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  • Articles  (2,282)
  • American Institute of Physics (AIP)  (2,282)
  • 2020-2024
  • 2020-2023
  • 1990-1994  (2,282)
  • Mathematics  (2,282)
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  • Articles  (2,282)
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  • 101
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    Universal bundle for gravity, local index theorem, and covariant gravitational anomalies (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5945-5968 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Consistent and covariant Lorentz and diffeomorphism anomalies are investigated in terms of the geometry of the universal bundle for gravity. This bundle is explicitly constructed and its geometrical structure will be studied. By means of the local index theorem for families of Bismut and Freed, the consistent gravitational anomalies are calculated. Covariant gravitational anomalies are shown to be related with secondary characteristic classes of the universal bundle and a new set of descent equations which also contains the covariant Schwinger terms is derived. The relation between consistent and covariant anomalies is studied. Finally a geometrical realization of the gravitational BRS, anti-BRS transformations is presented which enables the formulation of a kind of covariance condition for covariant gravitational anomalies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530721
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  • 102
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    Special functions from quantum canonical transformations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6018-6035 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the nonperiodic three-body Toda equation are also found. The derivation of these representations motivate the form of a two-dimensional generalized hypergeometric equation which contains the nonperiodic Toda equation as a special case and whose solutions may be obtained by quantum canonical transformation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530725
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  • 103
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    A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6076-6095 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A derivation of the Cesàro–Fedorov relation from the Selberg trace formula on an orbifolded 2-sphere is elaborated and extended to higher dimensions using the known heat-kernel coefficients for manifolds with piecewise-smooth boundaries. Several results are obtained that relate the coefficients, bi, in the Shephard–Todd polynomial to the geometry of the fundamental domain. For the 3-sphere, it is shown that b4 is given by the ratio of the volume of the fundamental tetrahedron to its Schläfli reciprocal.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530729
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  • 104
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    A no-go theorem for a Lie-consistent q-Campbell–Baker–Hausdorff expansion (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6172-6178 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Lie consistency is defined for commutator expansions and it is shown that while a weakly Lie-consistent q-Campbell–Baker–Hausdorff expansion for a product of two M-type (but not P-type) q exponentials can be formulated, a strongly Lie-consistent expansion only exists for the undeformed case, q=1.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530736
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  • 105
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    Erratum: Generalized Lorentz transformation for an accelerated, rotating frame of reference [J. Math. Phys. 28, 2379–2383 (1987)] (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6224-6225 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530669
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  • 106
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    Erratum: The half-Hartley and half-Hilbert transforms [J. Math. Phys. 35, 2648 (1994)] (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6226-6226 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530670
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  • 107
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    The Chern–Simons action in noncommutative geometry (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5195-5218 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general definition of Chern–Simons actions in noncommutative geometry is proposed and illustrated in several examples. These examples are based on "space–times'' which are products of even-dimensional, Riemannian spin manifolds by a discrete (two-point) set. If the * algebras of operators describing the noncommutative spaces are generated by functions over such "space–times'' with values in certain Clifford algebras the Chern–Simons actions turn out to be the actions of topological gravity on the even-dimensional spin manifolds. By constraining the space of field configurations in these examples in an appropriate manner one is able to extract dynamical actions from Chern–Simons actions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530748
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  • 108
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    Extended reflection equation algebras, the braid group on a handlebody, and associated link polynomials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5288-5305 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The correspondence of the braid group on a handlebody of arbitrary genus to the algebra of Yang–Baxter and extended reflection equation operators is shown. Representations of the infinite-dimensional extended reflection equation algebra in terms of direct products of quantum algebra generators are derived; they lead to a representation of this braid group in terms of R-matrices. Restriction to the reflection equation operators only gives the colored braid group. The reflection equation operators, describing the effect of handles attached to a three-ball, satisfy characteristic equations that give rise to additional skein relations and thereby invariants of links on handlebodies. The origin of the skein relations is explained and they are derived from an adequately adapted handlebody version of the Jones polynomial. Relevance of these results to the construction of link polynomials on closed three-manifolds via Heegard splitting and surgery is indicated.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530751
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  • 109
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    The semiclassical limit of the two-dimensional quantum Yang–Mills model (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5354-5361 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The semiclassical limit of the quantum Yang–Mills partition function on a compact oriented surface is related to the symplectic volume of the moduli space of flat connections, by using an explicit expression for the symplectic form. This gives an independent proof of some recent results of Witten and Forman.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530756
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  • 110
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    Geodesic multiplication and the theory of gravity (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 321-334 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Nonassociative algebraic systems called local geodesic loops and their tangent Akivis algebras are considered. The construction of geo-odular structure of a manifold with an affine connection is briefly reviewed. A possible role of these algebraic structures in classical and quantum gravity is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530773
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  • 111
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    On convergence to equilibrium for Kac's caricature of a Maxwell gas (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 190-208 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The trend towards equilibrium of the solution to the one-dimensional Kac's caricature of a Maxwell gas is investigated. When the initial value has finite energy and finite Linnik's entropy, it is proven that the solution converges in L1∩L∞ to the equilibrium Maxwellian distribution.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530787
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  • 112
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    Quantum flows associated to master equations in quantum optics (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1-12 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A stochastic dilation of master equation for a maser is constructed using the technique of quantum stochastic differential equations with unbounded operator coefficients. The associated quantum Markov flow is characterized and turns out to extend a classical birth and death process. Furthermore, the stationary distribution of the aforementioned process, which is connected to the stationary state of the micromaser, is obtained in a closed form.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530788
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  • 113
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    A Borel-like estimate for the rest of the heat kernel expansion (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 479-485 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that under some simple assumptions the rest of the truncated asymptotic expansion for the heat kernel has the form required for Borel summability, if N, the number of terms in the truncation, is sufficiently large. Rigorously speaking this result does not imply Borel summability, which requires a uniform bound in N, but it could be useful as a starting point for further investigation on global estimates for the zeta function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530737
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  • 114
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    Generalized multidimensional Epstein zeta functions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 459-470 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Explicit formulas are given for the expression of multiple-sum zeta functions of the type ∑l1,...,lN=−∞∞[a1(l1 − c1)2 +... + aN(lN − cN)2 + M2]−s, where ai(approximately-greater-than)0, M2≥0, i=1,...,N, in terms of Riemann and Hurwitz zeta functions and in terms of Kelvin functions. Using different analytical continuation methods several formulas, especially useful for different values of the involved parameters, are obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530793
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  • 115
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    On the arbitrariness of the general solution of an involutive partial differential equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 486-498 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The relationship between the strength of a differential equation as introduced by Einstein, its Cartan characters, and its Hilbert polynomial is studied. Using the framework of formal theory previous results are extended to nonlinear equations of arbitrary order and to overdetermined systems. The problem of computing the number of arbitrary functions in the general solution is treated. Finally, the effect of gauge symmetries is considered.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530739
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  • 116
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    Cocycles for boson and fermion Bogoliubov transformations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 96-112 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Unitarily implementable Bogoliubov transformations for charged, relativistic bosons and fermions are discussed, and explicit formulas for the two-cocycles appearing in the group product of their implementers are derived. In the fermion case this provides a simple field theoretic derivation of the well-known cocycle of the group of unitary operators on a Hilbert space modeled on the Hilbert–Schmidt class and closely related to the loop groups. In the boson case the cocycle is obtained for a similar group of pseudo-unitary (symplectic) operators. Formulas are also given for the phases of one-parameter groups of implementers and, more generally, families of implementers which are unitary propagators with parameter-dependent generators.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530744
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  • 117
