ALBERT

All Library Books, journals and Electronic Records Telegrafenberg

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • American Institute of Physics (AIP)  (9,740)
  • 2010-2014
  • 1995-1999  (9,740)
  • 1997  (9,740)
Collection
Years
  • 2010-2014
  • 1995-1999  (9,740)
Year
  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4730-4740 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This work addresses a specific technical question of relevance to canonical quantization of gravity using the so-called new variables and loop-based techniques of Ashtekar, Rovelli, and Smolin. In particular, certain "superselection laws" that arise in current applications of these techniques to solving the diffeomorphism constraint are considered. Their status is elucidated by studying an analogous system: 2+1 Euclidean gravity. For that system, these superselection laws are shown to be spurious. This, however, is only a technical difficulty. The usual quantum theory may still be obtained from a loop representation and the technique known as "Refined Algebraic Quantization." © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4128-4137 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We solve the constrained Kadomtsev–Petviashvili (cKP) hierarchy by using the gauge transformation technique. We show that there are two kinds of gauge transformations which preserve the form of the Lax operator of the cKP hierarchy. One of them is differential type and the other is integral type. Through two such gauge transformations we obtain not only the Wronskian-type τ-functions for the cKP hierarchy, but also the binary-type τ-functions which have not been obtained before. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4151-4164 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Integrable systems of nonlinear partial differential equations (PDEs) are obtained from integrable equations in 2+1 dimensions, by means of a reduction method of broad applicability based on Fourier expansion and spatio–temporal rescalings, which is asymptotically exact in the limit of weak nonlinearity. The integrability by the spectral transform is explicitly demonstrated, because the corresponding Lax pairs have been derived, applying the same reduction method to the Lax pair of the initial equation. These systems of nonlinear PDEs are likely to be of applicative relevance and have a "universal" character, inasmuch as they may be derived from a very large class of nonlinear evolution equations with a linear dispersive part. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4165-4178 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The properties of superintegrable systems in two degrees of freedom, possessing three independent globally defined constants of motion, are studied using as an approach, the existence of hidden symmetries and the generalized Noether's theorem. The potentials are obtained as solution of a system of two partial differential equations. First the case of standard Lagrangians is studied and then the method is applied to the case of Lagrangians with a pseudo-Euclidean kinetic term. Finally, the results are related with other approaches and with a family of potentials admitting a second integral of motion cubic in the velocities obtained by Drach. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4398-4398 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3435-3445 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We present the algebraic proof of a sum rule that is relevant in the theory of Stark broadening of hydrogen and hydrogenic lines. This is accomplished by applying Gauss' recursion formulas for the hypergeometric function to the analytical expression of the dipole matrix elements involved in the summation. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6648-6674 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we construct a set of five conditions necessary for the existence of generalized symmetries for a class of differential-difference equations depending only on nearest neighboring interaction. These conditions are applied to prove the existence of new integrable equations belonging to this class. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5634-5642 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The transformation bracket of hyperspherical harmonics with different sets of hyperspherical coordinates as arguments has been derived for an arbitrary number of particles with arbitrary masses in two space dimensions. The solution of the four-anyon problem is given as an example to illustrate its applications. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 1161-1182 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A relationship between quantum flag and Grassmann manifolds is revealed. This enables a formal diagonalization of quantum positive matrices. The requirement that this diagonalization defines a homomorphism leads to a left Uh(su(N))-module structure on the algebra generated by quantum antiholomorphic coordinate functions living on the flag manifold. The module is defined by prescribing the action on the unit and then extending it to all polynomials using a quantum version of the Leibniz rule. The Leibniz rule is shown to be induced by the dressing transformation. For discrete values of parameters occurring in the diagonalization one can extract finite-dimensional irreducible representations of Uh(su(N)) as cyclic submodules. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 639-647 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The quantum quartic oscillator is treated on the basis of a singularity-analytic approach to the central two-point connection problem of the triconfluent case of Heun's differential equation. We split off the asymptotic factors by means of a specific linear transformation of the independent variable and represent the solution in terms of a Jaffé expansion. The result is a fourth-order linear difference equation of Poincaré–Perron type the asymptotic behavior of which is significant for the connection problem. This is investigated by means of the Birkhoff-set of the difference equation and leads to the exact eigenvalue-condition of the problem. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 11
