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  • American Institute of Physics (AIP)  (9,667)
  • 2010-2014
  • 1995-1999  (9,667)
  • 1995  (9,667)
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  • 2010-2014
  • 1995-1999  (9,667)
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  • 1
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    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 36 (1995), S. 4553-4560 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the number of bound states of coupled systems of radial Schrödinger equations can be found by computing the number of zeros of a suitable determinant. This is related to the concept of conjugate points from Morse theory and is the basis for a numerically efficient method. © 1995 American Institute of Physics.
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  • 2
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    Journal of Mathematical Physics 36 (1995), S. 4138-4161 
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    Topics: Mathematics , Physics
    Notes: We obtain a classification of infinitesimal symmetries of an autonomous higher-order Lagrangian system by using the theory of lifts of vector fields to tangent bundles. Also, a classification of infinitesimal symmetries of a time-dependent higher-order Lagrangian system is obtained. The relationship between infinitesimal symmetries and constants of the motion is investigated. © 1995 American Institute of Physics.
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  • 3
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    Journal of Mathematical Physics 36 (1995), S. 4192-4202 
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    Topics: Mathematics , Physics
    Notes: It is shown that by considering the more general dressing operators, the matrix Kadomtsev–Petviashvili (KP) hierarchy can yield new integrable equations in (2+1) dimensions along with the corresponding Lax pair. In particular integrable extensions of the Davey–Stewartson (DS) equation with variable dependent coefficients, with derivative terms and with higher-order nonlinear terms, are obtained. One of such extended DS equations is found to be a higher-dimensional generalization of the Kundu–Eckhaus equation. Exact localized solutions of these DS equations are presented. The effect of such transformations on the constrained matrix KP system is analyzed. © 1995 American Institute of Physics.
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  • 4
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    Journal of Mathematical Physics 36 (1995), S. 4571-4589 
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    Topics: Mathematics , Physics
    Notes: In the Fock–Bargmann space, the complete harmonic-oscillator basis for the three-cluster system is constructed. The indices of the reduction U(6)&supuline;U(2)×U(3) are chosen as the quantum numbers. The Pauli-forbidden states are eliminated by the orthogonal transformation of basis functions. The basis states are obtained in terms of hypergeometric functions and the spherical Wigner functions. Their simple form allows one to solve the problem of calculating the matrix elements of the microscopic Hamiltonian needed for the study of three-cluster systems within the algebraic version of RGM. © 1995 American Institute of Physics.
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  • 5
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    Journal of Mathematical Physics 36 (1995), S. 4639-4666 
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    Topics: Mathematics , Physics
    Notes: The method of group quantization described in the preceding paper [J. Math. Phys. 36, 4612 (1995)] is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy model is studied that admits a pair of maximal transversal surfaces intersecting all orbits. The corresponding two quantum mechanics are constructed. The similarity of the canonical group actions in the classical phase spaces on the one hand and in the quantum Hilbert spaces on the other hand suggests how the two Hilbert spaces are to be pasted together. The resulting quantum theory is checked to be equivalent to that constructed directly by means of Dirac's operator constraint method. The complete system of partial Hamiltonians for any of the two transversal surfaces is chosen and the quantum Schrödinger or Heisenberg pictures of time evolution are constructed. © 1995 American Institute of Physics.
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  • 6
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    Journal of Mathematical Physics 36 (1995), S. 4340-4349 
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    Topics: Mathematics , Physics
    Notes: The linear, differential operators that preserve the N-dimensional vector space whose entries are polynomials of fixed, but arbitrary, degrees in one variable are considered herein. They are relevant for the classification of quasi-exactly solvable systems of equations. Generating elements are explicitly constructed and rules for ordering their products are derived. Some examples of equations that can be reduced to such systems are discussed. © 1995 American Institute of Physics.
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  • 7
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    Journal of Mathematical Physics 36 (1995), S. 4406-4435 
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    Topics: Mathematics , Physics
    Notes: We compute homotopy and cohomology groups for the Skyrmion bundle, which play an important role in the description of the monopole-induced proton decay within the Skyrme model. By use of spectral sequences, the differential forms on the bundle that allow for the calculation of baryon numbers and for the anomalous action are developed out of the ones on the fiber, and are adapted to the given Maxwell connection. © 1995 American Institute of Physics.
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  • 8
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    Journal of Mathematical Physics 36 (1995), S. 4363-4405 
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    Topics: Mathematics , Physics
    Notes: The Euclidean Hopf algebra Uq(eN) dual of Fun(RNq(large-closed-square)SOq−1(N)) is constructed by realizing it as a subalgebra of the differential algebra Diff(RNq) on the quantum Euclidean space RNq; in fact, the previous realization [G. Fiore, Commun. Math. Phys. 169, 475–500 (1995)] of Uq−1(so(N)) is extended within Diff(RNq) through the introduction of q derivatives as generators of q translations. The fundamental Hilbert-space representations of Uq(eN) turn out to be of highest weight type and rather simple "lattice-regularized'' versions of the classical ones. The vectors of a basis of the singlet (i.e., zero-spin) irrep can be realized as normalizable functions on RNq, going to distributions in the limit q → 1. © 1995 American Institute of Physics.
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  • 9
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    Journal of Mathematical Physics 36 (1995), S. 4914-4922 
    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: The solutions to the sine–Gordon equation which are derived from an ansatz based on the methods of twistor theory are shown to correspond to Darboux transformations for a certain linear equation. The linear problem is shown to arise in several different ways, and a relationship between the Darboux transformation for linear equations of this type and the Bäcklund transformation is examined. A possible extension to well known monopole ansatze is briefly considered. © 1995 American Institute of Physics.
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  • 10
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    Journal of Mathematical Physics 36 (1995), S. 4940-4951 
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    Topics: Mathematics , Physics
    Notes: We study the BKP hierarchy and prove the existence of an Adler–Shiota–van Moerbeke formula. This formula relates the action of the BW1+∞ algebra on tau functions to the action of the "additional symmetries'' on wave functions. © 1995 American Institute of Physics.
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  • 11
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    Journal of Mathematical Physics 36 (1995), S. 4952-4961 
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    Topics: Mathematics , Physics
    Notes: A new result on topological censorship is presented. Roughly speaking, the result shows that, under suitable conditions, the topology of space outside the event horizon must eventually be simple. In particular, cross sections of the event horizon must eventually be spherical. This latter consequence of the main result generalizes in many respects the classical theorem of Hawking that black hole boundaries in stationary black hole space–times are spherical. © 1995 American Institute of Physics.
