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  • Articles  (75,300)
  • 1990-1994  (75,300)
  • Mathematics  (75,300)
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  • 1
    Electronic Resource
    Electronic Resource
    Bäcklund transformations of linear Weingarten surfaces in Minkowski three-space (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4719-4724 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The classical Bäcklund transformation, which transforms surfaces of constant negative curvature, has been extended to surfaces in Minkowski three-space. In this article the tangency requirement of the Bäcklund transformation is relaxed to obtain a transformation of surfaces of Minkowski three-space with mean and Gaussian curvatures satisfying a linear relationship.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530809
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  • 2
    Electronic Resource
    Electronic Resource
    Compact homogeneous universes (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4855-4888 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are identified by discrete subgroups of the isometry group of the generalized Thurston geometries, which are related to the Bianchi and the Kantowski–Sachs–Nariai universes. Corresponding to this procedure their total degrees of freedom are shown to be categorized into those of the universal covering space and the Teichmüller parameters. The former are given by constructing homogeneous metrics on a simply connected manifold. The Teichmüller spaces are also given by explicitly constructing expressions for the discrete subgroups of the isometry group.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530819
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  • 3
    Electronic Resource
    Electronic Resource
    Spherically symmetric random walks in noninteger dimension (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4941-4963 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A previous article proposed a new kind of random walk on a spherically symmetric lattice in arbitrary noninteger dimension D. Such a lattice avoids the problems associated with a hypercubic lattice in noninteger dimension. This article examines the nature of spherically symmetric random walks in detail. A large-time asymptotic analysis of these random walks is performed and the results are used to determine the Hausdorff dimension of the process. Exact results are obtained in terms of Hurwitz functions (incomplete zeta functions) for the probability of a walker going from one region of the spherical lattice to another. Finally, it is shown that the probability that the paths of K independent random walkers will intersect vanishes in the continuum limit if D(approximately-greater-than)2K/(K−1).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530824
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  • 4
    Electronic Resource
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    Spherical wave expansion for any spin (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5000-5020 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The spherical wave expansion is derived for fields of particles of arbitrary spin and mass, and for arbitrary helicity, massless particles (such as the electromagnetic vector potential corresponding to photons). The starting point is Weinberg's characterization of relativistic, higher spin fields that transform according to general irreducible representations of the homogeneous Lorentz group. The expansion is a relativistic generalization of the familiar tensor and spinor spherical harmonics. It is useful for central force problems that arise, for example, in scattering processes off spherically symmetric solitonic backgrounds such as monopoles or skyrmions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530827
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  • 5
    Electronic Resource
    Electronic Resource
    Interpolation and partial differential equations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5035-5046 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: One of the main motivations for developing the theory of interpolation was to apply it to the theory of partial differential equations (PDEs). Nowadays interpolation theory has been developed in an almost unbelievable way {see the bibliography of Maligranda [Interpolation of Operators and Applications (1926–1990), 2nd ed. (Luleå University, Luleå, 1993), p. 154]}. In this article some model examples are presented which display how powerful this theory is when dealing with PDEs. One main aim is to point out when it suffices to use classical interpolation theory and also to give concrete examples of situations when nonlinear interpolation theory has to be applied. Some historical remarks are also included and the relations to similar results are pointed out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530829
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  • 6
    Electronic Resource
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    Properties of solutions of the Kadomtsev–Petviashvili I equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4683-4718 
    Details
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Kadomtsev–Petviashvili I (KPI) equation is considered as a useful laboratory for experimenting with new theoretical tools able to handle the specific features of integrable models in 2+1 dimensions. The linearized version of the KPI equation is first considered by solving the initial value problem for different classes of initial data. Properties of the solutions in different cases are analyzed in details. The obtained results are used as a guideline for studying the properties of the solution u(t,x,y) of the Kadomtsev–Petviashvili I (KPI) equation with given initial data u(0,x,y) belonging to the Schwartz space. The spectral theory associated to KPI is studied in the space of the Fourier transform of the solutions. The variables p={p1,p2} of the Fourier space are shown to be the most convenient spectral variables to use for spectral data. Spectral data are shown to decay rapidly at large p but to be discontinuous at p=0. Direct and inverse problems are solved with special attention to the behavior of all the quantities involved in the neighborhood of t=0 and p=0. It is shown in particular that the solution u(t,x,y) has a time derivative discontinuous at t=0 and that at any t≠0 it does not belong to the Schwartz space no matter how small in norm and rapidly decaying at large distances the initial data are chosen.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530808
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  • 7
    Electronic Resource
    Electronic Resource
    Matter collineations: The inverse "symmetry inheritance'' problem (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4832-4838 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Matter collineations, as a symmetry property of the energy-momentum tensor Tab, are studied from the point of view of the Lie algebra of vector fields generating them. Most attention is given to space–times with a degenerate energy-momentum tensor. Some examples of matter collineations are found for dust fluids (including Szekeres's space–times), and null fluid space–times.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530816
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  • 8
    Electronic Resource
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    Dyonic black holes in dilaton gravity (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4839-4847 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An exact solution of the low-energy string theory representing static, spherical symmetric dyonic black holes is found. The solution is labeled by their mass, electric charge, magnetic charge, and asymptotic value of the scalar dilaton. Some interesting properties of the dyonic black holes are studied.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530817
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  • 9
    Electronic Resource
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    Gauge potential decomposition, space-time defects, and Planck's constant (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4463-4468 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new geometrization of Planck's constant is proposed, which also bases on the torsion in the space-time. A quantity is introduced to describe the space-time dislocations that appear due to torsion. It will be pointed out that there is U(1)-like gauge invariance in this new geometrization. Using the gauge-potential decomposition, the quantity is quantized in units of the Planck length. The quantum number is determined by Hopf indices and Brouwer degrees.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530865
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  • 10
    Electronic Resource
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    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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  • 11
    Electronic Resource
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    Invariants of Lagrangians and their classifications (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4568-4593 
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    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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  • 12