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 867-881 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Quantum Stochastic Limit of a quantum mechanical particle coupled to a quantum field without the neglect of the response details of the interaction (i.e., not making the dipole approximation) is made following the scheme of Accardi and Lu and the corresponding Quantum Stochastic Structure is derived. The stochastic sector for the noise is constructed and is shown to be of a qualitatively new type. We also include a physical discussion on the limit noise which obeys Interacting-Free statistics and include a new shorter proof of the noise convergence and also a new construction of Interacting-Free Fock Space. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 12
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 882-901 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The solutions of a large class of hierarchies of zero-curvature equations that includes Toda- and KdV-type hierarchies are investigated. All these hierarchies are constructed from affine (twisted or untwisted) Kac–Moody algebras g. Their common feature is that they have some special "vacuum solutions" corresponding to Lax operators lying in some Abelian (up to the central term) subalgebra of g; in some interesting cases such subalgebras are of the Heisenberg type. Using the dressing transformation method, the solutions in the orbit of those vacuum solutions are constructed in a uniform way. Then, the generalized tau-functions for those hierarchies are defined as an alternative set of variables corresponding to certain matrix elements evaluated in the integrable highest-weight representations of g. Such definition of tau-functions applies for any level of the representation, and it is independent of its realization (vertex operator or not). The particular important cases of generalized mKdV and KdV hierarchies as well as the Abelian and non-Abelian affine Toda theories are discussed in detail. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 13
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5044-5086 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The causal structure of Minkowski spacetime M is discussed, in terms of the notions of causal complementation and causal completion. These geometric notions are relevant for quantum field theory and the theory of the Klein-Gordon equation. Particular attention is given to closed, convex, causally complete subsets of M, and the properties of such sets are discussed. The study of such sets is motivated by potential applications to the theory of local nets of von Neumann algebras. The notion of the envelope of uniqueness of a subset of M, familiar from the theory of the wave equation, is discussed, and some results about the relation of this envelope to the causal completion of the set are presented. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 14
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6304-6314 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider a single-band approximation to the random Schrödinger operator in an external magnetic field. The random potential consists of delta functions of random strengths whose positions have a Poisson distribution. We prove that if the magnetic field is sufficiently high compared to the density of scatterers, then with probability one there exists an infinitely degenerate eigenenergy coinciding with the first Landau level in the absence of a random potential. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 15
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6315-6327 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper, we introduce unitary and Hermitian phase-difference operators for the two modes of the electromagnetic field in the q-deformed case. The q-creation and annihilation operators of phase-difference quanta are given, and the algebraic properties of some operators in phase space are discussed. The phase-difference properties of two-mode q-coherent states are investigated. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 16
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6328-6366 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A plane harmonic electromagnetic wave obliquely incident on a plane stratified bianisotropic medium with multiple discontinuities in the parameters is considered. A covariant wave-splitting approach, based on the use of the formula of integration by parts for multiplicative integrals and the impedance concept, is presented. It encompasses various types of decomposition of the total internal field into two waves propagating in opposite directions, including the physical and vacuum wave splittings treated earlier in the literature, and provides a convenient means for both analytical investigation and numerical calculation of evolution operators (Green's functions) and impedance tensors of split waves as well as characteristic matrices and reflection and transmission tensors of stratified bianisotropic media. The potentialities of the approach are illustrated by its application to the problems of reflection, transmission, and guided propagation, and by generalizing the method of multiple reflections to the case of stratified bianisotropic media. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 17
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6428-6443 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Chen, Lee, and Liu presented in 1979 an algorithm for establishing integrability of two-dimensional partial differential systems. It is proved here that this algorithm is invariant under the point transformations, differential substitutions, and some integrodifferential substitutions. It is also proved that canonical conserved densities of linearizable systems arising in the frameworks of the method are almost all trivial. The integrability of the non-Newtonian liquid equations is investigated and it is proved that there exist two integrable systems only. A preliminary classification of the third-order integrable evolution systems is presented. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 18
