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  • Articles  (30,867)
  • American Chemical Society  (28,585)
  • American Institute of Physics (AIP)  (2,282)
  • 1990-1994  (22,720)
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  • Articles  (30,867)
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  • 1
    Electronic Resource
    Electronic Resource
    Compilation of two-point and four-point graphs in field theory in noninteger dimensions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3866-3880 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two-point and four-point graphs appearing in a three-loop approximation in the field theory renormalization group scheme are calculated in general dimensions. Combining Feynman parameterization and direct integration loop integrals are represented in the form of the expressions, depending on the space dimension d as a parameter. The expressions obtained enables one to consider renormalization group functions directly at noninteger d.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530452
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  • 2
    Electronic Resource
    Electronic Resource
    A connection between quantum dynamics and approximation of Markov diffusions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4505-4516 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is observed that the existence of an attracting set in the class of solutions to the stochastic Lagrangian variational principle leads to a natural problem of convergence of diffusions in the Carlen class. It is then shown how dynamical properties enable one to prove some convergence results in the two-dimensional Gaussian case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530800
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  • 3
    Electronic Resource
    Electronic Resource
    Invariants of Lagrangians and their classifications (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4568-4593 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A complete classification of natural transformations of finite order of Lagrangians into energies over n-dimensional manifolds, where n≥2, is given herein. The classification of natural transformations of finite order of vector fields and Lagrangians into energies and constants of the motion is also obtained for n≥3. By using these results, a classification of Lagrangians into Poincaré–Cartan one-forms and Legendre transformations is obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530804
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  • 4
    Electronic Resource
    Electronic Resource
    Dirac's equation on the quantum net (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3936-3958 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quantum net model differs from other quantizations and discretizations of space-time in being founded upon quantum-logical principles. Fermions are envisaged as arising from defects in the net. Such defects are investigated and it is found that the attempt to vary them infinitesimally gives rise to a reticular version of the Dirac operator, which now has a simple interpretation in terms of quantum mechanical infinitesimal parallel transport. The analog of the usual massless Weyl equations are found to hold on the net, and algebraic solutions are deduced by exploiting its inherent logical structure. A correspondence principle then applies to show that these equations and their solutions correspond precisely to the ones expected in the continuum. (In the course of this, new basis-independent expressions for the complex Minkowski-space Dirac matrices are found.) Finally, an attempt is made to introduce gravity into the net, and the flat space Dirac Lagrangian is modified accordingly.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530835
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  • 5
    Electronic Resource
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    The exact solutions of the equation for a composite particle in the external electromagnetic fields (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4497-4504 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Exact analytic solutions are provided for a class of equations describing a composite scalar particle in constant electric and magnetic fields, and also in plane electromagnetic fields. The external fields are taken in both classical and quantum cases. A detailed physical analysis of the results is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530799
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  • 6
    Electronic Resource
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    Knowledge about noncommuting quantum observables by means of Einstein–Podolsky–Rosen correlations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4534-4546 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is well known that quantum physics forbids the simultaneous measurement of two noncommuting projection operators. However, sometimes there exists a third projection (mirror projection) which may be measured together with the second one and whose outcomes are completely correlated, in the Einstein–Podolsky–Rosen sense, with the outcomes of the first projection. In this article the states for which such a mirror projection exists are characterized and a procedure for constructing the mirror is given. In particular, it is shown that for two noncommuting projections there are always states for which the mirror projection exists, but also states for which it does not exist.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530802
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  • 7
    Electronic Resource
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    Existence theorems for 90° vortex–vortex scattering (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4651-4660 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A Cauchy problem is formulated with data that describe the scattering of two vortices in a superconductor, and the following is proven: First, a unique global finite-energy solution exists. Second, the symmetry of the solution rules out all cases other than 0°, 90°, or 180° scattering. Third, a local analytic solution exists near the origin. The leading terms of this solution show that, of the three cases, 90° scattering is realized.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530806
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  • 8
    Electronic Resource
    Electronic Resource
    A Bäcklund transformation and nonlinear superposition formula of a modified Korteweg–de Vries-type bilinear equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4739-4745 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A modified Korteweg–de Vries (mKdV)-type bilinear equation that has been shown to pass the three-soliton solution and the Painlevé tests [see, J. Math. Phys. 2094, 28 (1987); 2572, 31 (1990)] is considered herein. In this article, a Bäcklund transformation and a nonlinear superposition formula are proven rigorously. As an application of the obtained results, N-soliton solutions are obtained. Therefore, the integrability of this mKdV-type bilinear equation is confirmed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530811
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  • 9
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    The potential constraints of the KP system and the corresponding Hamiltonian equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4725-4738 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper all the potential constraints (with or without first-order partial derivatives) of the KP system, from which the associated linear problem can be restricted into a (1+1)-dimensional Hamiltonian equation, are obtained by using the sufficient and necessary condition for a nonlinear equation to be a Hamiltonian system. Some well-known integrable systems, such as (1+1)-dimensional AKNS system, generalized NS system, and several new Hamiltonian equations, are deduced as particular examples.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530810
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  • 10
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    Soliton solutions and gauge equivalence for the quadratic bundle (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4799-4808 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A more simple form than the one given by Vaklev [J. Math. Phys. 33, 4111 (1992)] for the soliton solutions related to the quadratic bundle [E. A. Kuznetzov and A. V. Mikhailov, Teor. Mat. Fiz. 30, 303 (1977); D. J. Kaup and A. C. Newell, J. Math. Phys. 19, 798 (1978); V. S. Gerdjikov, M. I. Ivanov, and P. P. Kulish, Teor. Mat. Fiz. 44, 342 (1980); V. S. Gerdjikov and M. I. Ivanov, Bulg. J. Phys. 10, 13 (1983); 10, 2, 129 (1983)] is obtained. The corresponding solutions for the gauge equivalent case are obtained as well. Among them one can find the N-soliton solutions for the derivative nonlinear Schrödinger equation, their gauge equivalents, etc. The method used in the article allows one to express some integrals by means of appropriate determinants and thus the result is obtained without integration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530815
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  • 11
    Electronic Resource
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    Total mass-momentum of arbitrary initial-data sets in general relativity (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4157-4177 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For an asymptotically flat initial-data set in general relativity, the total mass-momentum may be interpreted as a Hermitian quadratic form on the complex, two-dimensional vector space of "asymptotic spinors.'' A generalization to an arbitrary initial-data set is obtained. The mass-momentum is retained as a Hermitian quadratic form, but the space of "asymptotic spinors'' on which it is a function is modified. Indeed, the dimension of this space may range from zero to infinity, depending on the initial data. There is given a variety of examples and general properties of this generalized mass-momentum.
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    URL: http://dx.doi.org/10.1063/1.530880
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  • 12
    Electronic Resource
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    Spectral functions and zeta functions in hyperbolic spaces (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4217-4246 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The spectral function (also known as the Plancherel measure), which gives the spectral distribution of the eigenvalues of the Laplace–Beltrami operator, is calculated for a field of arbitrary integer spin (i.e., for a symmetric traceless and divergence-free tensor field) on the N-dimensional real hyperbolic space (HN). In odd dimensions the spectral function μ(λ) is analytic in the complex λ plane, while in even dimensions it is a meromorphic function with simple poles on the imaginary axis, as in the scalar case. For N even a simple relation between the residues of μ(λ) at these poles and the (discrete) degeneracies of the Laplacian on the N sphere (SN) is established. A similar relation between μ(λ) at discrete imaginary values of λ and the degeneracies on SN is found to hold for N odd. These relations are generalizations of known results for the scalar field. The zeta functions for fields of integer spin on HN are written down. Then a relation between the integer-spin zeta functions on HN and SN is obtained. Applications of the zeta functions presented here to quantum field theory of integer spin in anti-de Sitter space–time are pointed out.