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    Hierarchical structures and asymmetric stochastic processes on p-adics and adeles (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4637-4650 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The space of states of some phenomena, in physics and other sciences, displays a hierarchical structure. When that is the case, it is natural to label the states by a p-adic number field. Both the classification of the states and their relationships are then based on a notion of distance with ultrametric properties. The dynamics of the phenomena, that is, the transition between different states, is also a function of the p-adic distance dp. However, because the distance is a symmetric function, probabilistic processes which depend only on dp have a uniform invariant probability measure, that is, all states are equally probable at large times. This being a severe limitation for cases of physical interest, processes with asymmetric transition functions have been studied. In addition to the dependence on the ultrametric distance, the asymmetric transition functions are allowed to depend also on the probability of the target state, leading to any desired invariant probability measure. When each state of a physical system is associated to several distinct hierarchical structures or parametrizations, an appropriate labeling set is the ring of adeles. Stochastic processes on the adeles are also constructed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530805
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  • 13
    Electronic Resource
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    Double three-wave interaction of four waves: Lax representations and exact solutions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4757-4778 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The nonlinear resonant interaction of coherent waves is a fundamental process in the study of wave phenomena which has received a great deal of attention in its many aspects. In the present article a system of four interacting waves which constitute two resonant triplets is considered. The system is described, in a simplified model, by a Hamiltonian system of eight autonomous ordinary differential equations, with time as the independent variable; both positive and negative energy waves are allowed in the interaction. Two distinct Lax representations for this system, two new classes of exact solutions in terms of elliptic functions, a solution in the form of a convergent generic Laurent series expansion around a movable pole in the independent variable, and a stabilization criterion for the explosive instability that may occur when waves of different energy sign interact are obtained herein.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530813
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  • 14
    Electronic Resource
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    Exotic Majorana spinors in (3+1)-dimensional space–times (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4848-4854 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Inequivalent spin structures on Lorentzian manifolds are studied and in particular the possibility of defining inequivalent Majorana spinors associated with real irreducible representations of the Clifford algebra corresponding to a metric of signature (3,1) is analyzed. Such exotic complex (Dirac) spinors were first discussed in 1979. It is shown that exotic real (Majorana) spinors can be defined in a consistent way, too. The main idea is the use of a "chiral'' U(1) group instead of a "complex'' U(1) which contains all the relevant topological information. This result may be interesting in the context of the geometry of supergravity–matter coupling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530818
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  • 15
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    Some remarks on representations of jet groups and gauge groups (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4897-4908 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Irreducible unitary representations of the three first jet (or Leibniz) extensions Gkm of a compact group G are studied, focusing on the neighborhood of the trivial representation. Some associated irreducible unitary (continuous tensor product) representations of the gauge (or current) groups of mappings from a Riemannian manifold into Gkm are described.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530821
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  • 16
    Electronic Resource
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    Functional determinants on spheres and sectors (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4989-4999 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The scalar functional determinants on sectors of the two-dimensional disc and spherical cap are determined for arbitrary angles (rational factors of π). The whole sphere and hemisphere expressions are also given, in low dimensions, for both the ordinary and the conformal Laplacian.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530826
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  • 17
    Electronic Resource
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    Hamiltonian properties of the canonical symmetry (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 4067-4087 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The properties of the canonical symmetry are investigated. The densities of the local conservation laws for the nonlinear Schrödinger equation are shown to change under the action of the canonical symmetry by total space derivatives. It is also shown how the canonical symmetry can be used to look for the hierarchy of the Hamiltonian operators relevant to the system under consideration. It appears that only the invariance condition can be used to solve the problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530843
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  • 18
    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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530880
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  • 19
    Electronic Resource
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    Order and spacings of energy levels for the Klein–Gordon equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3805-3816 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: One can prove and extend some results about the order and spacings of energy levels for the Klein–Gordon equation with vector-like and scalar-like potentials.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530449
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  • 20
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    Statistical conception of quantum field theory (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3922-3935 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two equivalent modes of statistical description of stochastic particle production are considered, exclusive and inclusive. Information about particle production processes are distributed inside exclusive and inclusive descriptions in different ways. The exclusive description realizes an "all or nothing'' investigation strategy, whereas the inclusive description realizes the "step by step'' investigation strategy. Conventional quantum field theory is shown to use essentially an exclusive description. The possibility of a transition to a more reasonable investigation strategy (inclusive description) of particle production description is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530834
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  • 21
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    Nodal-surface conjectures for the convex quantum billiard (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3881-3888 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Stemming from known properties of one-dimensional (1-D) and 2-D quantum billiards, it is conjectured that the nodal surface of the first-excited state of the convex 3-D quantum billiard intersects the billiard surface in a single simple closed curve. Examples of the validity of this conjecture are given for a number of elementary 3-D billiard configurations. From these examples a second conjecture is introduced that addresses convex quantum billiards which are figures of rotation and contain one and only one plane of mirror symmetry normal to the axis of rotation. Two characteristic displacement parameters are defined which are labeled an axis length, L, and diameter, a. It is conjectured that a parameter κ≈1, exists, whose exact value depends on the properties of the billiard, such that for L(approximately-greater-than)κa ("prolatelike'') the nodal surface of the first-excited state of a quantum billiard is a plane surface of mirror symmetry which divides the length of the billiard in half. For L〈κa ("oblatelike'') the nodal surface of the first-excited state is a plane surface of mirror symmetry which contains the rotation axis and divides the diameter of the billiard in half. Arguments are given in support of a third conjecture which addresses the regular polyhedra quantum billiards, termed "spherical-like.'' It is hypothesized that the nodal surface of the first-excited state for any of these billiards is any plane of reflection symmetry of the given polyhedron.