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5402-5415 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that any two generating families of the same isotropic submanifold are equivalent. Also the singularity theory of symmetric isotropic submanifolds is developed and the basic classification theorems on prenormal forms, in particular for Z2 action, are proved. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 19
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5416-5433 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 20
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5434-5446 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Intrinsic Hopf algebra structure of the Woronowicz differential complex is shown to generate quite naturally a bicovariant algebra of four basic objects within a differential calculus on quantum groups—coordinate functions, differential 1-forms, Lie derivatives, and inner derivations—as the cross-product algebra of two mutually dual graded Hopf algebras. This construction, properly taking into account Hopf-algebraic properties of Woronowicz's bicovariant calculus, provides a direct proof of the Cartan identity and of many other useful relations. A detailed comparison with other approaches is also given. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 21
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 139-172 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The Coleman–Mandula theorem, which states that space–time and internal symmetries cannot be combined in any but a trivial way, is generalized to an arbitrarily higher spacelike dimension. Prospects for further generalizations of the theorem (spacelike representations, larger timelike dimension, infinite number of particle types) are also discussed. The original proof relied heavily on the Dirac formalism, which was not well defined mathematically at that time. The proof given here is based on the rigorous version of the Dirac formalism, based on the theory of distributions. This work also serves to demonstrate the suitability of this formalism for practical applications. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 22
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5505-5514 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The operator algebras of a new family of relativistic geometric models of the relativistic oscillator [I. I. Cotaescu, Int. J. Mod. Phys. A 12, 3545 (1997)] are studied. It is shown that, generally, the operator of number of quanta and the pair of shift operators of each model are the generators of a nonunitary representation of the so(1,2) algebra, except for a special case when this algebra becomes the standard of the nonrelativistic harmonic oscillator. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 23
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5576-5589 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss the ADHMN construction for SU(N) monopoles and show that a particular simplification arises in studying charge N−1 monopoles with minimal symmetry breaking. Using this we construct families of tetrahedrally symmetric SU(4) and SU(5) monopoles. In the moduli space approximation, the SU(4) one-parameter family describes a novel dynamics where the monopoles never separate, but rather, a tetrahedron deforms to its dual. We find a two-parameter family of SU(5) tetrahedral monopoles and compute some geodesics in this submanifold numerically. The dynamics is rich, with the monopoles scattering either once or twice through octahedrally symmetric configurations. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 24
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5531-5558 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The use of internal variables for the description of relativistic particles with arbitrary mass and spin in terms of scalar functions is reviewed and applied to the stochastic phase space formulation of quantum mechanics. Following Bacry and Kihlberg a four-dimensional internal spin space S¯ is chosen possessing an invariant measure and being able to represent integer as well as half integer spins. S¯ is a homogeneous space of the group SL(2,C) parametrized in terms of spinors α∈C2 and their complex conjugates α¯. The generalized scalar quantum mechanical wave functions may be reduced to yield irreducible components of definite physical mass and spin [m,s], with m≥0 and s=0,〈fraction SHAPE="CASE"〉12,1,〈fraction SHAPE="CASE"〉32,... , with spin described in terms of the usual (2s+1)-component fields. Viewed from the internal space description of spin this reduction amounts to a restriction of the variable α to a compact subspace of S¯, i.e., a "spin shell" Sr=2s2 of radius r=2s in C2. This formulation of single particles or single antiparticles of type [m,s] is then used to study the geometro-stochastic (i.e., quantum) propagation of amplitudes for arbitrary spin on a curved background space–time possessing a metric and axial vector torsion treated as external fields. A Poincaré gauge covariant path integral-like representation for the probability amplitude (generalized wave function) of a particle with arbitrary spin is derived satisfying a second order wave equation on the Hilbert bundle constructed over curved space–time. The implications for the stochastic nature of polarization effects in the presence of gravitation are pointed out and the extension to Fock bundles of bosonic and fermionic type is briefly mentioned. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 25