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  • 12
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    Journal of Mathematical Physics 36 (1995), S. 4984-5004 
    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: We reformulate the Einstein equations as equations for families of surfaces on a four-manifold. These surfaces eventually become characteristic surfaces for an Einstein metric (with or without sources). In particular they are formulated in terms of two functions on R4×S2, i.e., the sphere bundle over space–time, one of the functions playing the role of a conformal factor for a family of associated conformal metrics, the other function describing an S2's worth of surfaces at each space–time point. It is from these families of surfaces themselves that the conformal metric, conformal to an Einstein metric, is constructed; the conformal factor turns them into Einstein metrics. The surfaces are null surfaces with respect to this metric. © 1995 American Institute of Physics.
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  • 13
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    Journal of Mathematical Physics 36 (1995), S. 3345-3352 
    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: The existence of an internal angular momentum induces nutations and periodic deviations from a mean precession. Motions are classified into three cases. In Case I, the nutation is regular during precessions so that the motion is a wobbling, the top behaves triaxially. This triaxiality may be involved in the triaxial deformations of nuclear shapes in nuclear physics. Case II is a limiting case of Case I at an infinite period of nutation. In Case III, the body symmetry axis is over nutated to cross over and to oscillate around the invariable plane. It is an overnutated wobbling. These three cases can be determined by whether the ratio of the internal angular momentum to the total angular momentum is less than or greater than a critical value. © 1995 American Institute of Physics.
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  • 14
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    Journal of Mathematical Physics 36 (1995), S. 3377-3394 
    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: The notion of center of mass is reviewed and three natural definitions for the relativistic regime are proposed. This construction can be explicitly calculated by means of an algorithm which is described below. © 1995 American Institute of Physics.
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  • 15
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    Journal of Mathematical Physics 36 (1995), S. 3413-3418 
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    Topics: Mathematics , Physics
    Notes: It is shown that any divergence-free vector field invariant under a group of volume-preserving transformations can be expressed locally in terms of two scalar potentials which depend on two variables only. It is also shown that the corresponding field line equations can be written in Hamiltonian form with one of these potentials as the Hamiltonian. © 1995 American Institute of Physics.
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  • 16
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    Journal of Mathematical Physics 36 (1995), S. 3419-3442 
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    Topics: Mathematics , Physics
    Notes: An affine sl(n+1) algebraic construction of the basic constrained KP hierarchy is presented. This hierarchy is analyzed using two approaches, namely linear matrix eigenvalue problem on hermitian symmetric space and constrained KP Lax formulation and it is shown that these approaches are equivalent. The model is recognized to be the generalized non-linear Schrödinger (@sG@sN@sL@sS) hierarchy and it is used as a building block for a new class of constrained KP hierarchies. These constrained KP hierarchies are connected via similarity-Bäcklund transformations and interpolate between @sG@sN@sL@sS and multi-boson KP-Toda hierarchies. Our construction uncovers the origin of the Toda lattice structure behind the latter hierarchy. © 1995 American Institute of Physics.
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  • 17
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    Journal of Mathematical Physics 36 (1995), S. 3619-3624 
    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: A scenario is discussed in a Kaluza–Klein type of space–time with a cosmological constant for an inhomogeneous matter field obeying an equation of state p=kρ≠p5, where k is a constant, p is the isotropic pressure in the three-space, and p5 is that for the extra fifth dimension. It is found that the usual three-dimensional space expands exponentially while, depending on the signature of the arbitrary constants of integration, the extra scale either expands indefinitely or exhibits the desirable feature of dimensional reduction. It is interesting to point out that in the former case both the scales do not show any big bang type of singularity. Moreover, p5 automatically vanishes in this model. The present work is very general in nature because in special cases it reduces to some well-known solutions in the relevant field. © 1995 American Institute of Physics.
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  • 18
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    Journal of Mathematical Physics 36 (1995), S. 3632-3643 
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    Topics: Mathematics , Physics
    Notes: The crossing of two dust shells is considered as a simplified model for shell crossing during the spherically symmetric collapse of dust. It is shown that one encounters the same problems as in the latter case if one wants to continue the space-time dynamically through the region of intersection. To get a unique solution of the equations of motion, detailed information on the interaction between the shells has to be given. A corresponding Newtonian model is discussed and compared with the relativistic case. Furthermore it is shown that dust shells cannot be obtained as limiting cases of extended dust regions. © 1995 American Institute of Physics.
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  • 19
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    Journal of Mathematical Physics 36 (1995), S. 3644-3662 
    ISSN: 1089-7658
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    Topics: Mathematics , Physics
    Notes: A sheaf of functions on a topological space is called a differential structure if it satisfies an axiom of a closure with respect to composition with the Euclidean functions. A differential structure on a nonempty set is called a structured space. It is a generalization of the smooth manifold concept and of an earlier concept of differential space. Differential geometry on structured spaces is developed (tangent space, vector fields, differential forms, exterior algebra, linear connection, curvature, and torsion). Some of its techniques are applied to the classical singularity problem in general relativity. It turns out that Einstein's equations can be defined on space–times with singularities. This can have important consequences for the search of the quantum theory of gravity. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3625-3631 
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    Notes: Two exact solutions of Einstein's field equations corresponding to a cylinder of dust with net zero angular momentum are considered. In one of the cases, the dust distribution is homogeneous, whereas in the other, the angular velocity of dust particles is constant [Nuovo Cimento B 21, 64 (1974)]. For both solutions the junction conditions to the exterior static vacuum Levi–Civita space–time were studied. From this study we find an upper limit for the energy density per unit length σ of the source equals 1/4 for both cases. Thus the homogeneous cluster provides another example [Class. Quant. Grav. 8, 727 (1991); J. Math. Phys. 27, 152 (1980)] where the limit of σ is 1/4. It was also found that the cluster of homogeneous dust has a superior limit for its radius, depending on the constant volumetric energy density ρ0. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3704-3721 
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    Topics: Mathematics , Physics