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    URL: http://dx.doi.org/10.1063/1.530453
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  • 22
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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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  • 23
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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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  • 24
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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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  • 25
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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.
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    URL: http://dx.doi.org/10.1063/1.530838
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  • 26
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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.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1063/1.530842
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  • 27
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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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  • 28
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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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    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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    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
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    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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    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
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    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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    Asymptotic behaviors of the heat kernel in covariant perturbation theory (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3543-3559 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of nth order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and late-time asymptotic behaviors of the trace of the heat kernel are presented with this accuracy. The late-time behavior gives the criterion of analyticity of the effective action in quantum field theory. The latter point is exemplified by deriving the effective action in two dimensions.
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    The role of the internal metric in generalized Kaluza–Klein theories (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3571-3586 
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    ISSN: 1089-7658
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    Notes: The dimensional reduction of a Weyl space WN of N=4+n dimensions to a principal fiber bundle P˜(W4,G˜n) over a four-dimensional space–time W4 with structural group G˜n of dimension n arising from the existence of n conformal Killing vector fields of the original N-metric is studied. The framework of a Weyl geometry is adopted in order to investigate conformal rescalings of the metric on the bundle P˜(W4,G˜n) obtained. The Weyl symmetry is then, finally, broken again by choosing a particular Weyl gauge in which the internal, i.e., fiber metric, is of constant Cartan–Killing form. This choice of gauge, yielding a Riemannian theory, forces the internal metric to play no dynamical role in the theory, as is usually assumed to be the case in non-Abelian gauge theories. However, this gauge induces a conformal transformation of the metric in the space–time base of P˜ compared to the space–time metric obtained by the ordinary Kaluza–Klein reduction of a Riemannian space VN. The role of vector torsion in this dimensional reduction by isometries and scale transformations is also investigated.
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    The Lorentz–Dirac equation in Minkowski space (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3482-3489 
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    Topics: Mathematics , Physics
    Notes: The Lorentz–Dirac equation is obtained by means of a modification imposed on Maxwell's tensor for the Liénard–Wiechert field. This procedure avoids the mass renormalization of the point charge.
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    Space–times admitting a three-parameter similarity group (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3560-3570 
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    Notes: Space–times admitting a similarity group are considered. Among them, special attention is given to the three-parameter ones. A classification of such space–times is given based on the Bianchi type of the similarity group H3, and the general form of the metric is provided in each case assuming the orbits are non-null.
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    Nonlinear systems related to an arbitrary space–time dependence of the spectral transform (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3504-3524 
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    Notes: A general algebraic analytic scheme for the spectral transform of solutions of nonlinear evolution equations is proposed. This allows one to give the general nonlinear evolution corresponding to an arbitrary time and space dependence of the spectral transform (in general nonlinear and with nonanalytic dispersion relations). The main theorem is that the compatibility conditions always give a true nonlinear evolution because it can always be written as an identity between polynomials in the spectral variable k. This general result is then used to obtain first a method to generate a new class of solutions to the nonlinear Schrödinger equation, and second to construct the spectral transform theory for solving initial-boundary value problems for resonant wave-coupling processes (like self-induced transparency in two-level media, or stimulated Brillouin scattering of plasma waves, or else stimulated Raman scattering in nonlinear optics, etc.).
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    Thermodynamics of ideal boson and fermion gases in the static Taub universe (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3594-3603 
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    Notes: Some thermodynamic quantities of nonrelativistic ideal boson and fermion gases in the static Taub universe are derived to first order in a small anisotropy parameter d measuring the deformation from the spherical Einstein universe. They are used to investigate the problem of how the curvature anisotropy affects the thermodynamic behaviors of an ideal gas. It is found that, when the universe is in the oblate configuration (i.e., d(approximately-greater-than)0), the effect of curvature anisotropy is to increase the number of the fraction in the Bose–Einstein condensation and to decrease the fermion distribution function at low temperature. When the universe is in the prolate configuration (i.e., d〈0), the effects of curvature anisotropy on the thermodynamic quantities is contrary to that in the oblate configuration. The density matrix of a two particle system is evaluated and it is used to define the "statistical interparticle potential'' as an attempt to give a "statistical interpretation'' about the found thermodynamic behaviors. It is found that when the universe is in the oblate (prolate) configuration the curvature anisotropy will enhance (reduce) both the "statistic attraction'' among the bosons and "statistical repulsion'' among the fermions. It is expected that such a behavior will also be shown in the relativistic system.
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    The superalgebra embedding of OSP(1||2) in SL(1||2) and the grade star representations of SL(1||2) (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3650-3658 
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    Notes: First, it is shown that the superalgebra embedding of osp(1||2) in sl(1||2) allows to characterize the irreducible representation states of sl(1||2) without any missing label. Through this embedding the general nonpositive definite scalar product in the osp(1||2) representation space can be generalized to the sl(1||2) representation space. Then grade star representations of sl(1||2) are derived by considering this nonpositive scalar product.