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    Spatial entropy of central potentials and strong asymptotics of orthogonal polynomials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4423-4428 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Boltzmann–Shannon information entropy of quantum-mechanical systems in central potentials can be expressed in terms of the entropy Sn of the classical orthogonal polynomials. Here, an asymptotic formula for the entropy of general orthogonal polynomials on finite intervals is obtained. It is shown that this entropy is intimately related to the relative entropy I (ρ0,ρ) of the equilibrium measure ρ0(x) and the weight function ρ(x) of the polynomials. To do so, the theory of strong asymptotics of orthogonal polynomials on compact sets is used.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530861
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  • 118
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    Quantization of a classical system on a coadjoint orbit of the Poincaré group in 1+1 dimensions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4405-4422 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The connection is investigated between quantization by means of coherent states and geometric quantization, when the base manifold is a coadjoint orbit, and hence a homogeneous space, of the (1+1)-dimensional Poincaré group. Coherent states of the Poincaré group stem from a representation that is square-integrable modulo closed subgroup, and so they depend on a measurable section on the given homogeneous space. For each section that leads to a tight frame, a geometric prequantization is constructed, i.e., a Hermitian line bundle with metric connection. Conditions are given under which the two forms associated to the connection and to the coadjoint orbit structure of the base manifold coincide.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530860
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  • 119
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    Five-dimensional cosmological models in induced matter theory (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4889-4896 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A class of five-dimensional space–times that contain four-dimensional hypersurfaces whose intrinsic metrics are Friedman–Robertson–Walker (FRW) metrics is examined (the four-dimensional intrinsic Lorentzian metrics are both spatially homogeneous and isotropic). The five-dimensional vacuum field equations, 5Gij=0, are shown to induce four-dimensional perfect-fluid FRW field equations, 4Gij=4Tij, and thus these FRW cosmological models may be interpreted as being purely geometrical in origin.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530820
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  • 120
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    Compact homogeneous universes (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4855-4888 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are identified by discrete subgroups of the isometry group of the generalized Thurston geometries, which are related to the Bianchi and the Kantowski–Sachs–Nariai universes. Corresponding to this procedure their total degrees of freedom are shown to be categorized into those of the universal covering space and the Teichmüller parameters. The former are given by constructing homogeneous metrics on a simply connected manifold. The Teichmüller spaces are also given by explicitly constructing expressions for the discrete subgroups of the isometry group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530819
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  • 121
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    Spherically symmetric random walks in noninteger dimension (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4941-4963 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A previous article proposed a new kind of random walk on a spherically symmetric lattice in arbitrary noninteger dimension D. Such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension. This article examines the nature of spherically symmetric random walks in detail. A large-time asymptotic analysis of these random walks is performed and the results are used to determine the Hausdorff dimension of the process. Exact results are obtained in terms of Hurwitz functions (incomplete zeta functions) for the probability of a walker going from one region of the spherical lattice to another. Finally, it is shown that the probability that the paths of K independent random walkers will intersect vanishes in the continuum limit if D(approximately-greater-than)2K/(K−1).
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    URL: http://dx.doi.org/10.1063/1.530824
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  • 122
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    Spherical wave expansion for any spin (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5000-5020 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The spherical wave expansion is derived for fields of particles of arbitrary spin and mass, and for arbitrary helicity, massless particles (such as the electromagnetic vector potential corresponding to photons). The starting point is Weinberg's characterization of relativistic, higher spin fields that transform according to general irreducible representations of the homogeneous Lorentz group. The expansion is a relativistic generalization of the familiar tensor and spinor spherical harmonics. It is useful for central force problems that arise, for example, in scattering processes off spherically symmetric solitonic backgrounds such as monopoles or skyrmions.
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    URL: http://dx.doi.org/10.1063/1.530827
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  • 123
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    The untruncated Marinari–Parisi superstring (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4469-4476 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the bosonic angular degrees of freedom in the one dimensional Marinari–Parisi superstring can be integrated out exactly in the Hamiltonian formulation. The resulting quantum mechanical Hamiltonian is that of a supersymmetric Calogero system plus a four fermions interaction. This extra interaction vanishes for all physical states with fermion number 0 or 1 where supersymmetry is manifest.
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    URL: http://dx.doi.org/10.1063/1.530866
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  • 124
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    Long time behavior of nonlinear stochastic oscillators: The one-dimensional Hamiltonian case (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4005-4027 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The long time behavior of nonlinear, nondissipative systems, which are perturbed by a white noise force are discussed herein. Considering special nonlinear forces and an appropriate scaling, a stochastic convergence theorem is proven. In particular the convergence of the energy process of the system to a limit diffusion is discussed. This corresponds to convergence of the system to a stationary distribution. Furthermore, the limit process is investigated and an explicit formula for its transition probability density is given. An analytic approach to the convergence theorem in terms of a singular perturbation theorem for semigroups is also presented.
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    URL: http://dx.doi.org/10.1063/1.530839
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  • 125
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    Qualitative analysis of diagonal Bianchi type V imperfect fluid cosmological models (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4117-4144 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Einstein field equations for diagonal Bianchi type V imperfect fluid cosmological models with both viscosity and heat conduction are set up as an autonomous system of differential equations using dimensionless variables and a set of dimensionless equations of state. Models with and without a cosmological constant, λ, are investigated using the techniques from dynamical systems theory. It is shown that all models that satisfy the weak energy conditions isotropize. The introduction of viscosity (in particular) allows for a variety of different qualitative behaviors (including, for example, models with a negative deceleration parameter). Exact solutions that correspond to the singular points of the dynamical system are found. It is shown that the past asymptotic states are represented by self-similar cosmological models and, if λ=0, the future asymptotic states are also, in general, represented by self-similar cosmological models; in the exceptional cases the late time asymptotic state is represented by a de Sitter model with constant expansion, as is the case for solutions with λ ≠ 0.
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    URL: http://dx.doi.org/10.1063/1.530845
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  • 126
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    Extension of the de Sitter kink (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4145-4156 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A space–time, locally identical to the usual de Sitter space–time but globally different because of a kink in its light cone field, is described in various coordinate systems. Two separate coordinate patches are needed. Each original patch is geodesically incomplete and so is extended by the Kruskal method. The space–time, which is not globally hyperbolic, is shown to be foliated by a family of hypersurfaces each of which is homeomorphic to a three-sphere but none of which is everywhere spacelike.
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    URL: http://dx.doi.org/10.1063/1.530846
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  • 127
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    A composite Fourier-wavelet transform and square-integrable group representations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4205-4216 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A formula for a composite Fourier-wavelet transform is suggested, from which the noncommutative Fourier and wavelet transforms can be obtained as particular examples, as well as several other Fourier-type transforms. It is shown how this composite transform can be used to extend certain results, originally obtained for square-integrable group representations, to more general measures, arising in quantum probability theory.
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    URL: http://dx.doi.org/10.1063/1.530849
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  • 128
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    New relations for two-dimensional Hermite polynomials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4277-4294 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The effective formulas reducing the two-dimensional Hermite polynomials to the classical one-dimensional orthogonal polynomials by Jacobi, Gegenbauer, Legendre, Laguerre, and Hermite are given. New one-parameter generating functions for the "diagonal'' multidimensional Hermite polynomials are derived. The factorial moments and cumulants of the distribution functions related to the Hermite polynomials of two variables with equal indices are expressed in terms of the Legendre and Chebyshev polynomials. Asymptotical formulas for the two-dimensional polynomials with large values of indices and zero arguments are found. The applications to the squeezed one-mode states and to the time-dependent quantum harmonic oscillator are considered.
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    URL: http://dx.doi.org/10.1063/1.530853
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  • 129
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    Feynman integrals and Fredholm determinants (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4357-4371 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this article simple properties of Feynman integrals such as the translation invariance, Fubini theorem, and Cameron–Martin formula are used in order to derive a product formula for Fredholm determinants. This formula enables us to compute explicitly some of such determinants as well as the index of the related Fredholm operators. Some examples are done which have applications in the semiclassical approximation ((h-dash-bar) → 0).
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    URL: http://dx.doi.org/10.1063/1.530857
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    Reduced coefficients of quantum algebra SUq(4) (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4391-4401 
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    Topics: Mathematics , Physics
    Notes: Irreducible representation and a recurrent formula to calculate reduced coefficients of quantum algebra SUq(4)&supuline;SUq(2)⊕SUq(2) has been obtained through a tensorlike method.