    Notes: Light cone cuts are the intersection of the light cones of space–time events with an initial data surface which is usually taken to be null infinity. These are determined by a "cut function,'' a function of the space–time coordinates and the sphere of generators of null infinity. The Bach equations and the conformal vacuum equations are shown to lead to a single scalar "main'' equation on the cut function. In simplified cases, i.e., when the Weyl curvature is either small or self-dual, this equation can be integrated to give a simple scalar conformally invariant elliptic equation on the sphere of null directions. It has the remarkable property that the general solution of the Einstein vacuum equations in these cases can be derived from the solution to this auxiliary equation in two dimensions. In general, it will not be possible to reduce it to an auxilliary equation on the sphere. Nevertheless, the main equation is still a necessary condition and it is conjectured that it is also sufficient to imply the Bach equations in general and supporting arguments are given. It is also shown how to extend the Kozameh–Newman framework to the case of light cone cuts of a spacelike Cauchy hypersurface. The analogous procedures for Yang–Mills are also discussed. A conformally invariant formalism for calculations on null infinity is described in an Appendix. This is used for all the calculations which are only described in brief form in the main text. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3733-3742 
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    Notes: A new action principle, in the which the field variables are a sl(2,C)⊕g valued connection one-form, two-form, and multiplier field, is proposed and discussed. The equations of motion are the complex Einstein–Yang–Mills equations with internal symmetry Lie algebra g. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3743-3758 
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    Notes: The notion of *-derivation on an algebra of unbounded operators is extended to partial O*-algebras, and the corresponding notion of spatiality is investigated. Special emphasis is given to *-derivations associated to one-parameter groups of *-automorphisms and to *-derivations of partial GW*-algebras. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3822-3835 
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    Notes: A noncommutative integration calculus arising in the mathematical description of Schwinger terms of fermion–Yang–Mills systems is discussed. The differential complexes of forms u0[cursive-epsilon,u1]...[cursive-epsilon,un] with cursive-epsilon a grading operator on a Hilbert space H and ui bounded operators on H which naturally contains the compactly supported de Rham forms on Rd (i.e., cursive-epsilon is the sign of the free Dirac operator on Rd and H is a L2-space on Rd) are considered. An elementary proof is presented in which the integral of d-forms ∫RdtrN(X0dX1...dXd) for Xi∈C0∞(Rd;glN) is equal, up to a constant, to the conditional Hilbert space trace of ΓX0[cursive-epsilon,X1]...[cursive-epsilon,Xd] where Γ=1 for d odd and Γ=γd+1 (‘γ5-matrix') a spin matrix anticommuting with cursive-epsilon for d even. This result provides a natural generalization of integration of de Rham forms to the setting of Connes' noncommutative geometry which involves the ordinary Hilbert space trace rather than the Dixmier trace. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3866-3866 
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    Journal of Mathematical Physics 36 (1995), S. 2581-2592 
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    Notes: An equation that arises out of the bifurcation analysis of an improvement of the nonperturbative equations for the electron mass function in quenched quantum electrodynamics is analyzed. In the quasilinear approximation, the integral equation is solved by Mellin transformation, followed by the calculation of the Muskhelishvili index of the resultant singular integral operator. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2741-2760 
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    Notes: In the article, the complete investigation is given of the large times behavior of the solutions of the Belavkin quantum filtering equation describing a quantum particle with continuously observed coordinate. It turns out that these solutions have an extraordinary property, namely: as t → ∞, any solution will tend to a Gaussian function (for almost all realizations of innovating Wiener process). As a consequence, it follows that the dispersion of coordinate will always tend to the same limit, as t → ∞, not depending on initial data. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2691-2701 
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    Notes: It is shown how the Moyal product of phase-space functions, and the Weyl correspondence between symbols and operator kernels, may be obtained directly using the procedures of geometric quantization, applied to the symplectic groupoid constructed by "doubling'' the phase space. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2720-2726 
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    Notes: The Heisenberg operator solutions for the multiphoton Jaynes–Cummings model will be presented. By solving the operator differential equations, the exact solutions for the photon annihilation operator a(t), the atomic dipole-moment operator σ−(t), and the population difference operator σz(t) are obtained. The time dynamical behaviors for the operators are compared with the results obtained by the density operator methods. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2777-2791 
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    Notes: The most general Dirac spinors globally invariant under the representatives of the conjugacy classes of the connected part to the identity of the Euclidean group in four dimensions are determined. The Dirac equation is reduced under each subgroup representative and a relation to the reduction by symmetry of a linear system of the self-dual Yang–Mills equations is given. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2792-2802 
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    Notes: Parametrized families of Landau Hamiltonians are introduced, where the parameter space is the Teichmüller space (topologically the complex upper half plane) corresponding to deformations of tori. The underlying SO(2,1) symmetry of the families enables an explicit calculation of the Berry phases picked up by the eigenstates when the torus is slowly deformed. It is also shown that apart from these phases that are local in origin, there are global non-Abelian ones too, related to the hidden discrete symmetry group Γcursive-theta (the theta group, which is a subgroup of the modular group) of the families. The induced Riemannian structure on the parameter space is the usual Poincare metric on the upper half plane of constant negative curvature. Due to the discrete symmetry Γcursive-theta the geodesic motion restricted to the fundamental domain of this group is chaotic. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2929-2940 
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    Notes: A class of spherically symmetric non-static models compatible with relativistic anisotropic magnetofluid systems is obtained under the special feature that flow lines are shear-free but expanding and non-geodesic. In addition, some conformally flat solutions leading to generalized versions of Robertson–Walker models are derived. Moreover, it is proved that if the space–time admits conformal motion then the associated solution does not admit proper conformal symmetry vectors. The models found are of Petrov type I, D, or O. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2880-2928 
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    Notes: The inverse scattering problem on the line is studied for the generalized Schrödinger equation (d2ψ/dx2)+k2H(x)2ψ=Q(x)ψ, where H(x) is a positive, piecewise continuous function with positive limits H± as x → ±∞. This equation, in the frequency domain, describes the wave propagation in a nonhomogeneous medium, where Q(x) is the restoring force and 1/H(x) is the variable wave speed changing abruptly at various interfaces. A related Riemann–Hilbert problem is formulated, and the associated singular integral equation is obtained and proved to be uniquely solvable. The solution of this integral equation leads to the recovery of H(x) in terms of the scattering data consisting of Q(x), a reflection coefficient, either of H±, and the bound state energies and norming constants. Some explicitly solved examples are provided. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2972-2984 
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    Notes: Integrable systems in 1+1 dimensions arise from the KP hierarchy as symmetry reductions involving square eigenfunctions. Exploiting the residual gauge freedom in these constraints new integrable systems are derived. They include generalizations of the hierarchy of the Kundu–Eckhaus equation and higher-order extensions of the Yajima–Oikawa and Melnikov hierarchies. Constrained modified KP flows yield further integrable equations such as the hierarchies of the derivative NLS equation, the Gerdjikov–Ivanov equation, and the Chen–Lee–Liu equation. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3174-3182 
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    Notes: Vector fields on a disk satisfying two types of boundary conditions are studied. These boundary conditions are selected by BRST-invariance in electrodynamics. They also appear in the de Rham complex. The construction of the harmonic expansion is presented. The eigenfunctions of the vector Laplace operator are expressed in terms of fields satisfying pure Dirichlet or Robin boundary conditions. For the case of four-dimensional disk several first coefficients of the heat kernel expansion are computed. An error in the analytical expression by Branson and Gilkey is corrected. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2985-2987 