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    Levinson's theorem, zero-energy resonances, and time delay in one-dimensional scattering systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2719-2733 
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    Notes: The one-dimensional Levinson's theorem is derived and used to study zero-energy resonances in a double-potential system. The low energy behavior of time delay is also investigated. In particular, it is shown that the quantum mechanical time delay admits a classical lower bound, in the low energy limit, if the potential has no bound-state solutions.
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    Parastatistics as Lie-supertriple systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2785-2803 
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    Notes: Parastatistics are reformulated herein in terms of Lie-supertriple systems. In this way, various new kinds of parastatistics discovered recently by Palev in addition to the standard one are reproduced. Also, bosonic and fermionic operators may not necessarily commute with each other.
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    Two classes of dynamical systems all of whose bounded trajectories are closed (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2914-2933 
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    Notes: According to the Bertrand theorem, the Kepler problem and the harmonic oscillator are the only central force dynamical systems that have closed orbits for all bounded motions. In this article, other dynamical systems having such a closed orbit property are found on T*(R3−{0}). Consider a natural dynamical system on T*(R4−{0}) whose Hamiltonian function is composed of kinetic and potential energies, and invariant under a SO(2) action. Then one can reduce the system to a Hamiltonian system on T*(R3−{0}) by the use of the Kustaanheimo–Stiefel transformation. If the original potential on R4−{0} is a central one, Bertrand's method is applicable to the reduced system for determining the potential so that any bounded motions may be periodic. As a result, two types of potential functions will be found; one is linear in the radial variable and the other proportional to the inverse square root of that. The dynamical systems obtained are capable of physical interpretation. In particular, the dynamical system with the inverse square root potential may be called the twofold Kepler system, whose bounded trajectories have a self-intersection point.
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    Gravitational perturbations of type-D vacuum space–times with cosmological constant (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3051-3058 
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    Notes: It is shown that in a type-D vacuum space–time with cosmological constant, the maximal spin weight components of the Weyl spinor perturbations, which obey separable decoupled equations, satisfy certain differential relations that are equivalent to the Teukolsky–Starobinsky identities fulfilled by the separated functions. It is also shown that the real and imaginary parts of the Starobinsky constants can be obtained from these relations.
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    A new method to introduce the Möbius function and the Möbius transform (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3099-3108 
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    Notes: The Möbius function and Möbius transform are introduced and derived in a manner that parallels a typical inverse problem of physics, rather than in the usual number-theoretic manner.
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    Study on the one dimensional boson–fermion model (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2833-2837 
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    Notes: The one dimensional boson–fermion model is introduced and the general eigenstates of the model Hamiltonian are constructed. The Cooper-pairlike bound state is given. It is concluded that the present model is exactly soluble via the Bethe ansatz.
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    Caustics in 1+1 integrable systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2934-2954 
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    Notes: Caustics arising in the asymptotic description of rapidly decaying solutions of the equations integrable via the inverse scattering transform are defined. Different asymptotic approaches to the description are considered. The appearance of members (Ρn2) of the hierarchy of the second Painlevé equation as special functions of wave catastrophies is discussed. The "adjoining'' problem Ρn2 → Ρk2(n(approximately-greater-than)k) for the simplest example Ρ22 → Ρ2 is considered in detail.
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    Integrability of difference Calogero–Moser systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2983-3004 
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    Notes: A general class of n-particle difference Calogero–Moser systems with elliptic potentials is introduced. Besides the step size and two periods, the Hamiltonian depends on nine coupling constants. We prove the quantum integrability of the model for n=2 and present partial results for n≥ 3. In degenerate cases (rational, hyperbolic, or trigonometric limit), the integrability follows for arbitrary particle number from previous work connected with the multivariable q-polynomials of Koornwinder and Macdonald. Liouville integrability of the corresponding classical systems follows as a corollary. Limit transitions lead to various well-known models such as the nonrelativistic Calogero–Moser systems associated with classical root systems and the relativistic Calogero–Moser system.
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    W gravity, N=2 strings, and 2+2 SU*(∞) Yang–Mills instantons (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3013-3024 
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    Notes: It is conjectured that W gravity can be interpreted as the gauge theory of φ diffeomorphisms in the space of dimensionally reduced D=2+2 SU*(∞) Yang–Mills instantons. These φ diffeomorphisms preserve a volume-three form and are those that furnish the correspondence between the dimensionally reduced Plebanski equation and the KP equation in (1+2) dimensions. A supersymmetric extension furnishes super-W gravity. The super-Plebanski equation generates self-dual complexified super gravitational backgrounds (SDSG) in terms of the super-Plebanski second heavenly form. Since the latter equation yields N=1, D=4 SDSG complexified backgrounds associated with the complexified-cotangent space of the Riemannian surface, (T*Σ)c, required in the formulation of SU*(∞) complexified Self-Dual Yang-Mills theory, (SDYM); it naturally follows that the recently constructed D=2+2 N=4 SDSYM theory, as the consistent background of the open N=2 superstring, can be embedded into the N=1 SU*(∞) complexified self-dual-super-Yang–Mills (SDSYM) in D=3+3 dimensions. This is achieved after using a generalization of self-duality for D(approximately-greater-than)4. Finally, the plausible relationship between the geometry of N=2 strings and the moduli of SU*(∞) complexified SDSYM in 3+3 dimensions is indicated.
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    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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    The trace of the heat kernel on a compact hyperbolic 3-orbifold (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3109-3116 
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    Notes: The heat coefficients related to the Laplace–Beltrami operator defined on the hyperbolic compact manifold H3/Γ are evaluated in the case in which the discrete group Γ contains elliptic and hyperbolic elements. It is shown that while hyperbolic elements give only exponentially vanishing corrections to the trace of the heat kernel, elliptic elements modify all coefficients of the asymptotic expansion, but the Weyl term, which remains unchanged. Some physical consequences are briefly discussed in the examples.