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    URL: http://dx.doi.org/10.1063/1.530850
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  • 13
    Electronic Resource
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    The q-gamma, q-beta functions, and q-multiplication formula (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4268-4276 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this article the q-deformed gamma function and q-deformed beta function are discussed in detail. Three definitions for the q-gamma function are obtained and the q-deformed duplication and multiplication formulas are proven. The q-beta function is defined and its useful properties are derived.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530852
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  • 14
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    Topological entropy for appropriately approximated C*-algebrasa) (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4303-4333 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: "Classical'' topological entropy is one of the main numerical invariants in topological dynamics on compact spaces. Here, the author's recent development of a noncommutative generalization of topological entropy, in the natural setting of general C*-algebras as the noncommutative counterpart of continuous function algebras on compact spaces, is presented in a slightly modified and improved form. This includes both a survey of earlier results with some important corrections, and also new general results in response to (and inspired by) a more recent counterproposal for a noncommutative topological entropy by Thomsen. Finally, some partially new examples for the calculation of the defined topological entropy are shown. The rather self-evident physical interpretation in the framework of (operator-algebraic) quantum statistical mechanics and of "chaotic'' quantum dynamical systems is briefly touched upon.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530855
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  • 15
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    Adjoint boson realization of SU(N) and a family of structural zeros of 6j coefficients (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4383-4390 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For the fundamental boson realization of SU(N) in its principal SO(3) basis, the generators of SU(N) are SO(3) tensor operators constructed out of one single type of boson, namely a boson with SO(3) multiplet label (N−1)/2. Here, the adjoint boson realization of SU(N) is given: this time the SO(3) tensor operators are constructed by means of N−1 types of bosons [those with SO(3) labels 1,2,..., N−1]. The validity of this realization depends upon a new identity between 6j coefficients. From this realization, or equivalently from this new identity, one can deduce the existence of a family of structural zeros of 6j coefficients.
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    URL: http://dx.doi.org/10.1063/1.530897
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  • 16
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    Nonstandard scalar quantum fields (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3817-3844 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This article presents a theory of scalar quantum fields based on nonstandard analysis. Free scalar momentum fields and free Klein–Gordon fields are treated first. It is shown that the nonrigorous formalism of the standard theory can be replaced by a mathematically rigorous nonstandard theory. The second quantized energy–momentum operators are derived and the free quantum fields are diagonalized. Interacting scalar fields are considered and a nonstandard scattering operator is derived. A nonstandard counterpart to Wick's theorem is developed and the φ4 interaction is briefly discussed.
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    URL: http://dx.doi.org/10.1063/1.530450
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  • 17
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    Precise exponential estimates in adiabatic theory (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3889-3915 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: General adiabatic evolutions associated to Hamiltonians, which admit a holomorphic extension with respect to the time variable in a complex strip, and whose spectrum satisfies a gap condition are studied. An explicit rate of exponential decay is given, which is related to simple geometric quantities associated to the spectrum of the Hamiltonian, for the transition probability between the two parts of the spectrum when the evolution is taken from −∞ to +∞.
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    URL: http://dx.doi.org/10.1063/1.530832
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  • 18
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    Phase space structure of non-Abelian Chern–Simmons particles (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3959-3968 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The classical phase space structure of N SU(n+1) non-Abelian Chern-Simons (NACS) particles is investigated by first constructing the product space of associated SU(n+1) bundle with CPn as the fiber. The Poisson bracket is calculated using the symplectic structure on the associated bundle and it is found that the minimal substitution in the presence of external gauge fields is equivalent to the modification of symplectic structure by the addition of field strength two form. Then, a direct product of the associated bundle is taken by the space of all connections and a specific connection is chosen by the condition of vanishing momentum map corresponding to the gauge transformation, thus recovering the quantum mechanical model of NACS particles in Lee and Oh [Phys. Rev. Lett. 72, 1141 (1994)].
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    URL: http://dx.doi.org/10.1063/1.530896
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  • 19
    Electronic Resource
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    Isotropic classical spin chains showing nearest neighbor correlated cationic distributions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3998-4004 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A model is proposed for calculating the magnetic susceptibility of isotropic classical spin chains showing nearest neighbor correlated cationic distributions. It allows one to obtain a general closed-form expression: This expression formally looks like previous ones obtained in the case of random chains for which the neighboring cationic species are not correlated; but here the previous intervening scalar parameters are replaced by vectorial and matricial expressions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530838
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  • 20
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    Lattice solitons directly by the bilinear method (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4057-4066 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Recently a doubly periodic solution of the Kadomtsev–Petviashvili equation was deduced by summing over component solitons. The same solution was derived directly by the Hirota bilinear method. This alternate route enables one to obtain a new solution. Such a mechanism can also be applied to wavepacket dynamics, e.g., the Davey–Stewartson equation.
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    URL: http://dx.doi.org/10.1063/1.530842
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  • 21
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    Gravitational mass anomaly (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4178-4183 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The mass of gravitational sources differs by a factor of 2 when computed by the Komar superpotential and when computed in the gravitational weak field limit. The difference has been recognized for some time since both the linearized theory and the Einstein pseudotensor yield the same value, different by a factor of 2 from the Komar mass. The great advantage of the Komar superpotential over other methods is its tensorial formulation, however it fails to produce a Noether quantity. A different tensorial method is suggested that is free of the mass anomaly, namely, the zero and first Taub numbers [Phys. Rev. D 47, 474 (1993)] which are indeed Noether quantities. The zeroth Taub number is obtained from the Penrose–Goldberg superpotential [Phys. Rev. D 41, 410 (1990)].
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    URL: http://dx.doi.org/10.1063/1.530847
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  • 22
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    Maximum entropy algorithm for spectral estimation problem with aipriori information (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4372-4382 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The power density estimation problem with a priori information about spectrum is considered. The problem is reduced to a power density estimation problem with spectral gaps. The solution of the problem is studied in the context of the trigonometric moment problem with gaps. The necessary and sufficient conditions are established for the existence of solution and all solutions are described in indeterminate cases. A new definition of the entropy functional is given. The effective algorithm to construct maximum entropy solution is proposed. A number of explicit illustrations are presented.
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    URL: http://dx.doi.org/10.1063/1.530858
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  • 23
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    A simple difference realization of the Heisenberg q-algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3253-3260 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A realization of the Heisenberg q-algebra whose generators are first-order difference operators on the full real line is discussed herein. The eigenfunctions of the corresponding q-oscillator Hamiltonian are given explicitly in terms of the q−1-Hermite polynomials. The nonuniqueness of the measure for these q-oscillator states is also studied.
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    URL: http://dx.doi.org/10.1063/1.530464
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  • 24
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    On integrable models related to the osp(1,2) Gaudin algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3261-3272 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The osp(1,2) Gaudin algebra is defined and integrable models described by it are considered. The models include the osp(1,2) Gaudin magnet and the Dicke model related to it. Detailed discussion of the simplest cases of these models is presented. The effect of the presence of fermions on the separation of variables is indicated.