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    Notes: It is shown that the conformal time parameter η for closed dust-filled Kantowski–Sachs models [J. Math. Phys. 7, 443 (1966)] cannot be taken as growing to infinity in subsequent cycles of evolution regardless of the values of the integration constants. This forces the energy density to remain constant in each subsequent cycle rather than decrease, which contradicts the original Kantowski and Sachs statement. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2988-3003 
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    Notes: All the solutions of a three-dimensional dynamical system describing the static and spherically symmetric solutions for a nonlinear scalar field of the Born–Infeld type are studied qualitatively. It is shown that a horizon exists for a large class of solutions in which the scalar field is finite. However, this horizon is singular. In another class of solutions, naked singularities with an everywhere well-behaved scalar field have been found. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3012-3022 
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    Notes: The Dirac formulation of massless spin-(3/2) fields is discussed. The existence and uniqueness for the solutions of the spin-(3/2) field equations in Dirac form is proven. It is shown that the system of equations can be split into a symmetric hyperbolic system of evolution equations and a set of constraint equations. The constraints are shown to propagate on a curved manifold if and only if it is an Einstein space. The gauge freedom present in the spin-(3/2) system is discussed and it is shown that the complete system "solutions modulo gauge'' has a well posed Cauchy problem if and only if the Einstein equations hold. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3085-3093 
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    Notes: The Itzykson–Zuber (IZ) integral is computed for the superunitary group U(m||n). As a consequence, the nonzero correlations of superunitary matrices can be found. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3074-3084 
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    Notes: An algebraic classification of second order symmetric tensors in five-dimensional Kaluza–Klein-type Lorentzian spaces is presented by using Jordan matrices. It is shown that the possible Segre types are [1,1111], [2111], [311], [zz¯111], and the degeneracies thereof. A set of canonical forms for each Segre type is found. The possible continuous groups of symmetry for each canonical form are also studied. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3054-3062 
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    Notes: The field equations governing Bianchi type I space–times having elastic media as sources are constructed. Such equations turn out to be a system of three ordinary differential equations for the three independent components of the gravitational field. Plane symmetric and Robertson–Walker space–times are also discussed, and some examples of solutions are given. In the Robertson–Walker case, it turns out that it is possible to "tune'' the elastic constitutive equations in such a way that any "required'' behavior of the scale factor may be obtained. This feature closely resembles the scalar-field dominated case. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 3126-3133 
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    Notes: A large class of braid group representations are proven unitary which means a Hermitian bilinear form left invariant by the representation under consideration exists. This generalizes and improves known results on the Burau and Gassner representations. The elementary methods are naturally suggested by the study of monodromy invariant Hermitian forms. Applications to conformal quantum field theory in two dimensions are mentioned. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2192-2236 
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    Notes: Localization techniques for functional integrals which have recently been used to perform calculations in and gain insight into the structure of certain topological field theories and low-dimensional gauge theories are reviewed. These are the functional integral counterparts of the Mathai–Quillen formalism, the Duistermaat–Heckman theorem, and the Weyl integral formula, respectively. In each case, the necessary mathematical background (Euler classes of vector bundles, equivariant cohomology, topology of Lie groups) is introduced, and the finite dimensional integration formulae described. Then some applications to path integrals are discussed and an overview of the relevant literature is given. The applications include supersymmetric quantum mechanics, cohomological field theories, phase space path integrals, and two-dimensional Yang–Mills theory. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1666-1672 
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    Notes: A path integral written in terms of the group theoretic coherent states by using the Kähler structure of the coherent state manifold with the particular emphasis on the boundary-fixing term derivation is considered herein. The path integral for a propagator of the system with Hamiltonian linear in the SU(2)/SU(1,1) generators is shown to be diagonalized by an appropriate motion in the phase space. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1681-1690 
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    Notes: The q-quantum mechanics of the one degree of freedom is studied. Among others the holomorphic representation of q-deformed Heisenberg–Weyl algebra and its realization by covariant Berezin symbols is described. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1776-1789 
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    Notes: Time domain wave-splitting of Maxwell's equations is applied to the inverse problem of determining the permittivity and conductivity in three dimensions (where the reflected field is produced by an impulse dipole, exterior to the scattering medium). The structure of the fundamental solution is analyzed, and the transport equation is used to derive a condition for the reconstruction. A numerical scheme to reconstruct the permittivity and conductivity simultaneously is given, using the tangential reflection fields due to a dipole with a fixed position and orientation. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1825-1833 
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    Notes: To obtain a thermal wave equation predicting finite phase velocity in the infinite-frequency limit Grad's 13-moment method and extended thermodynamics have added a term linear in the time derivative of the heat flux to Fourier's law. When nonlocal effects are added via a term linear in the heat flux Laplacian, the problem of nonhyperbolicity and infinite phase velocity recurs. One approach postulates an infinite hierarchy of coupled equations, each of which describes time evolution of a flux appearing in the preceding hierarchy equation. This is shown to disagree in the high-frequency limit with an evolution equation derived by projection operators from the Liouville equation, in which memory and nonlocal effects are represented by integrals over time and space. Nonlocal effects disappear in the infinite-frequency limit of the latter, but not of the former. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1834-1853 
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    Notes: A model for multichannel parallel relaxation is suggested based on the following assumptions: (a) an individual channel is characterized by a set of continuous state variables; the corresponding relaxation rate is a function of the state variables as well as of the time interval for which the channel is open; (b) the number of channels is a random variable described by a correlated point process defined in the space of state parameters of an individual channel. Analytical expressions for the generating functional of the overall relaxation rate and for the average survival function are derived in terms of the generating functional of the point process. The general formalism is applied to the problem of direct energy transfer from excited donors to acceptors in fractal systems with dynamic disorder. It is assumed that the number of acceptors obeys a Poissonian distribution law with a constant average density in a df-dimensional fractal structure embedded in a ds-dimensional Euclidean space (ds=1,2,3) and that an individual relaxation rate is an inverse power function of the distance between the acceptor and the donor molecules.The dynamic disorder is described in terms of three different functions: the rate ω(t) of opening of a channel at time t, the attenuation function cursive-phi(t) of the reactivity of an individual channel at time t, and the probability density ψ(t) of the time interval within which a channel is open. Several particular cases corresponding to different functions ω(t), cursive-phi(t), and ψ(t) are investigated. The static disorder corresponds to a survival function of the stretched exponential type exp[−(Ωt)β] with 1(approximately-greater-than)β(approximately-greater-than)0. For very strong dynamic disorder there is no attenuation of reactivity, the opening time is infinite and the survival function is given by a compressed exponential exp[−const.t1+β], 1(approximately-greater-than)β(approximately-greater-than)0. The other cases analyzed correspond to a slowly decreasing attenuation function and to an exponential distribution of the opening time, respectively; for them the efficiency of relaxation is between the ones corresponding to the two extreme cases of static and very strong dynamic disorder. The general conclusion is that the passage from static to the dynamic disorder results in an increase of the efficiency of the relaxation process. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2030-2052 