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    Representation of the five- and six-dimensional harmonic oscillators in a u(5)&supuline;so(5)&supuline;so(3) basis (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 3178-3189 
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    Notes: The duality that exists between the two subgroups SU(1,1) and O(5) of Sp(5,R) to construct basis states for the five-dimensional harmonic oscillator which simultaneously reduce the Sp(5,R)&supuline;U(5)&supuline;O(5)&supuline;SO(3) and Sp(5,R)&supuline; SU(1,1)&supuline;U(1) subgroup chains is used. It is shown that the vector-coherent-state wave functions of the fundamental five-dimensional SO(5) irrep [1,0] realize the traceless bosons introduced by Lohe and Hurst to classify the irreps of the orthogonal groups and employed in Chacon, Moshinsky, and Sharp's construction of a basis for the five-dimensional harmonic oscillator. Moreover, it is shown that VCS theory provides a simple mechanism for constructing matrix elements of the traceless boson operators. These matrix elements are used to extend the VCS representations of SO(5) in an SO(3) basis, given in a previous paper, to irreps of U(5) in an SO(5)&supuline; SO(3) basis. The extension to U(6)&supuline;U(5)&supuline;SO(5)&supuline;SO(3) is also given.
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    Asymptotic level state density for parabosonic strings (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2057-2063 
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    Notes: Making use of some results concerning the theory of partitions, relevant in number theory, the complete asymptotic behavior, for large N, of the level density of states for a parabosonic string is derived. It is also pointed out that there is a similarity between parabosonic strings and membranes.
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    Controlling quantum motion (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2083-2104 
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    Notes: The techniques of controlling the free evolution of a nonrelativistic charged particle by time-dependent magnetic fields are proposed and the possibility of more general operations upon the Schrödinger wave packet is discussed. It is found that a properly programmed sequence of magnetic pulses can invert the free evolution process, forcing an arbitrary wave packet to "go back in time'' to recover its past shape. Our manipulation prescriptions hold also for nonrelativistic particles of arbitrary spin.
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    Exchange relations and correlation functions for a quantum particle on the SU2 group manifold (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2130-2141 
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    Notes: The SO4 invariant quantum dynamics of a point particle moving on the 3 sphere (or equivalently, of the relative motion of the spherical top) is considered. Quantum exchange relations for different times are derived with an "R matrix'' depending on the time difference and on the conserved angular momentum. Their implications for correlation functions are spelled out. The chiral exchange relations of Alekseev and Faddeev [Commun. Math. Phys. 141, 413–422 (1991)] are also extended to different times.
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    Generating mass without the Higgs particle (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2199-2209 
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    Notes: The conformal group is added to the gauge group of a model of elementary particles based on the fiber bundle formalism. The inertial mass of a particle is interpreted as a manifestation of its interaction with the gauge bosons associated with the generators of the translation and special conformal subgroups. The generation of mass by this mechanism (together with the fact that the Higgs field is not necessarily required to effect bundle reduction) makes the Higgs and the Yukawa terms in the Lagrangian unnecessary: the Lagrangian then consists only of a Yang–Mills term and a covariantly free matter field term. A particular choice of gauge reproduces the usual mass terms for both fermions and gauge bosons. The "no-go theorem'' is not violated by the construction. The Poincaré generators commute with the internal symmetry generators after bundle reduction, and there is no mass splitting within symmetry multiplets. However, the left-handed/right-handed asymmetry allows the neutrino to remain massless; the definition of matter fields allows the up and down quarks to acquire different mass couplings; and the gauge bosons have different mass couplings determined by the inner product on the Lie algebra of the broken symmetry subgroup. The mass ratios of the gauge bosons—at tree level—are precisely those predicted by the Standard Model.
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    Nonperturbative treatment of singular potentials (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2229-2232 
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    Notes: A nonperturbative but absolutely convergent algorithm is applied to the determination of the eigenfunctions of Hamiltonian with a singular potential of the form H=−d2/dx2+x2+λ/xα in the domain [0, ∞] which obey Dirichlet boundary conditons. The formal structure of the algorithm is identical to that of the Lanczos algorithm when it is formally extended to self-adjoint operators.
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    A geometrical formulation of Abelian gauge structure in non-Abelian gauge theories and disconnected gauge group (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2270-2281 
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    Notes: A geometrical formalism of non-Abelian gauge theory with a topological term is constructed here with special reference to the role of Abelian gauge structures in non-Abelian theories. It is shown that when fermionic currents are written in chiral forms, we can take into account the disconnected gauge group which helps us to formulate a non-Abelian gauge structure so that the theory becomes asymptotically free.
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    Supersymmetry and the Atiyah–Singer index theorem. I. Peierls brackets, Green's functions, and a proof of the index theorem via Gaussian superdeterminants (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1095-1124 
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    Notes: The Peierls bracket quantization scheme is applied to the supersymmetric system corresponding to the twisted spin index theorem. A detailed study of the quantum system is presented, and the Feynman propagator is exactly computed. The Green's function and functional integral methods provide a direct derivation of the index as a single universal superdeterminant.
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    Differential equations for the entropy density, energy density, and number density of statistical mechanics (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 2371-2377 
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    Notes: A partial differential equation is derived for the number density as a function of position, temperature, and chemical potential. In the classical limit where Planck's constant is zero, it is shown that the expression for the classical number density of statistical mechanics satisfies the resulting equation. Similar partial differential equations are derived for the entropy density and energy density. It is then shown that these partial differential equations can be used to derive easily general expressions for the semiclassical number density, entropy density, and energy density of statistical mechanics.