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    Mass spectra from field equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3333-3339 
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    Notes: A type of field quantization is developed which, in some cases, leads directly from a field equation to a mass spectrum. The starting point is a field-Hamiltonian setup of the field equations. A Schrödinger-type wave function, a function of the field variables, is postulated and a Hamiltonian operator is inferred from the Hamiltonian function. A wave equation is suggested which has particle-type solutions only for special values of the rest mass. As examples, the spectra for the linear wave equation and for an equation with a sharply limited range of the field variable are discussed.
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    The classical limit of ultralocal scalar fields (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3400-3409 
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    Topics: Mathematics , Physics
    Notes: The classical limit of the quantum theory of ultralocal scalar fields is approached with the help of coherent state techniques. In the limit (h-dash-bar)→0, it is demonstrated that the coherent state expectation value of the Heisenberg field operators coincide with the solutions of the corresponding classical canonical equations of motion.
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    On acoustic Helmholtz resonator and on its electromagnetic analog (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3464-3481 
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    Notes: A study of the acoustic Helmholtz resonator and of its electromagnetic analog (a cylinder with a narrow slit) is performed. For the associated Green functions, power series asymptotics with respect to a small parameter ε ("radius'' of the resonator hole or the width of the slit), and ln ε of poles τε with small imaginary parts are obtained by using the method of matching asymptotic expansions. The principal terms of solution asymptotics for corresponding boundary value problems are given.
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    The basis of nonlocal curvature invariants in quantum gravity theory. Third order (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3525-3542 
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    Notes: A complete basis of nonlocal invariants in quantum gravity theory is built to third order in space–time curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality 2ω〈6. The present results are used in heat-kernel theory, theory of gauge fields and serve as a basis for the model-independent approach to quantum gravity and, in particular, for the study of nonlocal vacuum effects in the gravitational collapse problem.
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    Characterization of Riemann tensors using Ricci-type equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3587-3593 
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    Topics: Mathematics , Physics
    Notes: The extent to which Ricci-type equations characterize the Riemann curvature tensor of a metric connection is investigated and a geometric approach is followed to generalize the results of Edgar [J. Geom. Phys. 7, 191 (1990); Int. J. Theor. Phys. 32, 121 (1993)] to arbitrary dimension and signature. The difference between a Riemann (curvature) candidate satisfying Ricci-type equations and the actual Riemann tensor is related to the isotropy of the candidate. Some new examples are presented and the results are applied to conformally recurrent space–times.
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    Hilbert spaces of analytic functions for the SL(2,R) coherent states and a class of associated integral transforms (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3612-3623 
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    Notes: It is shown that the Bargmann–Segal Hilbert spaces of entire analytic functions and Bargmann's canonical Hilbert spaces of functions analytic within the open unit disc are connected by simple integral transform pairs. A further consequence of this analysis is the analog of the Bargmann transform for the SL(2,R) [or SU(1,1)] group.
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    Null cone evolution of axisymmetric vacuum space–times (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4184-4204 
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    Notes: The details of an algorithm for the global evolution of asymptotically flat, axisymmetric space–times, based upon a characteristic initial value formulation using null cones as evolution hypersurfaces is presented. A new static solution of the vacuum field equations which provides an important test bed for characteristic evolution codes is identified. It is also shown how linearized solutions of the Bondi equations can be generated by solutions of the scalar wave equation, thus providing a complete set of test beds in the weak field regime. These tools are used to establish that the algorithm is second order accurate and stable, subject to a Courant–Friedrichs–Lewy condition. In addition, the numerical versions of the Bondi mass and news function, calculated at scri on a compactified grid, are shown to satisfy the Bondi mass loss equation to second order accuracy. This verifies that numerical evolution preserves the Bianchi identities. Results of numerical evolution confirm the theorem of Christodoulou and Klainerman that in vacuum, weak initial data evolve to a flat space–time. For the class of asymptotically flat, axisymmetric vacuum space–times, for which no nonsingular analytic solutions are known, the algorithm provides highly accurate solutions throughout the regime in which neither caustics nor horizons form.
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    SO(5)q and contraction: Chevalley basis representations for q-generic and root of unity (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4247-4267 
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    Notes: Representations of SO(5)q are constructed explicitly on the Chevalley basis. The classical representations, once obtained on this basis, are very simply deformed for arbitrary q, generic, and root of unity. This is in sharp contrast to the classical canonical Gelfand–Zetlin (GZ) representations which lead to problems, studied elsewhere, in q deformations for orthogonal (though not for unitary) algebras. Our results are limited to irreducible representations labeled by three variable parameters, the maximal number being four. Within this restriction it is shown how to construct all representations for all q's. The contraction of the Chevalley generators (e2,f2) leads to an easily obtained complete Hopf algebra. The structure of the contracted algebra is quite different, even at the classical level, from the familiar E(4), the four-dimensional Euclidean algebra, obtained on contracting the generator J45 in the GZ formalism. The contracted representations are given. The SO(5)q representations have their own interest. Moreover they lead to a consistent Hopf algebra and representations for the nonsemisimple contracted case, for all q.
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    Harmonic analysis on tube-type affine homogeneous phase spaces (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4295-4302 
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    Topics: Mathematics , Physics
    Notes: In this paper, the coherent states and the POV measures on tube-type affine homogeneous phase spaces are studied. The results extend the continuous wavelet analysis of the affine group 'ax+b' and the phase space analysis of the Galilei and Poincaré groups to the general affine groups.
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    The behavior of hyperbolic heat equations' solutions near their parabolic limits (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4334-4356 
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    Notes: Standard energy methods are used to study the relation between the solutions of one parameter families of hyperbolic systems of equations describing heat propagation near their parabolic limits, which for these cases are the usual diffusive heat equation. In the linear case it is proven that given any solution to the hyperbolic equations there is always a solution to the diffusion equation which after a short time stays very close to it for all times. The separation between these solutions depends on the square of the ratio between the assumed very short decay time appearing in Cattaneo's relation and the usual characteristic smoothing time (initial data dependent) of the limiting diffusive equation. The techniques used in the linear case can be readily used for nonlinear equations. As an example we consider the theories of heat propagation introduced by Coleman, Fabrizio, and Owen, and prove that near a solution to the limiting diffusive equation there is always a solution to the nonlinear hyperbolic equations for a time which usually is much longer than the decay time of the corresponding Cattaneo relation. An alternative derivation of the heat theories of divergence type, which are consistent with thermodynamic principles, is given as an appendix.
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    Algebraic solution for the Natanzon hypergeometric potentials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3301-3307 
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    Notes: An algebraic method—based on a strategy that makes use of a realization of the algebra SO(2,1)—in terms of differential operators is used to solve the bound state problem for the most general Natanzon potentials for which the Schrödinger equation can be reduced to hypergeometric form (hence, hypergeometric potentials).
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    Asymptotic behaviors of the heat kernel in covariant perturbation theory (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3543-3559 
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    Notes: The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of nth order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and late-time asymptotic behaviors of the trace of the heat kernel are presented with this accuracy. The late-time behavior gives the criterion of analyticity of the effective action in quantum field theory. The latter point is exemplified by deriving the effective action in two dimensions.
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    Two-dimensional integrable systems and self-dual Yang–Mills equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2902-2913 
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    Notes: The relation between two-dimensional integrable systems and four-dimensional self-dual Yang–Mills equations is considered. Within the twistor description and the zero-curvature representation a method is given to associate self-dual Yang–Mills connections with integrable systems of the Korteweg–de Vries and nonlinear Schrödinger type or principal chiral models. Examples of self-dual connections are constructed that as points in the moduli do not have two independent conformal symmetries.