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    URL: http://dx.doi.org/10.1063/1.530465
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  • 25
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    An involutive system and integrable C. Neumann system associated with the modified Korteweg–de Vries hierarchy (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2978-2982 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this article, a system of finite-dimensional involutive functions is presented and proven to be integrable in the Liouville sense. By using the nonlinearization method, the C. Neumann system associated with the modified Korteweg–de Vries (mKdV) hierarchy is obtained. Thus, the C. Neumann system is shown to be completely integrable via a gauge transformation between it and an integrable Hamiltonian system. Finally, the solution of a stationary mKdV equation and the involutive solutions of the mKdV hierarchy are secured. As two examples, the involutive solutions are given for the mKdV equation: vt+1/4vxxx−3/2v2vx=0 and the 5th mKdV equation vt−1/16vxxxxx+5/8v2vxxx +5/2vvxvxx +5/8v3x−3/40v4vx=0.
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    URL: http://dx.doi.org/10.1063/1.530497
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  • 26
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    Note on a solution of the algebraically special perturbation of the Schwarzschild black hole (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3025-3028 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An algebraically special solution of the Regge–Wheeler–Zerilli equation that has not been noticed is examined. This solution is proved to be related to Chandrasekhar's solution but has a simpler analytical expression.
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    URL: http://dx.doi.org/10.1063/1.530501
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  • 27
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    Addendum to "The pseudodifferential operator square root of the Klein–Gordon equation'' [J. Math. Phys. 34, 3918 (1993)] (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3769-3769 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
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    URL: http://dx.doi.org/10.1063/1.530445
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  • 28
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    Fluctuations of a rotating impulsive wave (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3043-3050 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The vacuum fluctuations for an impulsive spherical gravitational wave due to the snapping of a "rotating'' cosmic string are calculated herein. This is complementary to the previous calculation due to a snapping string, which had the null result. Although the mathematical expressions are different at the intermediate steps, the same null result is found.
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    URL: http://dx.doi.org/10.1063/1.530503
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    Vector-coherent-state representations of so(5) in an so(3) basis (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3163-3177 
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    Notes: Vector coherent state theory is used to give an algorithm for constructing the so(5) irreps of type [N,0] and [N,N] in the physical so(3) basis. The construction is remarkably simple and permits the matrices of the so(5) operators, for irreps of low-dimension and/or small multiplicities, to be computed by hand. The construction is applied to the [2,0] and [2,2] irreps to illustrate the process.
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    An algorithm to calculate the invariants of any Lie algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3146-3162 
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    Notes: An analytical method to calculate invariants is developed, based on the theory of complete systems of simultaneous linear first order partial differential equations. The application of this algorithm to the general case, in which the invariants are not polynomials is included. For the case of Lie algebras with one invariant the procedure of finding the invariant can be computerized. As an example of this procedure, the algorithm is applied in the calculation of the invariants of the group SA(n,R). The explicit construction of its invariants for n=2, 3, 4 is given. A theorem determining the order of a polynomial invariant of a Lie group is proven allowing us to show that the invariant of SA(n,R) is a homogeneous polynomial of order 1/2n(n+1) in the generators. From this fact an immediate consequence is that the order in the generators of translations is n. The method is also applied in the calculation of invariants of the dimension six solvable Lie algebras, and dimension seven nilpotent.
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    Generalized supersymmetric quantum mechanics on Riemann surfaces with meromorphic superpotentials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2074-2082 
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    Notes: The structure of generalized supersymmetry with mutually commuting involutions for the meromorphic supersymmetric quantum mechanics on the compact Riemann surface is introduced. For this purpose a Riemann surface is considered as a self-conjugate complex manifold. On this basis the Witten index for the new involution is calculated.
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    Supersymmetric quantum mechanics and the Korteweg–de Vries hierarchy (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2142-2156 
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    Notes: The connection between supersymmetric quantum mechanics and the Korteweg–de Vries (KdV) equation is discussed, with particular emphasis on the KdV conservation laws. It is shown that supersymmetric quantum mechanics aids in the derivation of the conservation laws, and gives some insight into the Miura transformation that converts the KdV equation into the modified KdV equation. The construction of the τ function by means of supersymmetric quantum mechanics is discussed.
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    A nonprincipal value prescription for the temporal gauge (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2210-2217 
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    Notes: A nonprincipal value prescription is used to define the spurious singularities of Yang–Mills theory in the temporal gauge. Typical one-loop dimensionally regularized temporal-gauge integrals in the prescription are explicitly calculated, and a regularization for the spurious gauge divergences is introduced. The divergent part of the one-loop self-energy is shown to be local and has the same form as that in the spatial axial gauge with the principal-value prescription. The renormalization of the theory is also briefly mentioned.
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    On the possibility of localized wave propagation using a classical two-fluid model of superconductors (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2233-2258 
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    Notes: In this paper, the classical two-fluid model for superconductors is used to determine the time-dependent partial differential equations (PDEs) which govern wave propagation in superconducting media. These equations are then solved exactly in both two and three dimensions using localized wave solutions rather than the traditional eigenfunction solutions. We have applied these localized wave solutions to the problem of a symmetric superconducting slab, neglecting the normally conducting current density, and found that the resultant focus wave mode magnetic field solution expels flux from the interior of the slab and can regain its initial amplitude as it travels along the surface of the slab. A comparison of the transverse part of the localized wave solution with the transverse part of the more usual plane wave solution shows remarkable agreement.
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    Dirac equation and Clifford algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2309-2314 
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    Notes: The Dirac equation is rewritten in the framework of a Clifford algebra, revealing some new features, of which the most interesting is the U(1)×SU(2) symmetry of the corresponding Lagrangian.
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    Critical exponents in the imperfect and the free Bose gas (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2357-2370 
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    Notes: The field fluctuations are studied for the free and imperfect Bose gas. In the phase where there is condensation, these field fluctuations are abnormal, with critical exponents depending on the way the symmetry-breaking external field tends to zero in the thermodynamic limit. On the critical line there is also abnormal behavior, but the dependence on the way the field disappears, is slightly different. For densities below the critical density, the fluctuations are normal and independent of the way the external field goes to zero.
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    Symmetries of the KdV equation and four hierarchies of the integrodifferential KdV equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2390-2396 
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    Notes: Using the inverse strong symmetry of the Korteweg–de Vries (KdV) equation on the trivial symmetry and τ0 symmetry, one gets four new sets of symmetries of the KdV equation. These symmetries are expressed explicitly by the multi-integrations of the Jost function of the KdV equation and constitute an infinite dimensional Lie algebra together with two hierarchies of the known symmetries. Contrary to the general belief, the time-independent symmetry groups of the KdV and mKdV equations are non-Abelian and the infinite dimensional Lie algebras of the KdV and mKdV equations are nonisomorphic though two equations are related by the Miura transformation. Starting from these sets of symmetries, four hierarchies of the integrodifferential KdV equations, which can be solved by the Schrödinger inverse scattering transformation method, are obtained. Some of these hierarchies enjoy a common strong symmetry and/or same local conserved densities.
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    On the equivalence of two super Korteweg–deVries theories: A bi-Hamiltonian viewpoint (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2397-2407 
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    Notes: From a bi-Hamiltonian viewpoint the equivalence of two supersymmetric Korteweg–deVries theories, introduced by Manin–Radul and Laberge–Mathieu, is discussed herein. It is shown that the transformation connecting the two theories (proposed recently in the literature) preserves the bi-Hamiltonian structures; moreover, another derivation of this transformation, stemming from bi-Hamiltonian reduction theory and strongly emphasizing the geometrical meaning of the above equivalence is presented.
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    Comment on the solutions of the graded Yang–Baxter equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2485-2489 
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    Notes: In this comment we obtain two types of solutions of the graded Yang–Baxter equation whose symmetry group is GLqs(1||1).