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    Notes: Coherent state operators (CSOs) are defined as operator valued functions on G=SL(n,C) being homogeneous with respect to right multiplication by lower triangular matrices. They act on a model space containing all holomorphic finite dimensional representations of G with multiplicity 1. CSOs provide an analytic tool for studying G invariant 2- and 3-point functions, which are written down in the case of SU3. The quantum group deformation of the construction gives rise to a noncommutative coset space. A "standard'' polynomial basis is introduced in this space (related to but not identical with the Lusztig canonical basis) that is appropriate for writing down Uq(sl3) invariant 2-point functions for representations of the type (λ,0) and (0,λ). General invariant 2-point functions are written down in a mixed Poincaré–Birkhoff–Witt type basis. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 2085-2112 
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    Notes: The constraints on the index set I and on the function q of the (I,q)-graded Lie algebras over K containing the Poincaré Lie algebra are studied. By using the single-grading model, particular choices for I and q consistent with the found constraints are determined for K=C. Gradings are then found for which I⊆I=Z2×(Z4N×Z4N)×Gre, with N∈N and Gre an Abelian group. These gradings provide a way for algebraic extensions of the Poincaré Lie algebra beyond the Z2-gradings of supersymmetry and supergravity. In these algebraic extensions, each other commuting space–time parameter can either commute or anticommute with the further parameters of the (I,q)-graded (super) manifold. Different field representations can have—with each other—generalized commutative behavior beyond commutativity and anticommutativity. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1029-1037 
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    Notes: Improved rigorous high-energy upper bounds are established on the absorptive parts of the elastic scattering amplitudes for the momentum-transfer-squared variable t positive and within the Lehmann–Martin ellipse. These bounds are used to set upper bounds on Regge trajectories and also to extend the region in the complex t plane where the amplitudes cannot have zeros. No assumption is made about the high-energy behavior of the total cross sections. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1741-1752 
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    Notes: In a recent article all classical tensor systems which admit Fermi quantization are characterized as those having unitary Lie–Poisson brackets. Examples include Euler's tensor equation for a rigid body and Dirac's equation in tensor form. In this article it is shown that the tensor form of the Dirac Lagrangian can be derived from a tetrad formulation of a Kaluza–Klein model, which unifies the Dirac and Einstein Lagrangians. In this formulation, the isometric modes of the tetrad propagate as fermions, whereas the self-adjoint modes propagate as gravitons. An analogy is made with the rigid and elastic modes of a deformable body, where the rigid modes are Fermi quantized and the elastic modes are Bose quantized. However, unlike a deformable body for which the Euclidean metric is positive definite, fermion and graviton modes are not generally separable, unless the gravitational fluctuations are limited by a certain bound. It is shown that this bound applies whenever bispinors are defined in a general relativistic framework. That is, the bound does not depend on whether bispinors or tensors are used to describe the fermion modes. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1790-1811 
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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, an infinite number of dynamical systems having such a closed orbit property are found on T*(R3−{0}) by applying a slightly modified Bertrand's method to a spherical symmetric Hamiltonian with two undetermined functions of the radius. Actually, for any positive rational number ν, there exists a Hamiltonian system with the closed orbit property just mentioned, which system will be called the ν-fold Kepler system. Each of the systems is completely integrable and further allows the explicit expression of trajectories. The bounded trajectories in the configuration space R3−{0} may have self-intersection points. Moreover, the ν-fold Kepler system is reducible to a two-degrees-of-freedom system, which is completely integrable and gives rise to flows on the two-torus for bounded motions. If ν is allowed to take irrational numbers, any flow is shown to be dense in the torus. In conclusion, on the analogy of the Kepler problem, the Runge–Lenz-like vector for the ν-fold Kepler system is touched upon. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1854-1867 
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    Notes: In this paper we use the Lie symmetry method for finding rational and transcendental symmetry transformations and invariants for the 3D Lotka–Volterra system. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1877-1881 
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    Notes: A one-to-one correspondence is presented which enables one to pass from colliding plane waves with parallel polarizations and electromagnetic field to nonparallel polarized colliding plane waves in vacuum and conversely. This correspondence is used to derive new solutions to Einstein's equations in the context of colliding plane waves. This generating technique has its antecedent in the Bonnor trans- formation for stationary axisymmetric solutions. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1912-1933 
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    Notes: The Clebsch–Gordan coefficients of SUq(2) are here calculated by an integration over the group manifold following the Woronowicz prescription. A representation is obtained that is different from the one derived from the q-group algebra. The equivalency of the two results implies a q-identity and establishes a relation between q-hypergeometric functions. In the limit q=1, our result gives a different expression for the Clebsch–Gordan coefficients of SU(2), and the q-identity relation reduces to an identity between binomial coefficients. The Woronowicz technique is extended to calculate the integral of the product of many irreducible representations. A summary of the main results has already been presented elsewhere. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1971-1990 
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    Notes: New exact solutions of Burgers's equation, which is the simplest evolution equation to embody nonlinearity and dissipation, are obtained. These solutions are obtained by extending the method for finding symmetry reductions due to Clarkson and Kruskal ["New similarity solutions of the Boussinesq equation,'' J. Math. Phys. 30, 2201–2213 (1989)]. The novel feature of this extended method is that one can seek reductions to a system of ordinary differential equations, rather than the usual single equation and this leads to a wider class of solutions. One is able to complete the calculations necessary for Burgers's equation in all but a single case (where it is necessary to integrate an Abel equation of the second kind). This indicates that the method is practicable. In contrast it is often the case that new methods are of limited use in practice. In particular, solutions in terms of a class of confluent-hypergeometric functions are computed. By comparison, solutions found by the original method due to Clarkson and Kruskal, and other reduction methods, are in terms of parabolic-cylinder functions or Airy functions, which are special cases of this class. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1038-1053 