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    The vacuum energy density for spherical and cylindrical universes (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3308-3321 
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    Topics: Mathematics , Physics
    Notes: The vacuum energy density (Casimir energy) corresponding to a massless scalar quantum field living in different universes (mainly no-boundary ones), in several dimensions, is calculated. Hawking's zeta function regularization procedure supplemented with binomial expansion is shown to be a rigorous and well suited method for performing the analysis. It is compared with other more involved techniques. The principal-part prescription is used to deal with the poles that eventually appear. Results of the analysis are the absence of poles at four dimensions (4D) (for a 4D Riemann sphere and for a 4D cylinder of 3D Riemann spherical section), the total coincidence of the results corresponding to a 3D and a 4D cylinder (the first after pole subtraction), and the fact that the vacuum energy density for cylinders is (in absolute value) over an order of magnitude smaller than for spheres of the same dimension.
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    Algebraic structures of quantum projective field theory related to fusion and braiding. Hidden additive weight (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3368-3379 
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    Topics: Mathematics , Physics
    Notes: The interaction of various algebraic structures describing fusion, braiding, and group symmetries in quantum projective field theory is the object of investigation in this article. Structures of projective Zamolodchikov algebras, their representations, spherical correlation functions, correlation characters and enveloping quantum projective field theory (QPFT)-operator algebras, projective W¨-algebras, shift algebras, infinite-dimensional R matrices Rproj(u) and Rproj*(u) of the QPFT, braiding admissible QPFT-operator algebras, and projective G hypermultiplets are explored. It is proven (in the formalism of shift algebras) that sl(2,C)-primary fields are characterized by their projective weights and by the hidden additive weight, a hidden quantum number discovered in this article. Special attention is paid to various constructions of projective G hypermultiplets (QPFT-operator algebras with G symmetries).
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    On the Kolmogorov's condition for a special case of the Kirchhoff top (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3448-3463 
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    Notes: In this article the classical Kirchhoff case of motion of a rigid body in an infinite ideal fluid is considered. Then for the corresponding Hamiltonian system on the zero integral level, the Kolmogorov's condition which is important for Kolmogorov–Arnold–Moser theory is checked. In contrast to known similar results, there exists a curve in the bifurcation diagram along which the Kolmogorov's condition vanishes for certain values of the parameters.
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    Symplectic analysis of a Dirac constrained theory (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3497-3503 
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    Topics: Mathematics , Physics
    Notes: The symplectic formalism is applied to a system recently analyzed by the Dirac method. It is shown that this procedure is quite straightforward and elegant for the two versions of the model.
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    Nonlinear systems related to an arbitrary space–time dependence of the spectral transform (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3504-3524 
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    Notes: A general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations is proposed. This allows one to give the general nonlinear evolution corresponding to an arbitrary time and space dependence of the spectral transform (in general nonlinear and with nonanalytic dispersion relations). The main theorem is that the compatibility conditions always give a true nonlinear evolution because it can always be written as an identity between polynomials in the spectral variable k. This general result is then used to obtain first a method to generate a new class of solutions to the nonlinear Schrödinger equation, and second to construct the spectral transform theory for solving initial-boundary value problems for resonant wave-coupling processes (like self-induced transparency in two-level media, or stimulated Brillouin scattering of plasma waves, or else stimulated Raman scattering in nonlinear optics, etc.).
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    Thermodynamics of ideal boson and fermion gases in the static Taub universe (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3594-3603 
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    Notes: Some thermodynamic quantities of nonrelativistic ideal boson and fermion gases in the static Taub universe are derived to first order in a small anisotropy parameter d measuring the deformation from the spherical Einstein universe. They are used to investigate the problem of how the curvature anisotropy affects the thermodynamic behaviors of an ideal gas. It is found that, when the universe is in the oblate configuration (i.e., d(approximately-greater-than)0), the effect of curvature anisotropy is to increase the number of the fraction in the Bose–Einstein condensation and to decrease the fermion distribution function at low temperature. When the universe is in the prolate configuration (i.e., d〈0), the effects of curvature anisotropy on the thermodynamic quantities is contrary to that in the oblate configuration. The density matrix of a two particle system is evaluated and it is used to define the "statistical interparticle potential'' as an attempt to give a "statistical interpretation'' about the found thermodynamic behaviors. It is found that when the universe is in the oblate (prolate) configuration the curvature anisotropy will enhance (reduce) both the "statistic attraction'' among the bosons and "statistical repulsion'' among the fermions. It is expected that such a behavior will also be shown in the relativistic system.
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    Asymptotics of the multipositon–soliton τ function of the Korteweg–de Vries equation and the supertransparency (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2955-2970 
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    Notes: The asymptotics of the τ function generating the N-positon–M-soliton solution of the Korteweg–de Vries equation is calculated. This allows to prove that solitons do not experience any phase shift in a collision with positons. The positons themselves survive mutual collisions unchanged. This phenomenon is called the supertransparency or super-reflectionless property of the multipositon solutions. The linear aspects of this phenomenon are also discussed. It is demonstrated that positons acquire two additional but always finite phase shifts in collision with solitons. This result admits a natural extension to any number of solitons and positons in interaction.
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    Two classes of dynamical systems all of whose bounded trajectories are closed (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2914-2933 
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    Notes: According to the Bertrand theorem, the Kepler problem and the harmonic oscillator are the only central force dynamical systems that have closed orbits for all bounded motions. In this article, other dynamical systems having such a closed orbit property are found on T*(R3−{0}). Consider a natural dynamical system on T*(R4−{0}) whose Hamiltonian function is composed of kinetic and potential energies, and invariant under a SO(2) action. Then one can reduce the system to a Hamiltonian system on T*(R3−{0}) by the use of the Kustaanheimo–Stiefel transformation. If the original potential on R4−{0} is a central one, Bertrand's method is applicable to the reduced system for determining the potential so that any bounded motions may be periodic. As a result, two types of potential functions will be found; one is linear in the radial variable and the other proportional to the inverse square root of that. The dynamical systems obtained are capable of physical interpretation. In particular, the dynamical system with the inverse square root potential may be called the twofold Kepler system, whose bounded trajectories have a self-intersection point.
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    Local automorphism invariance: Gauge boson mass without a Higgs particle (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2701-2718 
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    Notes: The consequences of the assumption of invariance of a spinor theory under local automorphism transformations of the Clifford algebra basis elements are explored. This invariance is equivalent to allowing the orthonormal basis spinors of the spinor space to be chosen arbitrarily at each point in space–time and is analogous to the situation in general relativity where the orthonormal basis vectors of the tangent space are allowed to be chosen arbitrarily at each point in space–time. This invariance then dictates that the Clifford algebra generators be functions of space–time and is implemented by introducing new fields, the drehbeins ("spin legs''), which are somewhat akin to the vielbeins introduced in general relativity to invoke the concept of local Lorentz invariance. However, in contrast to general relativity, the covariant derivatives of the Clifford algebra generators do not vanish. The dynamical variables of the theory are then the spinors, the gauge fields of the automorphism group, and the drehbeins. The invariant Lagrangian density and the concomitant field equations for this theory are discussed. Interestingly, the "kinetic'' Lagrangian density term for the drehbein fields induces a gauge invariant mass term for the gauge fields. This constitutes a new mass generation mechanism, of different character and complementary to the familiar Higgs mechanism. Although the idea of local automorphism invariance is a natural generalization of the principle of equivalence, herein attention is restricted to the case of nondynamic flat space–time.
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    (2+1)-dimensional models of relativistic particles with curvature and torsion (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2772-2784 
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    Notes: (2+1)-dimensional models of relativistic particles with the action depending arbitrarily on the world-trajectory curvature and torsion are investigated. A special class of models, described by the action with a maximal symmetry allowing only spin internal degrees of freedom, is singled out. A classical analysis of the systems from this special class is carried out, and the quantization procedure for them is described. Within this class, tachyon-free models are pointed out and the systems having classical and quantum spectra with only massive spin states (whose number in the quantum case may be both finite and infinite) are considered as concrete examples of such models.
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    Study on the one dimensional boson–fermion model (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2833-2837 
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    Notes: The one dimensional boson–fermion model is introduced and the general eigenstates of the model Hamiltonian are constructed. The Cooper-pairlike bound state is given. It is concluded that the present model is exactly soluble via the Bethe ansatz.