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5605-5625 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We define and study the properties of the infinite-dimensional quantized Kronecker flow. This C*-dynamical system arises as a quantization of the corresponding flow on an infinite-dimensional torus. We prove an ergodic theorem for a class of quantized Kronecker flows. We also study the closely related, almost periodic quantum field theory of bosonic, fermionic, and supersymmetric particles. We prove the existence and uniqueness of KMS and super-KMS states for the C*-algebras of observables arising in these theories. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 26
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5643-5652 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A general quantum history theory can be characterized by the space of histories and by the space of decoherence functionals. In this note we consider the situation where the space of histories is given by the lattice of projection operators on an infinite dimensional Hilbert space H. We study operator representations for decoherence functionals on this space of histories. We first give necessary and sufficient conditions for a decoherence functional being representable by a trace class operator on H⊗H, an infinite dimensional analogue of the Isham–Linden–Schreckenberg representation for finite dimensions. Since this excludes many decoherence functionals of physical interest, we then identify the large and physically important class of decoherence functionals which can be represented, canonically, by bounded operators on H⊗H. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 27
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5653-5662 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: DeWitt's covariant formulation of path integration [B. De Witt, "Dynamical theory in curved spaces. I. A review of the classical and quantum action principles," Rev. Mod. Phys. 29, 377–397 (1957)] has two practical advantages over the traditional methods of "lattice approximations;" there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature −1. The Pauli–DeWitt curvature correction term arises, as in DeWitt's work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman–Kac formula for the automorphic Schrödinger equation on the Riemann surface Γ(backward-slash)H. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47–90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, "The path integral on the Poincare upper half plane and for Liouville quantum mechanics," Phys. Lett. A 123, 319–328 (1987). © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 28
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 84-97 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we use the Lie algebra of space-time symmetries to construct states which are solutions to the time-dependent Schrödinger equation for systems with potentials V(x,τ)=g(2)(τ)x2+g(1)(τ)x+g(0)(τ). We describe a set of number-operator eigenstates states, {Ψn(x,τ)}, that form a complete set of states but which, however, are usually not energy eigenstates. From the extremal state, Ψ0, and a displacement squeeze operator derived using the Lie symmetries, we construct squeezed states and compute expectation values for position and momentum as a function of time, τ. We prove a general expression for the uncertainty relation for position and momentum in terms of the squeezing parameters. Specific examples, all corresponding to choices of V(x,τ) and having isomorphic Lie algebras, will be dealt with in the following paper (II). © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 29
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5905-5943 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We propose a generalization of meanders, i.e., configurations of non-self-intersecting loops crossing a line through a given number of points, to SU(N). This uses the reformulation of meanders as pairs of reduced elements of the Temperley–Lieb algebra, a SU(2)-related quotient of the Hecke algebra, with a natural generalization to SU(N). We also derive explicit formulas for SU(N) meander determinants, defined as the Gram determinants of the corresponding bases of the Hecke algebra. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 30
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5968-5975 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The exponential solutions of the Darboux equations for conjugate nets is considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary linear space give solutions of the Darboux system, which can be understood as a vectorial Darboux transformation of the exponential background. The method is extended further to obtain vectorial Darboux transformations of the Darboux system. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 31
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5991-6007 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We provide a way of computing Casimir eigenvalues for Weyl orbits as well as for irreducible representations of Lie algebras. A κ(s) number of polynomials of rank N are obtained explicitly for AN Casimir operators of order s where κ(s) is the number of partitions of s into positive integers except 1. It is also emphasized that these eigenvalue polynomials prove useful in obtaining formulas to calculate weight multiplicities and in explicit calculations of the whole cohomology ring of classical and also exceptional Lie algebras. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 32
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6008-6017 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is well known that a complex four-component Dirac spinor defines an orthonormal tetrad on flat Minkowski spacetime. For example, a spinor solution to the Dirac equation determines the four-velocity and Pauli-Lubanski spin vector, comprising the timelike and first spacelike members of the particle's tetrad, as well as two other spacelike members that are rarely discussed. Also, of particular note is the complex null tetrad formalism that provides a map from a two-component SL(2, C) spinor and its complex conjugate to a tetrad. The inverse problem is studied here. Given a tetrad, a complex Dirac spinor valued function of the tetrad is explicitly defined in such a way that certain sums of bilinear products of the components of this spinor exactly reproduce the tetrad. This spinor may be used in the Feynman propagator representation of the solution to the Dirac equation to generate a Dirac wave spinor with desired initial properties. The mappings studied here represent a new class of nonlinear mappings SO(3,1)+↑→SO(3,1). © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 33