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    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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    Affine projection tensor geometry: Decomposing the curvature tensor when the connection is arbitrary and the projection is tilted (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1274-1301 
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    Notes: This paper constructs the geometrically natural objects which are associated with any projection tensor field on a manifold with any affine connection. The approaches to projection tensor fields which have been used in general relativity and related theories assume normal projection tensors of codimension one and connections which are metric compatible and torsion-free. These assumptions fail for projections onto lightlike curves or surfaces and other situations where degenerate metrics occur as well as projections onto two-surfaces and projections onto space–time in the higher dimensional manifolds of unified field theories. This paper removes these restrictive assumptions. One key idea is to define two different "extrinsic curvature tensors'' which become equal for normal projections. In addition, a new family of geometrical tensors is introduced: the cross-projected curvature tensors. In terms of these objects, projection decompositions of covariant derivatives, the full Riemann curvature tensor and the Bianchi identities are obtained and applied to perfect fluids, timelike curve congruences, string congruences, and the familiar 3+1 analysis of the spacelike initial value problem of general relativity.
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    Convergence of an infinite product of Lie transformations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1361-1371 
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    Notes: Sufficient conditions are given for convergence of a product of Lie transformations generated by homogeneous polynomials of increasing order. It is shown that if the coefficients of the polynomials do not grow more rapidly with order than exponential functions, then there exists a finite domain around the origin for which the infinite product is a convergent transformation.
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    Algebraic spinor solution to the Kähler equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1399-1407 
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    Notes: The Kähler equation for an inhomogeneous differential form is analyzed in some detail. Algebraic spinorial solution to the Kähler equation lying in a minimal left ideal characterized by a certain idempotent projector has been examined.
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    A class of new invariant surfaces under the trace maps for nary Fibonacci lattices (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1008-1019 
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    Notes: A class of new noncompact surfaces that are invariant under the trace maps for a series of nary Fibonacci lattices is derived herein. When n is fixed the lattice is constructed by a substitution scheme of n letters: A →ABCD...Z,B→A,C→B,D→C,... ,Z→Y, where the trace map is given by an n(n+1)/2-dimensional dynamical map. The invariant surface is of the (n+1)th degree and exists in Rn(n+1)/2. The existence of such surfaces is relevant to prove the universal criticality of the spectrum—whether or not all the states in the system belong to critical states, where the wave function is self-similar or fractal.
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    Sub-Hopf-algebra-induced twists of quantum enveloping algebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1931-1938 
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    Notes: It is shown that a quasitriangular Hopf algebra can be twisted by the universal R-matrix of any quasitriangular sub-Hopf algebra and examples are given of R-matrices of quantum groups obtained this way.
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    The Eq(2) group via direct quantization of the Lie–Poisson structure and its Lie algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1976-1983 
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    Notes: The quantum group dual to the deformed eq(2) algebra obtained by Celeghini et al. [J. Math. Phys. 31, 2548 (1990)] is constructed.
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    Taub numbers extended to Einstein–Maxwell space–time (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1834-1839 
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    Notes: Mass and angular momentum of asymptotically flat systems are computed by Taub number τ1. This work extends the Taub number method from a vacuum region outside the central source to a region with stationary electric and magnetic fields while preserving global mass and angular momentum. The Reissner–Nordström and Kerr–Newman solutions are treated. Function spaces for curves of solutions of the coupled Einstein–Maxwell equations are discussed, together with the linearized field equations which are directional derivatives of the field equations along the solution curves in the direction of the perturbation.
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    The stress tensor conformal anomaly and analytic regularizations (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1840-1849 
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    Notes: In this paper the stress tensor conformal anomaly of a conformally coupled scalar field defined in a d dimensional Riemannian manifold is derived with or without a boundary, using the zeta function analytic regularization method. It is found that the scalar anomaly is independent of any massless limit. In an odd dimensional manifold with a boundary, the anomaly is not zero owing the boundary condition dependent term. After briefly discussing the cutoff method, it is proven that the zeta function method is equivalent to the cutoff method with a subtraction of the polar terms.
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    Supersymmetry and the Atiyah–Singer index theorem. II. The scalar curvature factor in the Schrödinger equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1125-1138 
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    Notes: The quantization of the superclassical system used in the proof of the index theorem results in a factor of ((h-dash-bar)2/8)R in the Hamiltonian. The path integral expression for the kernel is analyzed up to and including the two-loop order. The existence of the scalar curvature term is confirmed by comparing the linear term in the heat kernel expansion with the two-loop order terms in the loop expansion. In the operator formalism this term arises from the fermionic sector whereas in the path integral formulation it comes from the bosonic sector.
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    Elliptic Baker–Akhiezer functions and an application to an integrable dynamical system (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1192-1201 
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    Notes: An ansatz for elliptic Baker–Akhiezer functions is used to find new solutions for various spectral problems—the Sturm–Liouville problem with four and five-gap Lamé potentials and two third-order problems. One of the third-order problems is the classical Halphen equation with a spectral parameter. The eigenfunctions are used to construct elliptic solutions for integrable cases of a generalized Hènon–Heiles system.
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    Why fundamental structures are first or second ordera) (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1803-1818 
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    Notes: The fundamental result is proven that no G-structures that are properly of higher order k≥3 can exist; that is, if a differentiable manifold has a geometric structure at all there must exist geometric structure at first or second order. Because this theorem limits the cases to be considered, it is relevant for the classification of G-structures. Also proven are several results that underscore the special role of second-order equation-of-motion structures for material bodies. In particular, it is proven that geodesic equation-of-motion structures of order k≥3 necessarily admit solutions that break the light barrier.