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    Caustics in 1+1 integrable systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2934-2954 
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    Notes: Caustics arising in the asymptotic description of rapidly decaying solutions of the equations integrable via the inverse scattering transform are defined. Different asymptotic approaches to the description are considered. The appearance of members (Ρn2) of the hierarchy of the second Painlevé equation as special functions of wave catastrophies is discussed. The "adjoining'' problem Ρn2 → Ρk2(n(approximately-greater-than)k) for the simplest example Ρ22 → Ρ2 is considered in detail.
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    Integrability of difference Calogero–Moser systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2983-3004 
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    Source: AIP Digital Archive
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    Notes: A general class of n-particle difference Calogero–Moser systems with elliptic potentials is introduced. Besides the step size and two periods, the Hamiltonian depends on nine coupling constants. We prove the quantum integrability of the model for n=2 and present partial results for n≥ 3. In degenerate cases (rational, hyperbolic, or trigonometric limit), the integrability follows for arbitrary particle number from previous work connected with the multivariable q-polynomials of Koornwinder and Macdonald. Liouville integrability of the corresponding classical systems follows as a corollary. Limit transitions lead to various well-known models such as the nonrelativistic Calogero–Moser systems associated with classical root systems and the relativistic Calogero–Moser system.
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    W gravity, N=2 strings, and 2+2 SU*(∞) Yang–Mills instantons (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3013-3024 
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    ISSN: 1089-7658
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    Notes: It is conjectured that W gravity can be interpreted as the gauge theory of φ diffeomorphisms in the space of dimensionally reduced D=2+2 SU*(∞) Yang–Mills instantons. These φ diffeomorphisms preserve a volume-three form and are those that furnish the correspondence between the dimensionally reduced Plebanski equation and the KP equation in (1+2) dimensions. A supersymmetric extension furnishes super-W gravity. The super-Plebanski equation generates self-dual complexified super gravitational backgrounds (SDSG) in terms of the super-Plebanski second heavenly form. Since the latter equation yields N=1, D=4 SDSG complexified backgrounds associated with the complexified-cotangent space of the Riemannian surface, (T*Σ)c, required in the formulation of SU*(∞) complexified Self-Dual Yang-Mills theory, (SDYM); it naturally follows that the recently constructed D=2+2 N=4 SDSYM theory, as the consistent background of the open N=2 superstring, can be embedded into the N=1 SU*(∞) complexified self-dual-super-Yang–Mills (SDSYM) in D=3+3 dimensions. This is achieved after using a generalization of self-duality for D(approximately-greater-than)4. Finally, the plausible relationship between the geometry of N=2 strings and the moduli of SU*(∞) complexified SDSYM in 3+3 dimensions is indicated.
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    Generalized intelligent states and squeezing (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2297-2308 
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    Topics: Mathematics , Physics
    Notes: The Robertson–Schrödinger uncertainty relation for two observables A and B is shown to be minimized in the eigenstates of the operator λA+iB, λ being a complex number. Such states, called generalized intelligent states (GIS), can exhibit arbitrarily strong squeezing of A or B. The time evolution of GIS is stable for Hamiltonians which admit linear in A and B invariants. Systems of GIS for the SU(1,1) and SU(2) groups are constructed and discussed. It is shown that SU(1,1) GIS contain all the Perelomov coherent states (CS) and the Barut and Girardello CS while the spin CS are a subset of SU(2) GIS. CS for an arbitrary semisimple Lie group can be considered as a GIS for the quadratures of the Weyl generators.
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    The trace of the heat kernel on a compact hyperbolic 3-orbifold (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3109-3116 
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    Topics: Mathematics , Physics
    Notes: The heat coefficients related to the Laplace–Beltrami operator defined on the hyperbolic compact manifold H3/Γ are evaluated in the case in which the discrete group Γ contains elliptic and hyperbolic elements. It is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace of the heat kernel, elliptic elements modify all coefficients of the asymptotic expansion, but the Weyl term, which remains unchanged. Some physical consequences are briefly discussed in the examples.
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    Representation of the five- and six-dimensional harmonic oscillators in a u(5)&supuline;so(5)&supuline;so(3) basis (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3178-3189 
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    ISSN: 1089-7658
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    Notes: The duality that exists between the two subgroups SU(1,1) and O(5) of Sp(5,R) to construct basis states for the five-dimensional harmonic oscillator which simultaneously reduce the Sp(5,R)&supuline;U(5)&supuline;O(5)&supuline;SO(3) and Sp(5,R)&supuline; SU(1,1)&supuline;U(1) subgroup chains is used. It is shown that the vector-coherent-state wave functions of the fundamental five-dimensional SO(5) irrep [1,0] realize the traceless bosons introduced by Lohe and Hurst to classify the irreps of the orthogonal groups and employed in Chacon, Moshinsky, and Sharp's construction of a basis for the five-dimensional harmonic oscillator. Moreover, it is shown that VCS theory provides a simple mechanism for constructing matrix elements of the traceless boson operators. These matrix elements are used to extend the VCS representations of SO(5) in an SO(3) basis, given in a previous paper, to irreps of U(5) in an SO(5)&supuline; SO(3) basis. The extension to U(6)&supuline;U(5)&supuline;SO(5)&supuline;SO(3) is also given.
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    Asymptotic level state density for parabosonic strings (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2057-2063 
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    Notes: Making use of some results concerning the theory of partitions, relevant in number theory, the complete asymptotic behavior, for large N, of the level density of states for a parabosonic string is derived. It is also pointed out that there is a similarity between parabosonic strings and membranes.
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    Controlling quantum motion (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2083-2104 
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    Notes: The techniques of controlling the free evolution of a nonrelativistic charged particle by time-dependent magnetic fields are proposed and the possibility of more general operations upon the Schrödinger wave packet is discussed. It is found that a properly programmed sequence of magnetic pulses can invert the free evolution process, forcing an arbitrary wave packet to "go back in time'' to recover its past shape. Our manipulation prescriptions hold also for nonrelativistic particles of arbitrary spin.
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    Exchange relations and correlation functions for a quantum particle on the SU2 group manifold (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2130-2141 
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    Notes: The SO4 invariant quantum dynamics of a point particle moving on the 3 sphere (or equivalently, of the relative motion of the spherical top) is considered. Quantum exchange relations for different times are derived with an "R matrix'' depending on the time difference and on the conserved angular momentum. Their implications for correlation functions are spelled out. The chiral exchange relations of Alekseev and Faddeev [Commun. Math. Phys. 141, 413–422 (1991)] are also extended to different times.
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    Generating mass without the Higgs particle (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2199-2209 
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    Notes: The conformal group is added to the gauge group of a model of elementary particles based on the fiber bundle formalism. The inertial mass of a particle is interpreted as a manifestation of its interaction with the gauge bosons associated with the generators of the translation and special conformal subgroups. The generation of mass by this mechanism (together with the fact that the Higgs field is not necessarily required to effect bundle reduction) makes the Higgs and the Yukawa terms in the Lagrangian unnecessary: the Lagrangian then consists only of a Yang–Mills term and a covariantly free matter field term. A particular choice of gauge reproduces the usual mass terms for both fermions and gauge bosons. The "no-go theorem'' is not violated by the construction. The Poincaré generators commute with the internal symmetry generators after bundle reduction, and there is no mass splitting within symmetry multiplets. However, the left-handed/right-handed asymmetry allows the neutrino to remain massless; the definition of matter fields allows the up and down quarks to acquire different mass couplings; and the gauge bosons have different mass couplings determined by the inner product on the Lie algebra of the broken symmetry subgroup. The mass ratios of the gauge bosons—at tree level—are precisely those predicted by the Standard Model.
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    Nonperturbative treatment of singular potentials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2229-2232 
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    Notes: A nonperturbative but absolutely convergent algorithm is applied to the determination of the eigenfunctions of Hamiltonian with a singular potential of the form H=−d2/dx2+x2+λ/xα in the domain [0, ∞] which obey Dirichlet boundary conditons. The formal structure of the algorithm is identical to that of the Lanczos algorithm when it is formally extended to self-adjoint operators.
