-dash-bar)) operators. Comparing with a Poisson algebra one of us introduced in the past for Weyl-ordered quantum operators, we find, using ideas closely related to topological graph theory, that these two Poisson algebras are, roughly speaking, the same. More precisely speaking, there exists an invertible Poisson morphism between them. © 1999 American Institute of Physics.
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    Differential equations for scaling relation in N=2 supersymmetric SU(2) Yang–Mills theory coupled with massive hypermultiplet (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1891-1900 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Differential equations for the scaling relation of prepotential in N=2 supersymmetric SU(2) Yang–Mills theory coupled with massive matter hypermultiplet are proposed and are explicitly demonstrated in one flavor (Nf=1) theory. By applying Whitham dynamics, the first-order derivative of the prepotential over the T0 variable corresponding to the mass of the hypermultiplet, which has a line integral representation, is found to satisfy a differential equation. As a result, the closed form of this derivative can be obtained by solving this equation. In this way, the scaling relation of massive prepotential is established. Furthermore, as an application of another differential equation for the massive scaling relation, the massive prepotential in a strong coupling region is derived. © 1999 American Institute of Physics.
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    Group invariant solutions for the N=2 super Korteweg–de Vries equation (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 1951-1965 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The method of symmetry reduction is used to solve Grassmann-valued differential equations. The (N=2) supersymmetric Korteweg–de Vries equation is considered. It admits a Lie superalgebra of symmetries of dimension 5. A two-dimensional subsuperalgebra is chosen to reduce the number of independent variables in this equation. We are then able to give different types of exact solutions, in particular soliton solutions. © 1999 American Institute of Physics.
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    Hirota bilinear approach to a new integrable differential-difference system (1999)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 40 (1999), S. 2001-2010 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new integrable differential-difference system is proposed. By the dependent variable transformation, the system is transformed into multilinear form. By introducing an auxiliary variable, we further transform it into the bilinear form. A corresponding Bäcklund transformation for it is obtained. Furthermore a nonlinear superposition formula is presented. As an application of the obtained results, soliton solutions to the system are derived. © 1999 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.532846
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