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6040-6040 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 34
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4909-4913 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: If a single particle obeys nonrelativistic QM in RN and has the Hamiltonian H=−Δ+∑q〉0 a(q)rq, a(q)≥0, then the lowest eigenvalue E is given approximately by the semiclassical expression E=minr〉0{(1/r2)+∑q〉0 a(q)(P(q,N)r)q}. It is proved that this formula yields a lower bound when P(q,N)=(Ne/2)1/2(N/qe)1/q[Γ(1+N/2)/Γ(1+N/q)]1/N and an upper bound when P(q,N)=(N/2)1/2[Γ((N+q)/2)/Γ(N/2)]1/q. An extension is made to allow for a Coulomb term when N〉1. The general formula is applied to the examples V(r)=r+r2+r3 and V(r)=r2+r4+r6 in dimensions 1 to 10, and the results are compared to accurate eigenvalues obtained numerically. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 35
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4929-4950 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We give a detailed computation of the bosonic action of the Chamseddine–Connes model which we performed using different techniques. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 36
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5272-5279 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We consider dissipative relativistic fluid theories on a fixed flat, globally hyperbolic, Lorentzian manifold (R×T3,gab). We prove that for all initial data in a small enough neighborhood of the constant equilibrium states (in an appropriate Sobolev norm), the solutions evolve smoothly in time forever and decay exponentially to some, in general undetermined, constant equilibrium state. To prove this, three conditions are imposed on these theories. The first condition requires the system of equations to be symmetric hyperbolic, a fundamental requisite to have a well posed and physically consistent initial value formulation. For the flat space-times considered here the equilibrium states are constant, which is used in the proof. The second condition is a generic consequence of the entropy law, and is imposed on the non-principal part of the equations. The third condition is imposed on the principal part of the equations and it implies that the dissipation affects all the fields of the theory. With these requirements we prove that all the eigenvalues of the symbol associated to the system of equations of the fluid theory have strictly negative real parts, which, in fact, is an alternative characterization for the theory to be totally dissipative. Once this result has been obtained, a straightforward application of a general stability theorem due to Kreiss, Ortiz, and Reula implies the results mentioned above. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 37
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5319-5349 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we obtain the orthogonality relations for the supergroup U(m|n), which are remarkably different from the ones for the U(N) case. We extend our results for ordinary representations, obtained some time ago, to the case of complex conjugated and mixed representations. Our results are expressed in terms of the Young tableaux notation for irreducible representations. We use the supersymmetric Harish–Chandra–Itzykson–Zuber integral and the character expansion technique as mathematical tools for deriving these relations. As a byproduct we also obtain closed expressions for the supercharacters and dimensions of some particular irreducible U(m|n) representations. A new way of labeling the U(m|n) irreducible representations in terms of m+n numbers is proposed. Finally, as a corollary of our results, new identities among the dimensions of the irreducible representations of the unitary group U(N) are presented. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 38
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 1-15 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The local formulations of the Markovian interpolating dynamics, which is constrained by the prescribed input-output statistics data, usually utilize strictly positive Feynman–Kac kernels. This implies that the related Markov diffusion processes admit vanishing probability densities only at the boundaries of the spatial volume confining the process. We discuss an extension of the framework to encompass singular potentials and associated non-negative Feynman–Kac-type kernels. It allows us to deal with a class of continuous interpolations admitted by general non-negative solutions of the Schrödinger boundary data problem. The resulting nonstationary stochastic processes are capable of both developing and destroying nodes (zeros) of probability densities in the course of their evolution, also away from the spatial boundaries. This observation conforms with the general mathematical theory (due to M. Nagasawa and R. Aebi) that is based on the notion of multiplicative functionals, extending in turn the well known Doob's h-transformation technique. In view of emphasizing the role of the theory of non-negative solutions of parabolic partial differential equations and the link with "Wiener exclusion" techniques used to evaluate certain Wiener functionals, we give an alternative insight into the issue, that opens a transparent route towards applications.© 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 39