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    Complex analytic realizations for quantum algebras (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1322-1333 
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    Notes: A method for obtaining complex analytic realizations for a class of deformed algebras based on their respective deformation mappings and their ordinary coherent states is introduced. Explicit results of such realizations are provided for the cases of the q oscillators (q-Weyl–Heisenberg algebra) and for the suq(2) and suq(1,1) algebras and their coproducts. They are given in terms of a series in powers of ordinary derivative operators which act on the Bargmann–Hilbert space of functions endowed with the usual integration measures. In the q→1 limit these realizations reduce to the usual analytic Bargmann realizations for the three algebras.
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    Multiparameter link invariants from quantum supergroups (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 1377-1386 
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    Notes: A method is developed for constructing multiparameter link invariants for a class of representations of the quantum supergroups Uq(gl(m||n)). The cases Uq(gl(1||1)) and Uq(gl(2||1)) are studied in detail. In the former we obtain a multiparameter generalization of the Alexander–Conway invariants.
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    q-difference intertwining operators for a Lorentz quantum algebra (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 971-985 
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    Notes: Representations πˆr,r¯ of a Lorentz quantum algebra U are constructed. They are labeled by two complex numbers r,r¯ and act in the space of formal power series of two noncommuting variables η,η¯. These variables are built from elements of the matrix Lorentz quantum group L which is dual to U. The conditions for reducibility of πˆr,r¯ are given. q-difference intertwining operators in η, η¯, which realize partial equivalences of the representations πˆr,r¯ , are constructed explicitly. The whole construction is a generalization of a known procedure for q=1. The case when q is a root of unity is also considered in detail.
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    Bifurcation solutions of the Schwinger–Dyson equation (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6270-6290 
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    Notes: As a function of the coupling constant, it is shown that the Schwinger–Dyson equation has many bifurcation solutions that branch off from the trivial solution. Three of these solutions are obtained explicitly, using the parameter imbedding method and the Liaponov–Schmidt method. Application of these methods to other nonlinear problems is discussed. © 1994 American Institute of Physics.
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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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    On the integrability of the inhomogeneous spherically symmetric Heisenberg ferromagnet in arbitrary dimensions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6498-6510 
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    Notes: The dynamics of an inhomogeneous spherically symmetric continuum Heisenberg ferromagnet in arbitrary (n-) dimensions is considered. By a known geometrical procedure the spin evolution equation equivalently is rewritten as a generalized nonlinear Schrödinger equation. A Painlevé singularity structure analysis of the solutions of the equation shows that the system is integrable in arbitrary (n-) dimensions only when the inhomogeneity is of inverse power in the radial coordinate in the form f(r)=cursive-epsilon1r−2(n−1)+cursive-epsilon2r−(n−2). This is confirmed by obtaining the associated Lax pair, Bäcklund transformation, and the solitonlike solution of the evolution equation. Further, calculations show that the one-dimensional linearly inhomogeneous ferromagnet acts as a universal model to which all the integrable higher-dimensional inhomogeneous spherically symmetric spin models can be formally mapped. © 1994 American Institute of Physics.
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    Padé-like approximation and maximum entropy formalism applied to chaotic systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6604-6608 
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    Notes: It is shown how the Padé-like approximation and the maximum entropy formalism can be applied in nonlinear chaotic systems. In particular, it is shown how one can use a few moments of the time evolution of a dynamical variable to infer the probability density and hence the Ljapunov exponent. © 1994 American Institute of Physics.
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    Constraint field systems in multimomentum canonical variables (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6584-6603 
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    Notes: To describe constraint field models, we apply the multimomentum Hamiltonian formalism where momenta correspond to derivatives of fields with respect to all world coordinates, not only time. If a Lagrangian density is degenerate, the Euler–Lagrange equations are underdetermined and need additional gauge-type conditions which remain elusive in general. One gets these conditions automatically as a part of the Hamilton equations, but must consider a family of Hamiltonian forms associated with the same Lagrangian density in order to exhaust solutions of the Euler–Lagrange equations. The case of degenerate quadratic and affine Lagrangian densities is elaborated. As a result, we get the universal procedure of describing constraint field systems. © 1994 American Institute of Physics.
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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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    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    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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    URL: http://dx.doi.org/10.1063/1.530700
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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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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    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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    URL: http://dx.doi.org/10.1063/1.530639
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    Quantum affine Lie algebras, Casimir invariants, and diagonalization of the braid generator (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6757-6773 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Let Uq(Gˆ) be an infinite-dimensional quantum affine Lie algebra. A family of central elements or Casimir invariants are constructed and their eigenvalues computed in any integrable irreducible highest weight representation. These eigenvalue formulas are shown to be absolutely convergent when the deformation parameter q is such that ||q||(approximately-greater-than)1. It is proven that the universal R-matrix R of Uq(Gˆ) satisfies the celebrated conjugation relation R°=TR with T the usual twist map. As applications, the braid generator is shown to be diagonalizable on arbitrary tensor product modules of integrable irreducible highest weight Uq(Gˆ)-module and a spectral decomposition formula for the braid generator is obtained which is the generalization of Reshetikhin's and Gould's forms to the present affine case. Casimir invariants acting on a specified module are also constructed and their eigenvalues, again absolutely convergent for ||q||(approximately-greater-than)1, computed by means of the spectral decomposition formula. © 1994 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.530641
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    More on Uq(su(1,1)) with q a root of unity (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6857-6874 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Highest weight representations of Uq(su(1,1)) with q=exp πi/N are investigated. The structures of the irreducible highest weight modules are discussed in detail. The Clebsch–Gordan decomposition for the tensor product of two irreducible representations is discussed. By using the results, a representation of SL(2,R)⊗Uq(su(2)) is also presented in terms of holomorphic sections which also have Uq(su(2)) index. Furthermore, ZN-graded supersymmetry is realized in terms of the representation. An explicit realization of Osp(1||2) via the highest weight representation of Uq(su(1,1)) with q2=−1 is given. © 1994 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.530646
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    Recursion operators: Meaning and existence for completely integrable systems (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 808-815 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Comments are made on the meaning and existence of recursion operators for completely integrable systems. It is shown that any nonresonant integrable system admits infinitely many Hamiltonian descriptions and recursion operators.