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    Reducible Boson fermion realizations for osp(1||2) and osp(3||2) superalgebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2505-2515 
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    Notes: The osp(1||2) algebra is first realized through one boson and two fermion pairs of creation annihilation operators and then both osp(1||2) and osp(3||2) are realized in terms of three boson and two fermion pairs. All these realizations are reducible, and the reduced states are labeled by the total occupation number.
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    Quantized braided groups (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2560-2569 
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    Notes: Algebras that represent a generalization of both quantum groups, quantum supergroups, and braided groups are defined. They are given by a pair of solutions of the Yang–Baxter equation that satisfy some additional conditions. Several examples are presented.
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    On the addition of quantum matrices (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2617-2632 
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    Notes: An addition law is introduced for the usual quantum matrices A(R) by means of a coaddition Δ(underbar)t=t⊗1+1⊗t. It supplements the usual comultiplication Δt=t⊗t and together they obey a codistributivity condition. The coaddition does not form a usual Hopf algebra but a braided one. The same remarks apply for rectangular m×n quantum matrices. As an application, left-invariant vector fields are constructed on A(R) and other quantum spaces. They close in the form of a braided Lie algebra. As another application, the wave functions in the lattice approximation of Kac–Moody algebras and other lattice fields can be added and functionally differentiated.
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    Braid group related algebras, their representations and generalized hydrogenlike spectra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3074-3088 
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    Notes: Representations of the n-braid group where generators are given by matrices whose elements belong to a noncommutative algebra are discussed. Representation of this algebra in a Hilbert space generalizes the Burau representation. Two algebras which are closely related and are physically indistinguishable provided that a particular eigenvalue is fine tuned are discussed. It is shown that the generalized oscillator system given by one of the algebras generates a hydrogenlike spectrum.
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    Dissipation in Wigner–Poisson systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1513-1521 
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    Notes: The Wigner–Poisson (WP) system (or quantum Vlasov–Poisson system) is modified to include dissipative terms in the Hamiltonian. By utilizing the equivalence of the WP system to the Schrödinger–Poisson system, global existence and uniqueness are proved and regularity properties are deduced. The proof differs somewhat from that for the nondissipative case treated previously by Brezzi–Markowich and Illner et al.; in particular the Hille–Yosida Theorem is used since the linear evolution is not unitary, and a Liapunov function is introduced to replace the energy, which is not conserved.
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    Quantum measurements and quantum logics (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1555-1572 
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    Notes: A quantum logic formulation of quantum measurements is introduced using Boolean powers of orthomodular σ-posets to the description of the coupled system. A comparison with the traditional Hilbert space approach to quantum measurements and a discussion of some important classes of measurements is given.
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    Nonlinear random wave equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1634-1643 
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    Notes: Nonlinear wave equations describing forced vibrations of a string subject to random perturbations of intensity ε are studied herein. Two kinds of random perturbations are considered; one is Gaussian in the form of initial white noise and the other is a non-Gaussian random forcing which involves the formal derivative of a Brownian sheet. The solutions uε(t,x) of the complete forced equation are a stochastic process in space and time which has a unique stochastic equilibrium. The time variable t varies in a finite interval I:=[0, T], where T is a fixed positive time, and the space variable x varies in an interval J. Assuming that the initial conditions are of sufficient regularity, the fluctuations uε(t,x) from u0(t,x), the unperturbed solution, are analyzed as the intensity of perturbation ε↓0.
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    Motion of particles in five-dimensional Kaluza–Klein space–time (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2423-2429 
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    Notes: Study of radial and circular geodesics including those of tachyons in two spherically symmetric vacuum five-dimensional space–time is done. One of them is of Schwarzschild type and the other the so-called soliton solution. We obtain results which are different from the usual analogous four-dimensional (4D) ones. It is found that all the circular geodesics irrespective of whether they are timelike, null, or spacelike will be stable in the region r(approximately-greater-than)6M. It has also been shown that in a homogeneous cosmological model where the isotropic 3 space expands but the extra space contracts with time, the existence of tachyon is possible. This is in contradiction to the analogous 4D result obtained previously.
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    Bäcklund transformations and zero-curvature representations of systems of partial differential equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2463-2484 
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    Notes: It is shown that Bäcklund transformations (BTs) and zero-curvature representations (ZCRs) of systems of partial differential equations (PDEs) are closely related. The connection is established by nonlinear representations of the symmetry group underlying the ZCR which induce gauge transformations relating different BTs. This connection is used to construct BTs from ZCRs (and vice versa). Furthermore a procedure is outlined which allows a systematic search for ZCRs of a given system of PDEs.
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    On Schrödinger superalgebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2516-2538 
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    Notes: Using the supersymplectic framework of Berezin, Kostant, and others, two types of supersymmetric extensions of the Schrödinger algebra (itself a conformal extension of the Galilei algebra) were constructed. An ‘I-type' extension exists in any space dimension, and for any pair of integers N+ and N−. It yields an N=N++N− superalgebra, which generalizes the N=1 supersymmetry Gauntlett et al. found for a free spin-1/2 particle, as well as the N=2 supersymmetry of the fermionic oscillator found by Beckers et al. In two space dimensions, new, ‘exotic' or ‘IJ-type' extensions arise for each pair of integers ν+ and ν−, yielding an N=2(ν++ν−) superalgebra of the type discovered recently by Leblanc et al. in nonrelativistic Chern–Simons theory. For the magnetic monopole the symmetry reduces to o(3)×osp(1/1), and for the magnetic vortex it reduces to o(2)×osp(1/2).
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    Finite-dimensional representations of the quantum superalgebra Uq[gl(2/2)]. I. Typical representations at generic q (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2583-2606 
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    Notes: In the present paper all typical finite-dimensional representations of the quantum Lie superalgebra Uq[gl(2/2)] are constructed at generic deformation parameter q. As in the nondeformed case, the finite-dimensional Uq[gl(2/2)]-module Wq obtained is irreducible and can be decomposed into finite-dimensional irreducible Uq[gl(2)⊕gl(2)]-submodules Vqk.
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    The relation between the Berry and the Anandan–Aharonov connections for U(N) bundles (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1463-1470 
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    Notes: The geometric phase has been defined as the holonomy of two bundles with different base spaces and different connections. In this article we establish the relation between the Berry–Simon and the Anandan–Aharonov definitions for a large class of cyclic Hamiltonians (with N-fold degeneracy) using the classifying theorem for principal fiber bundles.
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    The relativistic Hermite polynomial is a Gegenbauer polynomial (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1549-1554 
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    Notes: It is shown that the polynomials introduced recently by Aldaya, Bisquert, and Navarro-Salas [Phys. Lett. A 156, 381 (1991)] in connection with a relativistic generalization of the quantum harmonic oscillator can be expressed in terms of Gegenbauer polynomials. This fact is useful in the investigation of the properties of the corresponding wave function. Some examples are given, in particular, related to the asymptotic behavior and to the distribution of zeros of the polynomials for large quantum numbers.