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    A geometrical formulation of Abelian gauge structure in non-Abelian gauge theories and disconnected gauge group (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2270-2281 
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    Notes: A geometrical formalism of non-Abelian gauge theory with a topological term is constructed here with special reference to the role of Abelian gauge structures in non-Abelian theories. It is shown that when fermionic currents are written in chiral forms, we can take into account the disconnected gauge group which helps us to formulate a non-Abelian gauge structure so that the theory becomes asymptotically free.
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    Analysis of the Green's function approach to one-dimensional inverse problems. II. Simultaneous reconstruction of two parameters (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2315-2335 
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    Notes: The wave-splitting Green's function approach to one-dimensional electromagnetic inverse problems of simultaneous reconstructions with different types of scattering data is analyzed. Theorems of existence, uniqueness, and stability are given for the following types of scattering data: reflection and transmission data for one round trip, two-sided reflection data for one round trip, reflection data for two round trips.
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    Differential equations for the entropy density, energy density, and number density of statistical mechanics (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2371-2377 
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    Notes: A partial differential equation is derived for the number density as a function of position, temperature, and chemical potential. In the classical limit where Planck's constant is zero, it is shown that the expression for the classical number density of statistical mechanics satisfies the resulting equation. Similar partial differential equations are derived for the entropy density and energy density. It is then shown that these partial differential equations can be used to derive easily general expressions for the semiclassical number density, entropy density, and energy density of statistical mechanics.
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    Stable and unstable manifolds in a zone of instability (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2408-2412 
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    Notes: Applying Birkhoff's twist map theorem, it is shown that the closure of each of stable and unstable manifolds of any homoclinic Birkhoff saddle (see text for definition) in a zone of instability contains the boundary curves of the zone. It is shown as corollaries that (1) all the stable and unstable manifolds of different homoclinic Birkhoff saddles have heteroclinic points; (2) as soon as the boundary invariant curve, which separates two adjacent zones of instability, disintegrates, stable and unstable manifolds of all the homoclinic Birkhoff saddles of both zones intersect with each other; and (3) the stable and unstable manifolds of any homoclinic Birkhoff saddle have an infinite number of disjoint arcs which start in an cursive-epsilon-neighborhood of one boundary of the zone and end in an cursive-epsilon-neighborhood of the other boundary for any cursive-epsilon(approximately-greater-than)0.
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    Kerr–Schild metrics revisited. II. The complete vacuum solution (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2448-2462 
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    Notes: The complete solution of Einstein's gravitational equations with a vacuum–vacuum Kerr–Schild pencil of metrics gab+Vlalb is obtained. Our result generalizes the solution of the Kerr–Schild problem with a flat metric gab (represented by the Kerr theorem) to the case when gab is the metric of a curved space-time.
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    Quantum Z3-graded space (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2497-2504 
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    Notes: In this paper the quantum Z3-graded space is discussed and its differential calculus is investigated and the quantum matrices in quantum Z3-graded space are obtained.
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    On the group theory of the polarization states of a massless field (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1658-1667 
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    Notes: It is shown that the theory of representations of the Poincaré group applied to the vector potentials of a massless field yields in a simple and direct way (without assuming that the field is a gauge field, and without detailed assumption on the form of the equation of motion), the structure of the polarizations, the Gupta–Bleuler condition, and gauge invariance of the theory. The method is shown to apply to the Maxwell field and to a five-dimensional generalization of the Maxwell field (which properly contains the Maxwell theory) associated with manifestly covariant dynamics.
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    Quadrics on complex Riemannian spaces of constant curvature, separation of variables, and the Gaudin magnet (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1710-1731 
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    Notes: Integrable systems that are connected with orthogonal separation of variables in complex Riemannian spaces of constant curvature are considered herein. An isomorphism with the hyperbolic Gaudin magnet, previously pointed out by one of the authors, extends to coordinates of this type. The complete classification of these separable coordinate systems is provided by means of the corresponding L matrices for the Gaudin magnet. The limiting procedures (or ε calculus) which relate various degenerate orthogonal coordinate systems play a crucial role in the classification of all such systems.
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    Anomaly cancellation in six dimensions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1819-1833 
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    Notes: It is shown that anomaly cancellation conditions are sufficient to determine the two most important topological numbers relevant for Calabi–Yau (CY) compactification to six dimensions. This reflects the fact that K3 is the only nontrivial CY manifold in two complex dimensions. The Green–Schwarz counterterms are explicitly constructed and sum rules for charges of additional enhanced U(1) factors are derived and the results with all possible Abelian orbifold constructions of K3 are compared. This includes asymmetric orbifolds as well, showing that it is possible to regain a geometrical interpretation for this class of models. Finally, some models with a broken E7 gauge group which will be useful for more phenomenological applications are discussed herein.
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    Taub numbers extended to Einstein–Maxwell space–time (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1834-1839 
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    Notes: Mass and angular momentum of asymptotically flat systems are computed by Taub number τ1. This work extends the Taub number method from a vacuum region outside the central source to a region with stationary electric and magnetic fields while preserving global mass and angular momentum. The Reissner–Nordström and Kerr–Newman solutions are treated. Function spaces for curves of solutions of the coupled Einstein–Maxwell equations are discussed, together with the linearized field equations which are directional derivatives of the field equations along the solution curves in the direction of the perturbation.
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    The stress tensor conformal anomaly and analytic regularizations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1840-1849 
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    Notes: In this paper the stress tensor conformal anomaly of a conformally coupled scalar field defined in a d dimensional Riemannian manifold is derived with or without a boundary, using the zeta function analytic regularization method. It is found that the scalar anomaly is independent of any massless limit. In an odd dimensional manifold with a boundary, the anomaly is not zero owing the boundary condition dependent term. After briefly discussing the cutoff method, it is proven that the zeta function method is equivalent to the cutoff method with a subtraction of the polar terms.
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    Determination of f(∞) from the asymptotic series for f(x) about x=0 (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1914-1921 
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    Notes: A difficult and long-standing problem in mathematical physics concerns the determination of the value of f(∞) from the asymptotic series for f(x) about x=0. In the past the approach has been to convert the asymptotic series to a sequence of Padé approximants {Pnn(x)} and then to evaluate these approximants at x=∞. Unfortunately, for most physical applications the sequence {Pnn(∞)} is slowly converging and does not usually give very accurate results. In this paper the results of extensive numerical studies for a large class of functions f(x) associated with strong-coupling lattice approximations are reported. It is conjectured that for large n, Pnn(∞)∼f(∞)+B/ln n. A numerical fit to this asymptotic behavior gives an accurate extrapolation to the value of f(∞).
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    Cosmological CP violation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1573-1596 
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    Notes: Spinor fields are studied in infinite, topologically multiply connected Robertson–Walker cosmologies. Unitary spinor representations for the discrete covering groups of the spacelike slices are constructed. The spectral resolution of Dirac's equation is given in terms of horospherical elementary waves, on which the treatment of spin and energy is based in these cosmologies. The meaning of the energy and the particle–antiparticle concept is explained in the context of this varying cosmic background. Discrete symmetries, in particular inversions of the multiply connected spacelike slices, are studied. The violation of the unitarity of the parity operator, due to self-interference of P-reflected wave packets, is discussed. The violation of the CP and CPT invariance—already on the level of the free Dirac equation on this cosmological background—is pointed out.
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    Nöther formalism for conserved quantities in classical gauge field theories (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1644-1657 
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    Notes: Gauge theories coupled with the gravitational field and external matter fields are considered and Nötherian techniques are used to build the canonical conserved quantities. Their superpotentials are found and the relation between the canonical stress tensor and the Hilbert tensor is determined. The case of Yang–Mills theories coupled with gravity and scalar matter fields is considered in detail and it is shown that in this case the canonical stress tensor and the Hilbert tensor coincide.