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    Notes: The formula is obtained for the asymptotics of the splitting of the first two eigenvalues of the Schrödinger operator that stands for the discrete multidimensional φ4-model on tori. The behavior of the main term is investigated in the limit of the large number of particles. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1136-1145 
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    Notes: Some years ago, P. J. Price obtained an important (but not well recognized) bound on the structure factor in the ground state. A more general version is derived by means of sum rules, showing a limitation imposed on by the f sum rule. The condition for merging of the bound with the structure factor turns out to be the existence of a single branch in the excitation spectrum. Price's bound is tested in exactly solvable many-body models, most of which are models for Fermi particles, some not satisfying the f sum rule. This analysis sheds light on the structure factors of these models. Also, Price's bound is compared with other bounds obtained by convexity theory. Finally, by formulating it in terms of a moment, the existence of Price's bound in a wider class of models is established. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1217-1231 
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    Notes: The chemical potential and fluctuations in number of particles in a D-dimensional free Fermi gas at low temperatures are obtained by means of polylogarithms. This idea is extended to show that the density of any ideal gas, whether Fermi, Bose, or classical, can be expressed in polylogarithms. The densities of different statistics correspond to different domains of polylogarithms in such a way that there emerges a unifying picture. The density of the classical ideal gas represents a fixed point of polylogarithms. Inequalities for polylogarithms are used to provide a precise bound on errors in the fermion chemical potential at low temperatures. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1274-1283 
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    Notes: A coupled nonlinear Schrödinger–Poisson equation is considered which contains a time-dependent dissipation function as a specific model of dissipation effects in nonlinear quantum transport theory and other areas. The Wigner–Poisson equation associated with this system is derived. Using conservation and quasiconservation laws and certain growth assumptions for the nonlinearities and the dissipation function, global existence of solutions to the Cauchy problem of the time-dependent Schrödinger–Poisson system is shown both for small (attractive case) or arbitrary data (repulsive case). © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1324-1327 
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    Notes: The conservation of helicity in ideal barotropic fluids is discussed from a group theoretical point of view. A new symmetry group is introduced, i.e., the alpha group of translations. It is proven via the Noether theorem that this group generates helicity conservation. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1328-1346 
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    Notes: The principle of equivalence says that at any given space–time point, there exists a local coordinate system with respect to which the three-acceleration of a freely falling test body vanishes regardless of its three-velocity. In this article, a more intrinsic and geometric criterion for free fall motion is provided. The criterion is much simpler than a recently proposed criterion that is based on the Desargues property. For space–times of dimension greater than 2, the Desargues property is a theorem. It is shown that it suffices to require that a version of Pasch's axiom is satisfied; that is, two paths in a plane intersect up to corrections of order cursive-epsilon3, where cursive-epsilon is the scale parameter of a shrinking process. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 1413-1425 
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    Notes: A calculus for exact symplectic manifolds is presented. It consists of the familiar exterior calculus augmented by a set of operations, algebraic and differential, admitted naturally by the exact symplectic structure of the underlying space. The result is a high level calculus that is particularly well suited to deal with problems on this type of manifold. Natural differential operators admitted by an exact symplectic structure are identified. The results are also applied to the de Rham cohomology of this type of manifold. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 837-846 
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    Notes: In order to study the symplectic structures of the elementary relativistic free particles in general relativity, a nonvectorial associated fiber bundle is constructed over the space-time manifold. A foliation in the space-time is achieved which gives rise to the geodesics principle for massive particles and wave fronts for massless particles. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 648-663 
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    Notes: The symmetries associated with the closed bosonic string partition function are examined so that the integration region in Teichmuller space can be determined. The conditions on the period matrix defining the fundamental region can be translated to relations on the parameters of the uniformizing Schottky group. The growth of the lower bound for the regularized partition function is derived through integration over a subset of the fundamental region. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 714-724 
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    Notes: An asymptotic expansion of the Whittaker function Mα,β(x), for β→∞, with α and x fixed, is employed to obtain the asymptotic expansion of the Dirac–Coulomb radial Green's function Gκ(x2,x1,z) when the magnitude of the angular momentum quantum number κ is large. This result has application in numerical calculations of quantum electrodynamic effects in an external Coulomb field. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6596-6610 
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    Notes: Various semiclassical sum rules are obtained for matrix elements of smooth observables using semiclassical estimates of time evolved coherent states together with stationary phase theorems. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6583-6595 
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    Notes: In this paper, we study the Jaynes–Cummings model governed by the Milburn equation for quantum mechanics. We find the exact solution of the Milburn equation without diffusion approximation and apply this solution to studying nonclassical properties of Jaynes–Cummings model (JCM) in the full range of decoherence parameter γ. The influence of the decoherence on nonclassical properties of JCM for different ranges of γ is investigated in detail. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6970-6980 
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    Notes: It is shown that the only static asymptotically flat nonextrema black hole solution of the Einstein-conformally invariant scalar field equations having the scalar field bounded on the horizon is the Schwarzschild solution. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 7024-7042 
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    Notes: Discretizations of the Helmholtz, heat, and wave equations on uniform lattices are considered in various space–time dimensions. The symmetry properties of these finite-difference equations are determined and it is found that they retain the same Lie symmetry algebras as their continuum limits. Solutions with definite transformation properties are obtained; identities and formulas for these functions are then derived using the symmetry algebra. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6665-6672 
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    Notes: In a recent paper [J. Math. Phys. 35, 3333 (1994)] Good postulated new rules of quantization, one of the major features of which is that the quantum evolution of the wave function is always given by ordinary differential equations. In this paper we analyze the proposal in some detail and discuss its viability and its relationship with the standard quantum theory. As a byproduct, a simple derivation of the "mass spectrum'' for the Klein–Gordon field is presented, but it is also shown that there is a complete additional spectrum of negative "masses.'' Finally, two major reasons are presented against the viability of this alternative proposal: (a) It does not lead to the correct energy spectrum for the hydrogen atom. (b) For field models, the standard quantum theory cannot be recovered from this alternative description. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 7109-7127 