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    Semiclassical approximation for bound states of the Schrödinger equation with a Coulomb-like potential (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1597-1621 
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    Notes: The eigenvalue problem for the radial Schrödinger equation with an "almost'' Coulomb potential is considered. This problem provides the simplest example of a system whose classical trajectories have singularities. Thus the standard semiclassical quantization procedure (in the sense of Einstein–Brillouin–Keller–Maslov) cannot be applied straightforwardly to this situation. The equation under consideration has two transition points on the half axis 0〈x〈∞: a regular singular point at the origin and a turning point for some x0(approximately-greater-than)0; these points coalesce at low energy levels. The well-known comparison equation method provides uniform asymptotics for equations of this kind, but has the following shortcomings: it does not appeal to the corresponding classical mechanical problem and the formulas for the eigenvalues and eigenfunctions contain phase integrals which are not analytic with respect to the parameter characterizing the closeness of the transition points. In the present article we derive new formulas for the eigenfunctions in the form of inverse Fourier transforms of rapidly oscillating exponentials multiplied by some powers of x, together with simple formulas for the eigenvalues. These formulas are directly connected with the classical trajectories and do not have the shortcomings of the comparison equation method, i.e., all the functions entering the asymptotic expansions are analytic in x and energy. As a by-product, an asymptotic expansion of integrals having two stationary phase points which coalesce for some value of the parameter and tend to infinity when the parameter tends to zero is obtained.
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    Energy-momentum conservation in gauge theories (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1668-1687 
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    Notes: Using the formulation in terms of principal fiber bundles, it is shown that the external symmetry implies the conservation of the energy-momentum tensor for a general gauge theory. When applying this theory to the case of Dirac fields, one is naturally forced to replace the dependence on the metric by the dependence on the underlying spin structure in the variational problems.
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    Superconformal covariantization of superdifferential operator on (1||1) superspace and classical N=2 W superalgebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2570-2582 
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    Notes: A study of the superconformal covariantization of superdifferential operators defined on (1||1) superspace is presented. It is shown that a superdifferential operator with a particular type of constraint can be covariantized only when it is of odd order. In such a case, the action of superconformal transformation on the superdifferential operator is nothing but a Hamiltonian flow defined by the corresponding supersymmetric second Gelfand–Dickey bracket. The covariant form of a superdifferential operator of odd order is given.
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    The half-Hartley and the half-Hilbert transform (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2648-2656 
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    Notes: Inversion formulas are obtained for the restrictions of the Hartley and Hilbert transforms to R+. Regularity results are derived, and an illustrative example presented.
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    Noncommutative geometry for arbitrary braidings (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2633-2647 
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    Notes: The noncommutative geometry corresponding to arbitrary braidings is studied in a purely algebraical way. The new and original proposal of the geometry is given in terms of the theory of braided monoidal categories. The quantum oscillator is considered as an example of application of our geometry.
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    The m-function for Hamiltonians with Wigner–von Neumann potentials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1445-1462 
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    Notes: Hamiltonians with strong Wigner–von Neumann potentials are known to possess bound states in the continuous spectrum. For smaller couplings these bound states become resonances, which appear as singularities of the m-function. These singularities are intimately connected with the decay of the corresponding subordinate eigenfunction. For Coulomb-type potentials with Schrödinger operators this has recently be shown by Atkinson, the author, and Hinton, Klaus and Shaw. Here these results are extended to a general class of Wigner–von Neumann potentials for Dirac and Schrödinger operators.
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    N-body quantum scattering theory in two Hilbert spaces. VII. Real-energy limits (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1487-1512 
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    Notes: A study is made of the real-energy limits of approximate solutions of the Chandler–Gibson equations, as well as the real-energy limits of the approximate equations themselves. It is proved that (1) the approximate time-independent transition operator Tπ(z) and an auxiliary operator Mπ(z), when restricted to finite energy intervals, are trace class operators and have limits in trace norm for almost all values of the real energy; (2) the basic dynamical equation that determines the operator Mπ(z), when restricted to the space of trace class operators, has a real-energy limit in trace norm for almost all values of the real energy; (3) the real-energy limit of Mπ(z) is a solution of the real-energy limit equation; (4) the diagonal (on-shell) elements of the kernels of the real-energy limit of Tπ(z) and of all solutions of the real-energy limit equation exactly equal the on-shell transition operator, implying that the real-energy limit equation uniquely determines the physical transition amplitude; and (5) a sequence of approximate on-shell transition operators converges strongly to the exact on-shell transition operator. These mathematically rigorous results are believed to be the most general of their type for nonrelativistic N-body quantum scattering theories.
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    Models of q-algebra representations: q-integral transforms and "addition theorems'' (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1951-1975 
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    Notes: In his classic book on group representations and special functions Vilenkin studied the matrix elements of irreducible representations of the Euclidean and oscillator Lie algebras with respect to countable bases of eigenfunctions of the Cartan subalgebras, and he computed the summation identities for Bessel functions and Laguerre polynomials associated with the addition theorems for these matrix elements. He also studied matrix elements of the pseudo-Euclidean and pseudo-oscillator algebras with respect to the continuum bases of generalized eigenfunctions of the Cartan subalgebras of these Lie algebras and this resulted in realizations of the addition theorems for the matrix elements as integral transform identities for Bessel functions and for confluent hypergeometric functions. Here we work out q analogs of these results in which the usual exponential function mapping from the Lie algebra to the Lie group is replaced by the q-exponential mappings Eq and eq. This study of representations of the Euclidean quantum algebra and the q-oscillator algebra (not a quantum algebra) leads to summation, integral transform, and q-integral transform identities for q analogs of the Bessel and confluent hypergeometric functions, extending the results of Vilenkin for the q=1 case.
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    On symmetries, conservation laws, and variational problems for partial differential equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1998-2012 
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    Topics: Mathematics , Physics
    Notes: The problem of the correspondence between symmetries and conservation laws for partial differential equations is considered. For Lagrangian systems the set of Noether (variational) symmetries can be shown to lead to the set of all local conservation laws. For partial differential equations without well-defined Lagrangian functions there is no universal correspondence between symmetries and conservation laws. In this article it is shown that for a large class of differential equations there is a natural way to associate conservation laws with symmetries. The class consists of many interesting equations, e.g., Korteweg–de Vries equation, Kadomtsev–Petviashvili equation, Boussinesq equation, nonlinear diffusion equation, Monge–Ampère equation, regularized long-wave equation, and Navier–Stokes equations. Characteristics of the corresponding conservation laws are calculated and examples are given. For Lagrangian systems the consistency of the approach with the standard Noether results is discussed.
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    A Wigner-function approach to (semi)classical limits: Electrons in a periodic potential (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1066-1094 
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    Notes: A rigorous derivation of the semiclassical Liouville equation for electrons which move in a crystal lattice (without the influence of an external field) is presented herein. The approach is based on carrying out the semiclassical limit in the band-structure Wigner equation. The semiclassical macroscopic densities are also obtained as limits of the corresponding quantum quantities.
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    Coherent state approach to electron nuclear dynamics with an antisymmetrized geminal power state (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1139-1170 
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    Notes: A formulation of the complete dynamics of electrons and nuclei is presented. The dynamical equations are derived using the time-dependent variational principle (TDVP). The approximate electronic state vectors are antisymmetrized geminal power (AGP) states parameterized as projected coherent states, while the nuclei are treated as classical point particles. This leads to a formulation of time-dependent AGP theory that generalizes time-dependent Hartree–Fock (TDHF) theory and explicitly includes the dynamics of the nuclei. The linear approximation to the evolution equations (the classical harmonic approximation) which corresponds to a generalized random phase approximation (RPA) based on an AGP electronic reference state and which explicitly includes the dynamics of the nuclei, is studied and presented in this paper. The equations are formulated in terms of the primitive nonorthogonal electronic atomic basis thus avoiding any transformation to orthonormal molecular orbitals during the evolution.