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    A generalized Henon–Heiles system and related integrable Newton equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1693-1709 
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    Notes: A detailed description is given of integrable cases of the generalized Henon–Heiles systems which differs from the standard H–H ones by the term α/q22. Their connection with fifth-order one-component soliton equations is discussed. Lax representations are constructed, and the bi-Hamiltonian formulation of dynamics is given. It is also shown that the gH–H system can be mapped onto another system of Newton equations with a nonstandard Hamiltonian structure.
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    New integrable systems related to a Kupershmidt's equation by Miura maps (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 816-820 
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    Notes: A multicomponent KdV system, Kupershmidt's coupled KdV equation, is considered. The system is shown to be a modification of some system, and it can be modified.
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    Super-Toda lattices (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1233-1251 
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    Notes: The Lax formalism, as described by Oevel et al. and in an earlier and more fundamental form by Semenov, Kostant, Symes, and Adler, can easily be generalized to the case where anticommuting variables are involved, the so-called supercase. In this article this super-Lax formalism is applied to the well-known associative superalgebra G=Mat(m,n,Λ). Subspaces of G to which the super-Poisson structures can be restricted arise in a natural way. Taking L in one of these subspaces formally leads to superextensions of the hierarchy of nonrelativistic Toda lattices. In the simplest case, where only nearest-neighbor interaction is involved, the equations are explicitly solved. Furthermore, the relevant two super-Hamiltonian structures are explicitly calculated. Finally a superextension of the relativistic Toda lattice with a super-Hamiltonian structure is described herein.
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    Curvature of gravitationally bound mechanical systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1850-1880 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In the present work mathematical aspects of determining the local instability parameters are focused on by using invariant characteristics of the internal Riemannian geometry with the Jacobi metric (in principle, for Hamiltonian dynamical systems with the natural Lagrangian). First, it is shown that the Ricci scalar indeed measures the sectional curvature averaged upon all two-directions. Second, necessary and sufficient criteria for non-negativity and of nonpositivity of the sectional curvature for any system with the natural Lagrangian are given. Third, analytical formulas allowing us to compute the separation rate of nearby trajectories are given. Fourth, it is shown that for any collisionless problem of n gravitationally bounded bodies, the sectional curvature in every direction is negative if n tends to infinity.
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    URL: http://dx.doi.org/10.1063/1.530575
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    The abstract complex Lorentz transformation group with real metric. II. The invariance group of the form ||t||2−(parallel)x(parallel)2 (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1881-1913 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Let TX=C×V∞ be equipped with the Hermitian form ||t||2−(parallel)x(parallel)2, where t∈C is a complex number and x∈V∞ is a vector in an abstract complex inner product space V∞. The abstract complex Lorentz group (with real metric) is the invariance group of this form. A novel formalism to deal with the abstract real Lorentz transformation group has recently been developed by Ungar [Am. J. Phys. 59, 824–834 (1991); Am. J. Phys. 60, 815–828 (1992)], allowing one to solve in an abstract context previously poorly understood problems in one time and three space dimensions. Intrigued by the success of the abstract real Lorentz group formalism, resulting in the understanding of Thomas gyration in its abstract context, a formalism to deal with the abstract complex Lorentz group is proposed in this article. The extension from the real to the complex Lorentz group is not trivial. Complex Lorentz groups involve two interacting gyrations, a complex-time gyration and a complex-space gyration, as opposed to the real case which involves a single gyration, that is, a real-space gyration called Thomas gyration. The proposed formalism allows one to manipulate the seemingly involved abstract complex Lorentz group in a way analogous to the way one commonly manipulates Galilei transformation groups. Thus, for instance, equipped with the proposed formalism, one can readily (i) compose abstract complex Lorentz transformations, and (ii) determine those which link any two given events by manipulations analogous to Galilei group manipulations. When the abstract complex inner product space V∞ associated with the underlying abstract complex Minkowski space is realized by a finite-dimensional complex Hilbert space of dimension n, the abstract complex Lorentz group studied in this article reduces to the group U(1,n) or SU(1,n), depending on whether unitary or special unitary transformations are being considered.
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    URL: http://dx.doi.org/10.1063/1.530576
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    Noncommutative differential geometry on deformed quantum mechanical phase spaces (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1984-1991 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The problem of formulating noncommutative differential geometry on multiparametric deformations of arbitrary quantum mechanical phase spaces involving bosonic or (even or odd-dimensional) fermionic variables is investigated. A suitable enlargement of the basic quadratic algebras enables one to solve all the consistency conditions on the calculus with the help of plausible ansatzes.
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    URL: http://dx.doi.org/10.1063/1.530583
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    The abstract complex Lorentz transformation group with real metric. I. Special relativity formalism to deal with the holomorphic automorphism group of the unit ball in any complex Hilbert space (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1408-1426 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Viewing the unit ball in a complex Hilbert space as a set of relativistically admissible complex velocities, the holomorphic automorphisms of the ball emerge as "complex relativistic velocity additions'' and "complex rotations'' (that is, unitary transformations). Hence, newly discovered properties of the abstract real Lorentz group [A. A. Ungar, Am. J. Phys. 59, 824 (1991); A. A. Ungar, Am. J. Phys. 60, 815 (1992)], which turn out to provide powerful tools for the study of the holomorphic automorphisms of the unit ball in any complex Hilbert space, are of interest in the literature [W. Rudin, Function Theory in the Unit Ball of Cn (Springer-Verlag, New York, 1980) ]. A particularly useful and important tool turns out to be provided by Thomas gyration, which is an abstraction of the well-known Thomas precession of special relativity theory, and which gives rise to a gyrogroup structure underlying the ball. Results of this article set the stage for the study, in a subsequent article, of complex Lorentz transformation groups, U(1,n), in a way analogous to the study of Galilean groups. The dimension n is finite or infinite, and a real parameter c is involved in such a way that in the limit of large c, c→∞, the Lorentz groups that we study reduce to their Galilean counterparts.
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    URL: http://dx.doi.org/10.1063/1.530597
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    Finite dimensional irreducible representations of the quantum algebra Uq(C2) (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1037-1043 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this article, the communtation relations of the generators of quantum algebra Uq(C2) are analyzed and irreducible q-tensor operators of rank (1/2) of quantum algebra SUq(2) are constructed. By means of the property of a q-tensor operator, finite irreducible representations of Uq(C2) can be easily obtained. Some low dimensional representations are tabulated.
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    URL: http://dx.doi.org/10.1063/1.530650
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    The polygon quantum-billiard problem (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 596-607 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The present work addresses the quantum polygon billiard problem with attention given to analytic and degeneracy properties of energy eigenstates. The "polygon ground-state theorem'' is proven which states that the only polygons that contain respective ground states that are analytic in the closed domain of the entire polygon are the "elemental polygons'' (defined in the text). The "polygon first excited-state theorem'' is established which states that for every N-sided regular polygon, N equivalent first excited states exist, each of which contains a nodal curve that is a line of mirror symmetry of the related polygon. A vector description of nodal diagonal eigenstates is introduced to establish the second component of this theorem which indicates that the space of first excited states for the N-sided regular polygon is spanned by any two of these N nodal-diagonal eigenstates (i.e., the first excited state is twofold degenerate). At various levels of the discussion attention is drawn to the correspondence between the quantum and classical solutions for these configurations. Thus, for example, correspondence is demonstrated in the common source of integrability in the classical and quantum domains for three inclusive, nonoverlapping classes of polygons. Stemming from the preceding conclusions, a discussion is included on the possibility of employing transverse magnetic (TM) modes in a metal waveguide to determine if an equivalent quantum billiard configuration is chaotic.
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    URL: http://dx.doi.org/10.1063/1.530874
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    Becchi–Rouet–Stora–Tyutin structure of polynomial Poisson algebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1334-1347 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Becchi–Rouet–Stora–Tyutin (BRST) structure of polynomial Poisson algebras is investigated. It is shown that Poisson algebras provide nontrivial models where the full BRST recursive procedure is needed. Quadratic Poisson algebras may already be of arbitrarily high rank. Explicit examples are provided, for which the first terms of the BRST generator are given. The calculations are cumbersome but purely algorithmic, and have been treated by means of the computer algebra system reduce. Our analysis is classical (=nonquantum) throughout.