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    Notes: We construct the general solutions of the system of nonlinear differential equations (D'Alembertian)nu=0, uμuμ=0 in the four- and five-dimensional complex pseudo-Euclidean spaces. The results obtained are used to reduce the multidimensional nonlinear d'Alembert equation (D'Alembertian)4u=F(u) to ordinary differential equations and to construct its new exact solutions. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6232-6254 
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    Notes: The noncommutative approach of the standard model produces a relation between the top and the Higgs masses. We show that, for a given top mass, the Higgs mass is constrained to lie in an interval. The length of this interval is of the order of m2τ/mt. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6299-6339 
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    Notes: We show how it is possible to formulate Euclidean two-dimensional quantum gravity as the scaling limit of an ordinary statistical system by means of dynamical triangulations, which can be viewed as a discretization in the space of equivalence classes of metrics. Scaling relations exist and the critical exponents have simple geometric interpretations. Hartle–Hawking wave functionals as well as reparametrization invariant correlation functions which depend on the geodesic distance can be calculated. The discretized approach makes sense even in higher-dimensional space–time. Although analytic solutions are still missing in the higher-dimensional case, numerical studies reveal an interesting structure and allow the identification of a fixed point where we can hope to define a genuine non-perturbative theory of four-dimensional quantum gravity. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6746-6757 
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    Notes: For quantum lattice systems, it is proven that anomalously scaled fluctuations have a natural Lie algebra structure. The harmonic lattice in the ground state is given as an illustration of the general theorem. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6510-6528 
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    Notes: In this paper we review the status of several solutions to all the constraints of quantum gravity that have been proposed in terms of loops and extended loops, based on knot polynomials. We discuss pitfalls of several of the results, and in particular the issues of covariance and regularization of the constraints in terms of extended loops. We also propose a formalism for "thickened out loops,'' which does not face the covariance problems of extended loops and may allow to regularize expressions in a consistent manner. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 5246-5261 
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    Notes: The relation between the unitary group SU(n) and the symmetric group Sn is treated using the induced characters of Sn. By means of this approach the L-S coupling for four electrons is solved. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 5305-5309 
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    Notes: We shall be concerned with the explicit construction of the kernel of transformation operator used in the scattering theory associated with the Gelfand–Levitan–Marchenko equations. The kernel of the transmutation is well known to play an important role in the inverse scattering theory, and nonlinear integrable systems such as KdV equations. Our method shall use operational calculus. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 5355-5391 
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    Notes: The paper studies spectral theory of Schrödinger operators H=(h-dash-bar)2Δ+V on the sphere from the standpoint of integrability and separation. Our goal is to uncover the fine structure of spec H, i.e., asymptotics of eigenvalues and spectral clusters, determine their relation to the underlying geometry and classical dynamics and apply this data to the inverse spectral problem on the sphere. The prototype model is the celebrated Neumann Hamiltonian p2+V with quadratic potential V on Sn. We show that the quantum Neumann Hamiltonian (Schrödinger operator H) remains an integrable and find an explicit set of commuting integrals. We also exhibit large classes of separable potentials {V} based on ellipsoidal coordinates on Sn. Several approaches to spectral theory of such Hamiltonians are outlined. The semiclassical problem (small (h-dash-bar)) involves the EKB(M)-quantization of the classical Neumann flow along with its invariant tori, Maslov indices, etc., all made explicit via separation of variables. Another approach exploits Stäckel–Robertson separation of the quantum Hamiltonian and reduction to certain ODE problems: the Hill's and the generalized Lamè equations. The detailed analysis is carried out for S2, where the ODE becomes the perturbed classical Lamè equation and the Schrödinger eigenvalues are expressed through the Lamè eigendata. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 5453-5464 
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    Notes: Delta-function potentials in two- and three-dimensional quantum mechanics are analyzed by incorporating the self-adjoint extension method within the Green's-function method. The energy-dependent Green's functions for free particle plus delta-function potential systems are explicitly determined and similar calculations are carried out for the spin-1/2 Aharonov–Bohm system. It is found that the time-dependent propagator for the latter cannot be evaluated analytically except for a particular value of the self-adjoint extension parameter. It corresponds to the case in which the singular solution alone contributes for the partial wave defined by ||m+α||〈1. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 5522-5539 
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    Notes: We present an alternative approach to the usual treatments of singular Lagrangians. It is based on a Hamiltonian regularization scheme inspired on the coisotropic embedding of presymplectic systems. A Lagrangian regularization of a singular Lagrangian is a regular Lagrangian defined on an extended velocity phase space that reproduces the original theory when restricted to the initial configuration space. A Lagrangian regularization does not always exists, but a family of singular Lagrangians is studied for which such a regularization can be described explicitly. These regularizations turn out to be essentially unique and provide an alternative setting to quantize the corresponding physical systems. These ideas can be applied both in classical mechanics and field theories. Several examples are discussed in detail. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6991-7008 
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    Notes: We present derivations of su(2) and su(3)&supuline;so(3) Clebsch–Gordan coefficients in the limit of large quantum numbers. For su(3), we derive simple analytic expressions for the asymptotic coefficients needed for the decomposition of the product (λ1,0)⊗(λ2,0), in the limit of λ1→∞, in an so(3) basis. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 7073-7080 
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    Notes: The boson–fermion correspondence is given for the case of the Hall–Littlewood polynomials, which is a t-deformation of the correspondence realizing the Schur polynomials. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 7103-7108 
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    Notes: We propose a simple and concise method to construct the inhomogeneous quantum group IGLq(n) and its universal enveloping algebra Uq(igl(n)). Our technique is based on embedding an n-dimensional quantum space in an n+1-dimensional one as the set xn+1=1. This is possible only if one considers the multiparametric quantum space whose parameters are fixed in a specific way. The quantum group IGLq(n) is then the subset of GLq(n+1), which leaves the xn+1=1 subset invariant. For the deformed universal enveloping algebra Uq(igl(n)), we will show that it can also be embedded in Uq(gl(n+1)), provided one uses the multiparametric deformation of U(gl(n+1)) with a specific choice of its parameters. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 7128-7128 
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    Journal of Mathematical Physics 36 (1995), S. 6130-6136 
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    Notes: A positive, diffeomorphism-invariant generalized measure on the space of metrics of a two-dimensional smooth manifold is constructed. We use the term generalized measure analogously with the generalized measures of Ashtekar and Lewandowski and of Baez. A family of actions is presented which, when integrated against this measure gives the two-dimensional axiomatic topological quantum field theories, or TQFTs, in terms of which Durhuus and Jonsson decompose every two-dimensional unitary TQFT as a direct sum. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6161-6179 
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    Notes: The physics of quantum gravity is discussed within the framework of topological quantum field theory. Some of the principles are illustrated with examples taken from theories in which space–time is three dimensional. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6255-6275 