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 387-410 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The recently discovered point-group symmetrized boson representation (SBR) is constructed for the icosahedral group Ih. With the aid of the SBR, succinct algebraic expressions for the irreducible bases and irreducible matrices have been found. Irreducible bases for non-regular representations can be found easily from those of the regular representation without projections. Explicit expressions of the irreducible bases are given for the molecule B12H12 for several important cases. It is shown that, far from being "chaotic" in structure, the 120 irreducible matrices of Ih have a high degree of symmetry in that the 14 400 entries can be reproduced from a few dozen entries according to three rules. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 40
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4561-4569 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A quadratic first integral of the Kepler problem, obtained by Benenti ("Orthogonal separable dynamical systems," 5th International Conference on Differential Geometry and its Applications, 24–28 August 1992, Silesian University at Opava) through separation in elliptic coordinates, is shown to be intimately connected with the pre-quantization of the Kepler manifold, thus acquiring a physical interpretation. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 41
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4576-4593 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new set of nonlinear evolution equations is introduced and studied. These equations derive from a local Lagrangian and are (i) homogeneous and (ii) invariant under the Galilei group or the Lorentz group (including time reversal). Some of them have confined solutions with a solitonlike behavior, irrespective of the space dimension. Moreover, these solutions are shown to be stable against small and localized perturbations. Another family of localized solutions is worked out, and briefly discussed with regard to the elusive integrability properties of the new equations. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 42
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4675-4679 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this note, we prove that the recently proposed new higher-dimensional nonlinear partial differential equation admits the Painlevé property. We briefly discuss the integrability properties of the equation. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 43
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4692-4695 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We define Vandermonde-like determinants and analyze their structure. The resulting scheme is well-suited to achieve a remarkable compactness and transparency in N-soliton formulas or, more generally, in formulas for N-fold Darboux or Bäcklund transformations. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 44
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4763-4770 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We show how moments of stochastic integrals can be expressed explicitly as expectation values of ordinary Lebesgue integrals. This result generalizes the well known relationship for the second moment. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 45
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4815-4831 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An orthogonal function set called distributed Gaussian orthogonal polynomials is constructed from equally spaced Gaussians and the corresponding quadrature is studied. The infinite chain limit of both polynomials and the quadrature is studied and analytical expressions are found for polynomials, quadrature points, weights, and Lagrange functions. The connections to Wannier functions are explored, and a way of constructing Wannier functions from Gaussians is proposed. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 46
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4854-4862 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the Gelfand-Weyl pattern for SU(3) can be uniquely expressed in terms of four non-negative and one positive or negative free integers. This provides an optimal, albeit non-linear, boson calculus for SU(3) in terms of four harmonic oscillators and one planar rotor. (By optimal it is meant that every irreducible representation is obtained once and once only.) Our techniques can be generalized to other groups. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 47
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4872-4881 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An action with n parameters, which generalizes the O(N)−RPN−1 model, is considered in one dimension for general N. We use asymptotic expansion techniques to determine where the model becomes critical and show that for the actions considered there exists a family of hypersurfaces whose asymptotic behavior determines a one-parameter family of new universality classes. They interpolate between the O(N) vector model class and the RPN−1 model class. Furthermore continuum limits are discussed, including the exceptional case N=2. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 48
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3997-4012 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We elucidate the behavior of the operator (p2+m2)1/2−α/r near the critical value α=αc where it ceases to be bounded below, by obtaining a family H(z) of operators which is self-adjoint holomorphic in a domain including all real z〉−αc−αc′, and such that H(αc−α)(α≤αc) is just the operator (p2+m2)1/2−α/r or its Friedrich extension, while H(−αc−α)(αc′〈α〈αc) is another self-adjoint extension. The operators H(z) (z real) are shown to be positive, and to have only discrete spectrum below m. The eigenvalues are then analytic functions of αc−α near α=αc (and become the eigenvalues of a non-self-adjoint operator when α〉αc). We show that these eigenvalues cannot vanish, but that the lowest eigenvalue of H(−αc−α) goes to zero when α→αc′. The L〉0 eigenvalues are analytic in α at α=αc. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 49