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    A geometric criterion for adiabatic chaos (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1202-1218 
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    Notes: Chaos in adiabatic Hamiltonian systems is a recent discovery and a pervasive phenomenon in physics. In this work, a geometric criterion is discussed based on the theory of action from classical mechanics to detect the existence of Smale horseshoe chaos in adiabatic systems. It is used to show that generic adiabatic planar Hamiltonian systems exhibit stochastic dynamics in large regions of phase space. To illustrate the method, results are obtained for three problems concerning relativistic particle dynamics, fluid mechanics, and passage through resonance, results which either could not be obtained with existing methods, or which were difficult and analytically impractical to obtain with them.
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    Five-dimensional axisymmetric stationary solutions as harmonic maps (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1302-1321 
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    Notes: The complete scheme of the application of one- and two-dimensional subspaces and the subgroups method to five-dimensional gravity with a G3 group of motion are presented here in space–time and in potential space formalisms. From this method one obtains the Kramer, Belinsky–Ruffini, Dobiasch–Maison, Clément, Gross–Perry–Sorkin solutions, etc., as special cases.
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    An inequality for Legendre polynomials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1348-1360 
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    Notes: The following inequality is established: ||Pn(cos cursive-theta)||〈 [(square root of)1+(π4/16)(n+1/2)4 sin4 cursive-theta]−1, 0〈cursive-theta〈π, n=1,2,..., where Pn(x) denotes the Legendre polynomial of degree n. The relation P2n(cos cursive-theta) + (4/π2)× Q2n(cos cursive-theta) 〈 [(square root of)1+(π4/16)(n+1/2)4 sin4 cursive-theta]−1, n=1,2,..., on [θn1,θn,n+1], is proven where Qn(x) denotes the Legendre function of second kind, cos θn1 the largest zero of Qn(x), and cos θn,n+1=−cos θn1. Similarly we obtain the inequalities ||J0(x)|| 〈 [(square root of)1+(π4/16)x4]−1, x≠0, and J20(x) + Y20(x)〈 [(square root of)1+(π4/16)x4]−1, x≥y1, where y1=0.893577... is the first positive zero of Y0(x), and J0(x), Y0(x) denote the Bessel functions of the first and second kind, respectively. The results of the present paper arise out of some problems of nuclear and particle physics.
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    New family of asymptotic solutions of Helmholtz equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1387-1398 
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    Notes: A new family of asymptotic solutions of the Helmholtz equation can be derived. It is shown that new solutions are regular at caustics and turning points and do not require any special functions.
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    Taylor series expansions for eigenvalues and eigenfunctions of parametrized composition operators (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2024-2035 
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    Notes: Operators of the form Tβf(x)=∑Jj=1 cursive-phij(βx)f(σj +ρjx) are considered herein where β is a real parameter; σj and ρj are real numbers, and {cursive-phij} are holomorphic functions which satisfy certain additional conditions. Transfer operators of this form appear in statistical physics: the leading eigenvalue may be interpreted as the free energy of a lattice of interacting particles, as a function of inverse temperature β. A method for obtaining Taylor series expansions in β of the leading and second leading eigenvalues, and the leading eigenfunction are given. The method may be extended to find series expansions for other eigenvalues and eigenfunctions. The radii of convergence of these series have not been found. These results generalize the author's findings in another article [J. Math. Phys. 32, 2718 (1991)].
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    Algebraic structure of parabose Fock space. I. The Green's ansatz revisited (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1054-1065 
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    Notes: A description of the Fock space of a parabose oscillator of order p based on commutation relations bilinear in creation and annihilation operators rather than trilinear ones is developed. A new statement of the well-known Green's ansatz is introduced to help understand the significance of the bilinear commutation relations. It is also applied to show how all parabose oscillators of even order (respectively, odd order) can be obtained as irreducible constituents of the Fock space associated with a Green's ansatz of two (three) terms. Analogs of the form in which the parabose Green's ansatz is presented are provided for one parafermi oscillator and for systems of many parabose and parafermi oscillators of the same order. Methods used in the paper allow various new results for q-deformed parabose oscillators to be derived.
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    Path integral for the damped harmonic oscillator coupled to its dual (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1185-1191 
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    Notes: The time independent Bateman model which describes the damped harmonic oscillator coupled to its dual is studied using the path integral approach. The related propagator is calculated by means of the matrix representation.
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    An integrable three-particle system (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1219-1232 
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    Notes: A study of the existence of some integrable systems with nonlinear constants of motion is presented using the approach of the theory of generalized (dynamical or hidden) symmetries. Two Lagrangians are considered, both obtained by modifying the Toda Lagrangian. First a two-particle system is studied and then the results are generalized to a three-particle system. It is shown that in both cases the Lagrangians possess nonlinear constants of motion in involution and, thus, they are integrable.
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    Resolution of simple singularities yielding particle symmetries in a space–time (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 646-655 
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    Notes: A finite subgroup of the conformal group SL(2,C) can be related to invariant polynomials on a hypersurface in C3. The latter then carries a simple singularity, which resolves by a finite iteration of basic cycles of deprojections. The homological intersection graph of these cycles is the Dynkin graph of an ADE Lie group, i.e., a Lie group from the cartan series A, D, or E. The deformation of the simple singularity corresponds to ADE symmetry breaking. A (3+1)-dimensional topological model of observation is constructed, transforming consistently under SL(2,C), as an evolving three-dimensional system of world tubes, which connect "possible points of observation.'' The existence of an initial singularity for the four-dimensional space–time is related to its global topological structure. Associating the geometry of ADE singularities to the vertex structure of the topological model puts forward the conjecture on a likewise relation of inner symmetries of elementary particles to local space–time structure.
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    Metric of two arbitrary Kerr–Newman sources located on the symmetry axis (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6644-6657 
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    Notes: An exact asymptotically flat axisymmetric solution of the Einstein–Maxwell equations representing the exterior field of two arbitrary Kerr–Newman masses located on the symmetry axis is constructed in explicit form. In a particular case, when the solution describes two identical Kerr–Newman sources, simple analytical formulas are obtained which allow a straightforward analysis of the equilibrium of two charged rotating masses. Some arguments are given in favor of the possibility of the balance of stationary black holes due to their gravitational spin–spin interaction. © 1994 American Institute of Physics.
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    Universal central extensions of elliptic affine Lie algebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6685-6692 
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    Notes: Let @Fg be a simple complex (finite dimensional) Lie algebra, and let R be the ring of regular functions on a compact complex algebraic curve with a finite number of points removed. Lie algebras of the form @Fg⊗CR are considered; these generalize Kac–Moody loop algebras since for a curve of genus zero with two punctures R(approximately-equal-to)C[t,t−1]. The universal central extension of @Fg⊗R is analogous to an untwisted affine Kac–Moody algebra. By Kassel's theorem the kernel of the universal central extension is linearly isomorphic to the Kähler differentials of R modulo exact differentials. The dimension of the kernel for any R is determined first. Restricting to hyperelliptic curves with 2, 3, or 4 special points removed, a basis for the kernel is determined. Restricting further to an elliptic curve with punctures at two points (of orders one and two in the group law) we explicitly determine the cocycles which give the commutation relations for the universal central extension. The results involve Pollaczek polynomials, which are a genus-one generalization of ultraspherical (Gegenbauer) polynomials. © 1994 American Institute of Physics.