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    Notes: We studied the Riemannian aspect and the Hilbert–Einstein gravitational action of the noncommutative geometry underlying the Connes–Lott construction of the action functional of the standard model. This geometry involves a two-sheeted, Euclidian space–time. We show that if we require the space of forms to be locally isotropic and the Higgs scalar to be dynamical, then the Riemannian metrics on the two sheets of Euclidian space–time must be identical. We also show that the distance function between the two sheets is determined by a single, real scalar field whose vacuum expectation value (VEV) sets the weak scale. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6288-6298 
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    Notes: We show that the partition function of the Ponzano–Regge quantum gravity model can be written as a sum over surfaces in a (2+1)-dimensional space–time. We suggest a geometrical meaning, in terms of surfaces, for the (regulated) divergences that appear in the partition function. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 6004-6027 
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    Notes: The closure conditions for a quasi-exactly solvable operator is the requirement that a second-order Lie algebraic differential operator be equivalent, up to scale-change, to a Schrödinger operator on curved space. The present work begins with an invariant characterization of the closure conditions, and after a series of steps gives a reformulation of the closure conditions in terms of finite-dimensional representations of the underlying Lie algebra. These techniques are used to give a complete solution to the closure condition for two different planar realizations of @Fsl(2). Along the way two theorems about homogeneous solutions to the closure conditions are introduced and proved. Also introduced is the class of "Abelian'' solutions to the closure conditions. Such solutions appear on flat spaces and give rise to a Schrödinger operator with zero potential. The concluding remarks highlight remaining questions and give references to research that address said questions. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 133-141 
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    Notes: The usual Bell-type inequalities involve correlations between observables. Inequalities of the Bell-type are presented which involve correlations between the probabilities associated with states and which can be used as a test for hidden variables in quantum mechanics independent of the Bell inequalities. The inequalities are universal in the sense that they are valid for all separable metric state spaces, as opposed to the usual Bell inequalities whose specific form is a function of the state space of the candidate classical model. The inequalities are harder to prove than the usual Bell-type inequalities because no essential restrictions on the state space are made. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 142-176 
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    Notes: The present article is devoted to the explanation of the irreversible behavior of quantum systems as a limiting case (in a sense to be made precise) of usual quantum dynamics. One starts with a system, whose Hamiltonian has a continuous spectrum, interacting with a reservoir and studies the limits of quantities related to the whole compound system. A macroscopic equation is obtained for the limit of the compound system, which is a quantum stochastic differential equation of Poisson type on some Hilbert module (no longer a space) and whose coefficients are uniquely determined by the one-particle Hamiltonian of the original system and whose driving noises are the creation, annihilation, and number (or gauge) processes living on the Fock module over this module. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 426-434 
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    Notes: A formula is developed for the number of cusps in certain congruence subgroups equivalent to a given cusp in certain larger subgroups. In particular, necessary and sufficient conditions for this number to be independent of the particular cusp are given. Applications to statistical mechanics are surveyed. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 414-425 
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    Notes: The scattering processes on multiloop infinite graphs with one and the same valence p+1 of all vertices are studied herein. These graphs are discrete spaces of a constant negative curvature since they can be interpreted as quotients of the p-adic hyperbolic plane over free acting discrete subgroups of the projective group PGL(2,Qp). They are, in fact, identical to p-adic multiloop surfaces. Releasing from a graph its subgraph containing all loops, which is called the reduced graph Tred, we can get L functions corresponding to these finite closed graphs. For an infinite graph, the notion of spherical functions is introduced. These are the eigenfunctions of a discrete Laplace operator acting on the graph. s-wave scattering processes are considered and in this way they define the scattering amplitudes ci. In the discrete case, their number coincides with ||Tred||—the number of vertices of the reduced graph. Taking the product over all ci, we obtain the determinant of the scattering matrix which turns out to be presented as a ratio of two L functions: C∼L(α+)/L(α−). Here the L function is the Ihara–Selberg function depending only on the form of Tred. All the dependence on the initial value of p remains in arguments α± = t/2p ±(square root of)t2/4p2−1/p, t being the eigenvalue of the Laplacian. The Hashimoto–Bass theorem is used for expressing L function L(u) of any finite graph via the determinant of a local operator Δ(u) acting on this graph. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 5598-5626 
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    Notes: We base a treatment of the dissipative, multi-mode version of Dicke laser model on the theory of completely positive dynamical semigroups and quantum Markov processes. This leads to new results at both the mathematical and physical levels. On the physical side, it provides a generalization of the Hepp–Lieb model that admits both chaotic and polychromatic laser radiation. On the mathematical side, it extends the theory of dynamical semigroups to a regime where the generators are perturbed by unbounded derivations. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 574-595 
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    Notes: For ||q|| ≠ 1, the integral definition of the gamma function in terms of the exponential function is generalized to a definition of a q-gamma function, or a family of q-gamma functions, in the standard and symmetric cases, using the q-exponential functions and their asymptotic behavior as z → ∞ on geometric sequences {zn(ζ)= qnζ}n∈Z with common ratio q. The properties of the q-gamma functions (poles, zeros, product expansions) are also determined. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 596-604 
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    Notes: It has been conjectured by Rovelli that there is a correspondence between the space of link classes of a Riemannian 3-manifold and the space of 3-geometries (on the same manifold). An exact statement of his conjecture will be established and then verified for the case when the 3-manifold is compact, orientable, and closed. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 307-320 
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    Notes: By using the multiple scale method with the simultaneous introduction of multiple times, we study the propagation of long surface-waves in a shallow inviscid fluid. As a consequence of the requirements of scale invariance and absence of secular terms in each order of the perturbative expansion, we show that the Korteweg–de Vries hierarchy equations do play a role in the description of such waves. Finally, we show that this procedure of eliminating secularities is closely related to the renormalization technique introduced by Kodama and Taniuti. © 1995 American Institute of Physics.
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    Journal of Mathematical Physics 36 (1995), S. 4248-4262 
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    Notes: We present cylindrically symmetric solutions of the Einstein–Maxwell electrovacuum equations, considering a δ=2 Tomimatsu–Sato solution, describing a cylindrical symmetric space–time. The solutions exhibit an angle deficit, are asymptotically flat, smooth everywhere without curvature singularities and for various values of the parameters may be interpreted as open cosmic strings with gravity and electromagnetism coupled in a relativistic manner. © 1995 American Institute of Physics.
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