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4052-4072 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A nonstandard path space * -measure is constructed to justify the path integral formula for the Dirac equation in two-dimensional space–time. A standard measure as well as a standard path integral is obtained from it. We also show that, even for the Schrödinger equation, for which there is no standard measure appropriate for a path integral, there exists a nonstandard measure to define a * -path integral whose standard part agrees with the ordinary path integral as defined by a limit from time-slice approximant. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 50
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4104-4107 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: By using the assumptions that the entropy must (i) be a continuous function of the probabilities {pi}(pi∈(0,1)∀i), only; (ii) be a monotonic increasing function of the number of states W, in the case of equiprobability; (iii) satisfy the pseudoadditivity relation Sq(A+B)/k=Sq(A)/k+Sq(B)/k+(1−q)Sq(A)Sq(B)/k2 (A and B being two independent systems, q∈R and k a positive constant), and (iv) satisfy the relation Sq({pi})=Sq(pL,pM)+pL qSq({pi/pL})+pM qSq({pi/pM}), where pL+pM=1(pL=∑i=1WLpi and pM=∑i=WL+1Wpi), we prove, along Shannon's lines, that the unique function that satisfies all these properties is the generalized Tsallis entropy Sq=k(1−∑i=1Wpiq)/(q−1). © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 51
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4255-4272 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss relations between the approach of Fokas and Gelfand to immersions on Lie algebras and the theory of soliton surfaces of Sym. We show that many results concerning immersions on Lie algebras can be reduced to or interpreted within the soliton surfaces approach. We present also some new results, including a generalization of the Fokas–Gelfand formula for integrable classes of surfaces in Lie algebras [and, in particular, in (pseudo)-Euclidean n-dim. spaces]. The generalized formula is used to formulate a method of constructing integrable classes of surfaces. As an example we discuss the class of linear Weingarten surfaces defined by the linear relationship between Gaussian and mean curvatures. We construct explicitly a one-parameter family of linear Weingarten surfaces parallel (equidistant) to a given pseudospherical surface. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 52
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4301-4322 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Complete solution of the decomposition problem for finite-dimensional representations π of the BRST algebra A is presented. As shown earlier by the authors [Rev. Math. Phys. 5, 191 (1993)], A coincides with the Lie superalgebra l(1,1). It is proved that an arbitrary π either has the decomposition into a direct sum of irreducible and/or indecomposable representations (IR and IDR, respectively) or has the set of indecomposable subrepresentations that does not admit any classification. All the series of IDR are explicitly described, and all the unclassifiable cases are reduced to definite unsolvable algebraic problems. The absence of classification is established by means of a special computer method, which opens a new possibility to search for unsolvable algebraic problems. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 53
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4363-4388 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A recent paper gave an explicit construction for inducing shift tensors of a compact reductive Lie group from shift tensors of a suitably defined subgroup. The shift tensors were defined on model spaces of holomorphic vector-coherent-state wave functions. In this paper, we use these shift tensors to obtain an algorithm for computing Clebsch–Gordan coefficients. The approach reproduces the known analytical results for SU(2) and gives a simple algorithm for computing SU(3) coefficients. The algorithm is shown to yield analytical expressions for the multiplicity-free SU(3) couplings of type (λ20)⊗(λ10).© 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 54
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 3399-3413 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A class of new non-Abelian gauge theories for vector fields on three manifolds is presented. The theories describe a generalization of three-dimensional Yang–Mills theory featuring a novel nonlinear gauge symmetry and field equations for Lie-algebra-valued vector potential fields. The nonlinear form of the gauge symmetry and field equations relies on the vector cross-product and vector curl operator available only in three dimensions, and makes use of an auxiliary Lie bracket together with the Lie bracket used in Yang–Mills theory. A gauge covariant formulation of the new theories is given which utilizes the covariant derivative and curvature from the geometrical formulation of Yang–Mills theory. Further features of the new theories are discussed. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 55
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6675-6682 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We discuss here the role of different information measures vis-a-vis the maximum entropy-minimum norm method of Baker Jarvis et al. (BJ) for dealing with under-determined inverse linear transforms. It is shown that the structure of the approximate solutions provided by the BJ approach does not depend upon the functional form of the information measure. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 56