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    Complex Wishart matrices and conductance in mesoscopic systems: Exact results (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6736-6747 
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    Notes: It is noted that the hypothesis of independent random complex elements for the off diagonal blocks (say, M2 and M3) of the transfer matrix describing conductance in a mesoscopic wire allows the eigenvalue distribution of the matrix product M3°M3 (or M2°M2) to be computed exactly. Exact expressions, in terms of double Wronskian and Toeplitz determinants, are derived for the distribution of the smallest and second smallest eigenvalue of this and similar random matrix products. © 1994 American Institute of Physics.
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    Bound states and inverse scattering for the Schrödinger equation in one dimension (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6231-6236 
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    Notes: The one-dimensional Schrödinger equation is considered when the potential and its first moment are absolutely integrable. When the potential has support contained on the left (right) half-line, it is uniquely constructed by using only the reflection coefficient from the right (left). The bound state norming constants determine whether the potential has support contained on a half-line or on the full-line. The bound state energies and the unique set of norming constants yielding the potential with support contained on the left (right) half-line are completely determined by the reflection coefficient from the right (left). An explicit example is provided. © 1994 American Institute of Physics.
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    W*-KMS structure from multi-time Euclidean Green functions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6291-6303 
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    Notes: An axiomatic approach to the problem of reconstruction of a dynamics from the Euclidean multi-time Green functions is proposed. The existence of a W*-algebra on which the reconstructed dynamics acts as the canonical group of modular automorphisms is shown. A condition under which the reconstruction from the one-time and multi-time Green functions are equivalent is formulated. © 1994 American Institute of Physics.
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    The classification of decoherence functionals: An analog of Gleason's theorem (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6360-6370 
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    Notes: Gell-Mann and Hartle have proposed a significant generalization of quantum theory with a scheme whose basic ingredients are "histories'' and decoherence functionals. Within this scheme it is natural to identify the space UP of propositions about histories with an orthoalgebra or lattice. This raises the important problem of classifying the decoherence functionals in the case where UP is the lattice of projectors P(V) in some Hilbert space V; in effect, one seeks the history analog of Gleason's famous theorem in standard quantum theory. In the present article the solution to this problem for the case where V is finite dimensional is presented. In particular, it is shown that every decoherence functional d(α,β), α,β∈P(V) can be written in the form d(α,β)=trV⊗V(α⊗βX) for some operator X on the tensor-product space V⊗V. © 1994 American Institute of Physics.
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    Fully relativistic plasma dispersion function (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6471-6488 
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    Notes: Properties of a relativistic plasma dispersion function (PDF) that is required for the description of waves propagating perpendicular to a magnetic field in a fully relativistic, magnetized, Maxwellian plasma, are presented. Series, asymptotic series, recurrence relations, integral representations, derivatives, generating functions, approximations, differential equations, and connections with standard transcendental functions are discussed, as are the PDF's analytic properties. © 1994 American Institute of Physics.
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    Closed orbits and their stable symmetries (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6525-6535 
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    Notes: What will be shown is the first-order perturbation of closed orbits for two-body problems using approximate symmetry theory. A complete group classification with respect to approximate symmetries of the first-order perturbation of the closed orbit equations corresponding to Kepler's law and Hooke's law is made. A discussion then follows of the connection between closed orbits and their stable symmetries. © 1994 American Institute of Physics.
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    A new integrable Toda-related three-particle system (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6577-6583 
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    Notes: A study of a three-particle system that possesses, in addition to the energy function, two nonlinear constants of motion is presented herein. The system is obtained by modification of the Lagrangian of the Toda lattice. The explicit expression of the two integrals is obtained and it is proven that this new three-particle Lagrangian is integrable. Finally, the possible generalization to the case of n particles is discussed. © 1994 American Institute of Physics.
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    An algebraic extension of Dirac quantization: Examples (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6434-6470 
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    Notes: An extension of the Dirac procedure for the quantization of constrained systems is necessary to address certain issues that are left open in Dirac's original proposal. These issues play an important role especially in the context of nonlinear, diffeomorphism invariant theories such as general relativity. Recently, an extension of the required type was proposed using algebraic quantization methods. In this paper, the key conceptual and technical aspects of the algebraic program are illustrated through a number of finite dimensional examples. The choice of examples and some of the analysis is motivated by certain peculiar problems endemic to quantum gravity. However, prior knowledge of general relativity is not assumed in the main discussion. Indeed, the methods introduced and conclusions arrived at are applicable to any system with first class constraints. In particular, they resolve certain technical issues which are present also in the reduced phase space approach to quantization of these systems. © 1994 American Institute of Physics.
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    On a class of "skewed'' self-similar and hyperbolic fractals (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6511-6524 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Probabilistic (recurrent) renewal theory is used herein to describe the geometry of a new class of self-similar distributions in a "skewed'' multiplicative mass splitting procedure. It is shown how this model class can account for a deterministic and conservative treelike structure, in connection with recent developments on "anomalous'' multiplicative multifractals. Coexistence of both micro- and macroscopic scales in such objects is a consequence of the underlying renewal phenomena being transient, as is shown in a second part of the article. Various "entropylike'' measures of the intrinsic disorder prevailing in these structures are proposed. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530688
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    Perturbed factorization of the singular anharmonic-oscillator eigenequation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6244-6269 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The perturbed-ladder-operator method is applied to the solution of the perturbed eigenequation {(d2/dx2)−[m(m+1)/x2]−b2x2+V(x)+Λ}Ψ θix)=0 where V(x)=b1(1/x)2+b2(1/x)4+... is a singular perturbation. This method, which is the extension of the Schrödinger–Infeld–Hull factorization method within the perturbation scheme, provides closed form expressions of the perturbed eigenvalues and ladder functions, by means of algebraic manipulations. As an illustrative application, an analytical solution of the spiked-harmonic-oscillator eigenequation {(d2/dx2)−b2x2−(λ/x4)+E}Ψ(x)=0 is worked out up to the second order of the perturbation, by considering specifically adapted m- and λ-dependent perturbing and unperturbed potentials in order to tentatively avoid the known difficulties of convergence of the perturbation series. Closed form expressions of the λ/x4-anharmonic-oscillator energies are obtained in terms of the coupling constant λ and the quantum number v: results following from these expressions are compared with exact available values. © 1994 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.530673
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    Stochastic interpretation of Feynman path integral (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6344-6359 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A class of functions HnF was chosen, which are boundary values of holomorphic functions. It was shown that if the potential V∈HnF and the initial wave function ψ∈HnF then the solution of the Schrödinger equation is ψt∈HnF. The unitary evolution ψ → ψt can be expressed by an integral with respect to the Wiener measure. To each ψt∈HnF is associated a complex Markov process qt fulfilling stochastic Hamilton equations. The time evolution of ψ as well as multitime correlation functions of arbitrary observables in quantum mechanics take the form of expectation values with respect to qt. Some statistical and ergodic aspects of quantum mechanics resulting from the stochastic interpretation of Feynman's sum over trajectories are discussed.
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    URL: http://dx.doi.org/10.1063/1.530678
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    Equivariance, BRST symmetry, and superspace (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6418-6433 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The structure of equivariant cohomology in non-Abelian localization formulas and topological field theories is discussed. Equivariance is formulated in terms of a nilpotent Becchi–Rouet–Stora–Tyutin (BRST) symmetry, and another nilpotent operator which restricts the BRST cohomology onto the equivariant, or basic sector. A superfield formulation is presented and connections to reducible [Batalin–Fradkin–Vilkovisky (BFV)] quantization of topological Yang–Mills theory are discussed. © 1994 American Institute of Physics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530683
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    Affine collineations in general relativity and their fixed point structure (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5930-5944 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general discussion of affine vector fields (collineations) in space–time is given following a previous article by Hall and da Costa. Some general remarks are presented on the zeros of affine vector fields and then the general theory of such zeros is established. Some preliminary results regarding homothetic symmetries in two- and three-dimensional space–times are also given. The impossibility of reducing an affine algebra containing proper affine vector fields to homothetic or Killing vector fields, by means of a change of compatible metric, is demonstrated.