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    URL: http://dx.doi.org/10.1063/1.530592
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    Deformations of Gabor frames (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1372-1376 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quantum mechanical Harmonic oscillator Hamiltonian H=(t2−∂2t)/2 generates a one-parameter unitary group W(θ)=eiθH in L2(R) which rotates the time–frequency plane. In particular, W(π/2) is the Fourier transform. When W(θ) is applied to any frame of Gabor wavelets, the result is another such frame with identical frame bounds. Thus each Gabor frame gives rise to a one-parameter family of frames, which we call a deformation of the original. For example, beginning with the usual tight frame F of Gabor wavelets generated by a compactly supported window g(t) and parameterized by a regular lattice in the time–frequency plane, one obtains a family {Fθ: 0≤θ〈2π} of frames generated by the noncompactly supported windows gθ=W(θ)g, parameterized by rotated versions of the original lattice. This gives a method for constructing tight frames of Gabor wavelets for which neither the window nor its Fourier transform have compact support. When θ=π/2, Fθ is the well-known Gabor frame generated by a window with compactly supported Fourier transform. The family {Fθ} therefore interpolates these two familiar examples.
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    URL: http://dx.doi.org/10.1063/1.530594
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    Deformations of nilpotent parts of the Neveu–Schwarz and Ramond superalgebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1427-1440 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Deformations of nilpotent parts of the Neveu–Schwarz superalgebra and of the Ramond superalgebra are studied herein. This study consists of the computation of the second cohomology space with coefficients in the adjoint representation by means of spectral sequences, the explicit construction of infinitesimal deformations, the extension of these infinitesimal deformations to one-parameter deformations, the realization of these deformations, and the construction of multiparameter deformations.
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    URL: http://dx.doi.org/10.1063/1.530598
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    Almost commutative algebra and differential calculus on the quantum hyperplane (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 959-970 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A notion of almost commutative algebra is given that makes it possible to extend differential geometric ideas associated with commutative algebras in a simple manner to certain classes of noncommutative algebras. As an example differential calculus on the N-dimensional quantum hyperplane is discussed.
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    URL: http://dx.doi.org/10.1063/1.530888
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    Quantum affine Lie algebras, Casimir invariants, and diagonalization of the braid generator (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6757-6773 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Let Uq(Gˆ) be an infinite-dimensional quantum affine Lie algebra. A family of central elements or Casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation. These eigenvalue formulas are shown to be absolutely convergent when the deformation parameter q is such that ||q||(approximately-greater-than)1. It is proven that the universal R-matrix R of Uq(Gˆ) satisfies the celebrated conjugation relation R°=TR with T the usual twist map. As applications, the braid generator is shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight Uq(Gˆ)-module and a spectral decomposition formula for the braid generator is obtained which is the generalization of Reshetikhin's and Gould's forms to the present affine case. Casimir invariants acting on a specified module are also constructed and their eigenvalues, again absolutely convergent for ||q||(approximately-greater-than)1, computed by means of the spectral decomposition formula. © 1994 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.530641
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    More on Uq(su(1,1)) with q a root of unity (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6857-6874 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Highest weight representations of Uq(su(1,1)) with q=exp πi/N are investigated. The structures of the irreducible highest weight modules are discussed in detail. The Clebsch–Gordan decomposition for the tensor product of two irreducible representations is discussed. By using the results, a representation of SL(2,R)⊗Uq(su(2)) is also presented in terms of holomorphic sections which also have Uq(su(2)) index. Furthermore, ZN-graded supersymmetry is realized in terms of the representation. An explicit realization of Osp(1||2) via the highest weight representation of Uq(su(1,1)) with q2=−1 is given. © 1994 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.530646
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    Covariant flux-limited diffusion theory in Bianchi cosmologies (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 885-898 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A covariant flux-limited diffusion theory is presented for homogeneous and anisotropic cosmologies. Explicit formulas for radiation stress tensor and applications are given for a Bianchi-type I model.
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    URL: http://dx.doi.org/10.1063/1.530619
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    Geometry of canonical correlation on the state space of a quantum system (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 780-795 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A Riemannian metric is defined on the state space of a finite quantum system by the canonical correlation (or Kubo–Mori/Bogoliubov scalar product). This metric is infinitesimally induced by the (nonsymmetric) relative entropy functional or the von Neumann entropy of density matrices. Hence its geometry expresses maximal uncertainty. It is proven that the metric is monotone under stochastic mappings, however, an example shows that it is not the only such Riemannian metric. This fact is remarkable because in the probabilistic case, the Markovian monotonicity property characterizes the Fisher information metric. The essential difference appears in the curvatures of a classical state space and a quantum one. A conjecture is made that the scalar curvature is monotone with respect to the "more mixed'' (statistical) partial order of density matrices. Furthermore, an information inequality resembling the Cramér–Rao inequality of classical statistics is established. The inequality provides a lower bound for the canonical correlation matrix (of an unbiased observable) and it is saturated when a (partial) observation level and the corresponding family of coarse-grained states are considered.
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    Integrable mechanical systems related to the Harry–Dym hierarchy (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 834-847 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that all stationary and restricted flows of the Harry–Dym hierarchy have a parametrization as a set of Newton equations. They are new classes of integrable mechanical systems. Properties of the Harry–Dym hierarchy are used for deriving systematically spectral-parameter-dependent Lax representations and bi-Hamiltonian formulation for some of these systems. They yield complete sets of integrals in involution which render these systems to be completely integrable.
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    URL: http://dx.doi.org/10.1063/1.530616
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    Self-gravitating Yang–Mills solitons and their Chern–Simons numbers (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 899-919 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A classification of the possible regular, spherically symmetric solutions of the Einstein–Yang–Mills system which is based on a bundle theoretical analysis for arbitrary gauge groups is presented herein. It is shown that such solitons must be of magnetic type, at least if the magnetic Yang–Mills charge vanishes. Explicit expressions for the Chern–Simons numbers of these self-gravitating Yang–Mills solitons are derived, which involve only properties of irreducible root systems and some information about the asymptotics of the solutions. It turns out, as an example, that the Chern–Simons numbers are always half integers or integers for the gauge groups SU(n). Possible physical implications of these results, which are based on analogies with the unstable sphaleron solution of the electroweak theory, are briefly indicated.
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    URL: http://dx.doi.org/10.1063/1.530620
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    The N=2 super-Wess–Zumino–Novikov–Witten model valued in superdiffeomorphism (SDIFF) M2 is self-dual supergravity in four dimensions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 920-928 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the pure topological term of the N=2 super-Wess–Zumino–Novikov–Witten (SWZNW) model, valued in the area-preserving diffeomorphisms group of a two-dimensional Euclidean surface, is self-dual supergravity (SDSG) in 3+1 dimensions. This is achieved by a suitable slicing and pasting procedure of the (2,0); (0,2) N=2 SWZNW models determined by the embedding of the (2,0); (0,2) superspace supercovariant derivatives into the (3+1) superspace ones. Preliminary steps are provided to show that the N=1 SWZNW model, valued in the area-preserving superdiffeomorphism group of a super Riemann surface (SRS) whose signature is (1+1), is self-dual supergravity in (2+2) dimensions: the so-called Atiyah–Ward space–times.
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    On diff(S1) covariantization of pseudodifferential operator (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 993-1007 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A study of diff(S1) covariant properties of a pseudodifferential operator of integer degree is presented. First, it is shown that the action of diff(S1) defines a Hamiltonian flow defined by the second Gelfand–Dickey bracket if and only if the pseudodifferential operator transforms covariantly. Second, the covariant form of a pseudodifferential operator of degree n ≠ 0,±1 is constructed by exploiting the inverse of the covariant derivative. This, in particular, implies the existence of a primary basis for WKP(n) (n ≠ 0,±1).
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    URL: http://dx.doi.org/10.1063/1.530626
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