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    URL: http://dx.doi.org/10.1063/1.530613
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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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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    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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    URL: http://dx.doi.org/10.1063/1.530689
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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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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    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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    URL: http://dx.doi.org/10.1063/1.530692
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    Radiating sphere in a Kaluza–Klein space–time (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6619-6627 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The well-known solution of Vaidya for a radiating sphere in a Kaluza–Klein-type of space–time is extended. The field equations yield a two-parameter solution—either an exactly four-dimensional Vaidya metric with a flat extra space tucked to it or a flat Minkowski space–time. The geodesic trajectories of test particles in this field are studied and some astrophysical consequences due to the presence of the extra space are also briefly discussed. © 1994 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.530696
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    Self-gravitating Yang–Mills solitons and their Chern–Simons numbers (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 899-919 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A classification of the possible regular, spherically symmetric solutions of the Einstein–Yang–Mills system which is based on a bundle theoretical analysis for arbitrary gauge groups is presented herein. It is shown that such solitons must be of magnetic type, at least if the magnetic Yang–Mills charge vanishes. Explicit expressions for the Chern–Simons numbers of these self-gravitating Yang–Mills solitons are derived, which involve only properties of irreducible root systems and some information about the asymptotics of the solutions. It turns out, as an example, that the Chern–Simons numbers are always half integers or integers for the gauge groups SU(n). Possible physical implications of these results, which are based on analogies with the unstable sphaleron solution of the electroweak theory, are briefly indicated.
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    URL: http://dx.doi.org/10.1063/1.530620
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    The N=2 super-Wess–Zumino–Novikov–Witten model valued in superdiffeomorphism (SDIFF) M2 is self-dual supergravity in four dimensions (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 920-928 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the pure topological term of the N=2 super-Wess–Zumino–Novikov–Witten (SWZNW) model, valued in the area-preserving diffeomorphisms group of a two-dimensional Euclidean surface, is self-dual supergravity (SDSG) in 3+1 dimensions. This is achieved by a suitable slicing and pasting procedure of the (2,0); (0,2) N=2 SWZNW models determined by the embedding of the (2,0); (0,2) superspace supercovariant derivatives into the (3+1) superspace ones. Preliminary steps are provided to show that the N=1 SWZNW model, valued in the area-preserving superdiffeomorphism group of a super Riemann surface (SRS) whose signature is (1+1), is self-dual supergravity in (2+2) dimensions: the so-called Atiyah–Ward space–times.
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    URL: http://dx.doi.org/10.1063/1.530621
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    On diff(S1) covariantization of pseudodifferential operator (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 993-1007 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A study of diff(S1) covariant properties of a pseudodifferential operator of integer degree is presented. First, it is shown that the action of diff(S1) defines a Hamiltonian flow defined by the second Gelfand–Dickey bracket if and only if the pseudodifferential operator transforms covariantly. Second, the covariant form of a pseudodifferential operator of degree n ≠ 0,±1 is constructed by exploiting the inverse of the covariant derivative. This, in particular, implies the existence of a primary basis for WKP(n) (n ≠ 0,±1).
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    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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    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.
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    URL: http://dx.doi.org/10.1063/1.530683
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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.
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    URL: http://dx.doi.org/10.1063/1.530724
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    Symplectic reduction of higher order Lagrangian systems with symmetry (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6546-6556 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: One can develop a symplectic reduction procedure for higher order Lagrangian systems with symmetry. The reconstruction procedure of the dynamics is also studied and an application (spinning particle) is given at the end of the work. © 1994 American Institute of Physics.
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    URL: http://dx.doi.org/10.1063/1.530890
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    A class of graded Lie algebras of vector fields and first order differential operators (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 6838-6856 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Finite-dimensional Lie algebras of polynomial vector fields on Rn, that contain the elements ∂/∂xi and xi(∂/∂xi) for i=1...n were studied. To any Lie algebra @FL of this class, an N-valued n×n matrix A and a set of special elements S⊆{1,...,n} are associated. It is proven that the pair (A,S) necessarily satisfies two properties. Conversely, to any pair (A,S) satisfying those two properties is associated a Lie algebra @FL(A,S), such that @FL(A,S) is maximal in the class of all @FL with matrix A and special elements S. For the Lie algebras @FL(A,S) the possible extensions to first order differential operators, and its modules of C∞ functions are discussed. © 1994 American Institute of Physics.
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    A new lattice formulation of the continuum (1994)
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 35 (1994), S. 5600-5629 
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    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new lattice formulation of the continuum is presented, which can be applied to quantum or classical field theories in any space–time dimension. The method is illustrated with an application to relativistic nontopological solitons. This approach also provides an effective means of removing the spurious lattice fermion degenerate solutions for the Dirac equation.
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    URL: http://dx.doi.org/10.1063/1.530767
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