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    URL: http://dx.doi.org/10.1063/1.530720
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    Wavelike exact solutions of R+R2+Q2 gravity (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6001-6017 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The spinorial methods are applied to the analysis of the wavelike exact solutions of the gauge theory of gravitation with dynamical torsion. The N-type plane-fronted metric-torsion-electromagnetic wave for the most general quadratic in the torsion and curvature Lagrangian with nonvanishing cosmological constant are presented. A series of non-plane-fronted exact solutions with nontrivial torsion are found also. The question about equivalence of equations of the gauge theory of gravitation and the general relativity in the vacuum torsionless case are clarified. The example of non-Einsteinian vacuum solution for exceptional choice of cosmological constant are presented.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530724
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    Representation theory approach to the polynomial solutions of q-difference equations: Uq(sl(3)) and beyond (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6058-6075 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new approach to the theory of polynomial solutions of q-difference equations is proposed. The approach is based on the representation theory of simple Lie algebras G and their q-deformations and is presented here for Uq(sl(n)). First a q-difference realization of Uq(sl(n)) in terms of n(n−1)/2 commuting variables and depending on n−1 complex representation parameters, ri, is constructed. From this realization lowest weight modules (LWM) are obtained which are studied in detail for the case n=3 (the well-known n=2 case is also recovered). All reducible LWM are found and the polynomial bases of their invariant irreducible subrepresentations are explicitly given. This also gives a classification of the quasi-exactly solvable operators in the present setting. The invariant subspaces are obtained as solutions of certain invariant q-difference equations, i.e., these are kernels of invariant q-difference operators, which are also explicitly given. Such operators were not used until now in the theory of polynomial solutions. Finally, the states in all subrepresentations are depicted graphically via the so-called Newton diagrams.
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    URL: http://dx.doi.org/10.1063/1.530728
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    The orthogonality relations for SUq(2) (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6123-6143 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The orthogonality relations for SUq(2) are here formulated with the aid of the Woronowicz integral. The first part of this paper is devoted to a summary of the relevant parts of the Woronowicz theory and the second part to its implementation in terms of completely explicit representations of the irreducible unitary representations. The purpose of this presentation is to provide background for a separate study of the q deformation of the Coulomb problem.
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    URL: http://dx.doi.org/10.1063/1.530732
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    Polynomial relations in the Heisenberg algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6144-6149 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Polynomial relations between the generators of the classical and quantum Heisenberg algebras are presented. Some of those relations can have the meaning of the formulas of the normal ordering for the creation/annihilation operators which occur in the method of the second quantization. Polynomial relations of a special type invariant under quantization and q deformation are discovered.
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    URL: http://dx.doi.org/10.1063/1.530733
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    The Kaup–Broer system and trilinear odes of Painlevé type (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5850-5861 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Kaup–Broer hierarchy can be considered as a certain reduction of the KP hierarchy. Upon introducing the τ-function the Kaup–Broer system can be formulated in trilinear form giving rise to Wronskian solutions. In this paper several odes of the Painlevé type obtained through reductions of the Kaup–Broer system are considered. Those odes take a trilinear form which allows a linearization.
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    URL: http://dx.doi.org/10.1063/1.530714
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    The patchwork divergence theorem (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5922-5929 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting patchwork divergence theorem which is independent of the metric signature in either region, and which is thus valid if the signature changes.
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    URL: http://dx.doi.org/10.1063/1.530719
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    Anosov actions on noncommutative algebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5582-5599 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An axiomatic framework for a quantum mechanical extension to the theory of Anosov systems is constructed, and it is shown that this retains some of the characteristic features of its classical counterpart, e.g., nonvanishing Lyapunov exponents, a vectorial K-property, and exponential clustering. The effects of quantization are investigated on two prototype examples of Anosov systems, namely, the iterations of an automorphism of the torus (the "Arnold Cat'' model) and the free dynamics of a particle on a surface of negative curvature. It emerges that the Anosov property survives quantization in the case of the former model, but not of the latter one. Finally, we show that the modular dynamics of a relativistic quantum field on the Rindler wedge of Minkowski space is that of an Anosov system.
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    URL: http://dx.doi.org/10.1063/1.530766
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    Global potentials for general relativistic flows of ideal charged fluids (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5718-5725 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that general relativistic nondissipative flows of a possibly charged one component fluid, submitted to the action of its own electromagnetic field, admit a representation in terms of global potentials. A corresponding variational principle is presented, from which the equations of motion for the fluid and the fields can be obtained.
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    URL: http://dx.doi.org/10.1063/1.530706
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    Deformation of the exterior algebra and the GLq(r, C) (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6096-6099 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The deformation of the associative algebra of exterior forms is performed. This operation leads to a Yang–Baxter equation. Its relation with the braid group Bn−1 is analyzed. The correspondence of this deformation with the GLq(r,C) algebra is developed.
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    URL: http://dx.doi.org/10.1063/1.530730
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    Quantum temporal logic and decoherence functionals in the histories approach to generalized quantum theory (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5452-5476 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalized form of quantum theory based on the ideas of histories and decoherence functionals is analyzed and developed herein. Particular stress is placed on properties of the space of decoherence functionals, including one way in which certain global and topological properties of a classical system are reflected in a quantum history theory.
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    URL: http://dx.doi.org/10.1063/1.530759
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    Topology change in (2+1)-dimensional gravity (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5477-5493 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In (2+1)-dimensional general relativity, the path integral for a manifold M can be expressed in terms of a topological invariant, the Ray–Singer torsion of a flat bundle over M. For some manifolds, this makes an explicit computation of transition amplitudes possible. In this paper, the amplitude for a simple topology-changing process is evaluated. It is shown that certain amplitudes for spatial topology change are nonvanishing—in fact, they can be infrared divergent—but that they are infinitely suppressed relative to similar topology-preserving amplitudes.
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    URL: http://dx.doi.org/10.1063/1.530760
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    Random time evolution and direct integrals: Constants of the motion and the mass operator (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 113-126 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The members Hω=p2+Vω(x) of ergodic families of random operators, defined in H=L2(Rd), are considered as acting in fibers in a direct integral decomposition of K=L2(Ω,P(dω);H), (Ω,P) being the underlying probability space. Such a formulation may turn out to be useful in providing a rigorous background for theoretical physical methods employed in treating random systems. As an example a rigorous definition of the mass operator Σ(z) is presented and the formulation of transport equations in a functional analytic setting is briefly indicated. In case there is translational invariance in the probability law the operator H is shown to be unitarily equivalent to an operator Hˆ, which can be decomposed, Hˆ→Hˆ(k), in a way that diagonalizes p. Thus problems about averaged time evolution can be formulated entirely in terms of Hˆ(k) in L2(Ω,P).
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    URL: http://dx.doi.org/10.1063/1.530781
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    Reduction of space–time by a constraint for C(0) metrics (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 173-180 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown how a constraint imposed by the physical relevance of the solutions reduces the dimension of space–time. The C(0) metric given by Nutku is used to describe gravitational shock waves and the trivial case is looked at. It is found that imposing triviality on the solutions reduces the dimension of space–time by one.
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    URL: http://dx.doi.org/10.1063/1.530785
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