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5453-5482 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A closed expression of the Euclidean Wilson-loop functionals is derived for pure Yang–Mills continuum theories with gauge groups SU(N) and U(1) and space-time topologies R1×R1 and R1×S1. (For the U(1) theory, we also consider the S1×S1 topology.) The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all (piecewise analytic) loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder–Schrader axioms for gauge theories is proposed. These axioms are satisfied in the present model. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 57
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5682-5689 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: It is shown that the elliptic Ruijsenaars–Schneider model can be obtained from the cotangent bundle over the two-dimensional current group by means of the Hamiltonian reduction procedure. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 58
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5663-5681 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Quantum gauge theory in the connection representation uses functions of holonomies as configuration observables. Physical observables (gauge and diffeomorphism invariant) are represented in the Hilbert space of physical states; physical states are gauge and diffeomorphism invariant distributions on the space of functions of the holonomies of the edges of a certain family of graphs. Then a family of graphs embedded in the space manifold (satisfying certain properties) induces a representation of the algebra of physical observables. We construct a quantum model from the set of piecewise linear graphs on a piecewise linear manifold, and another manifestly combinatorial model from graphs defined on a sequence of increasingly refined simplicial complexes. Even though the two models are different at the kinematical level, they provide unitarily equivalent representations of the algebra of physical observables in separable Hilbert spaces of physical states (their s-knot basis is countable). Hence, the combinatorial framework is compatible with the usual interpretation of quantum field theory. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 59
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5707-5710 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Classical kinetic theory using Boltzmann statistics shows that the potential distribution φ(r) in the screening cloud surrounding a single test charge at rest within a plasma is governed by a three-dimensional spherically symmetric plasma screening equation ∇2φ(r)=A(exp(+αφ)−exp(−βφ)), r≠0, where A=4πn0ε, α=ε/Te, β=ε/Ti, ε=electronic charge, Te=electron temperature, Ti=ion temperature, and n0=electron and ion density at large distances from the charge Q. In this paper it is proved rigorously that any nontrivial solution of the screening equation must have the following property: If φ(r)=potential at a radial distance r and limr→∞ φ(r)=0, then, for any positive integer n, as r→0 either rnφ→+∞ and rnφ′→−∞ or rnφ→−∞ and rnφ′→+∞. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 60
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5756-5773 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We construct the Miura and auto-Bäcklund transformations for the cKP and cmKP hierarchies. Both the eigenfunctions and the adjoint eigenfunctions of the hierarchies are used to trigger the transformations. The canonical properties of the constructed Miura and auto-Bäcklund transformations are also investigated. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 61
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5774-5791 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the residual gauge freedom within the null quasi-spherical (NQS) gauge for space–times admitting an expanding shear-free null foliation. By constructing the most general NQS coordinates subordinate to such a foliation, we obtain both a clear picture of the geometric nature of the residual coordinate freedom, and an explicit construction of nontrivial NQS metrics representing some well-known space–times, such as Schwarzschild, accelerated Minkowski, and Robinson–Trautman. These examples will be useful in testing numerical evolution codes. The geometric gauge freedom consists of an arbitrary boost and rotation at each coordinate sphere—and this freedom may be used to normalise the coordinate to an "inertial" frame. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 62
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5807-5819 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We describe the analytical extension of certain cylindrical multi-cosmic string metrics to wormhole spacetimes with only one region at spatial infinity, and investigate in detail the geometry of asymptotically Minkowskian wormhole spacetimes generated by one or two cosmic strings. We find that such wormholes tend to lengthen rather than shorten space travel. Possible signatures of these wormholes are briefly discussed. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 63
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5820-5832 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this work, the problem of generation of electromagnetic waves by gravitational wave propagating in external stationary electromagnetic field has been studied. It is shown that the equation of this process can be transformed into much simpler equations for superpotentials of electromagnetic field. The exact solutions for the superpotentials in the case of plane and spherical gravitational waves have been found. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 64
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 582-598 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Octonionic algebra being nonassociative is difficult to manipulate. We introduce left/right octonionic barred operators which enable us to reproduce the associative GL(8,R) group. Extracting the basis of GL(4,C), we establish an interesting connection between the structure of left/right octonionic barred operators and generic 4×4 complex matrices. As an application we give an octonionic representation of the four-dimensional Clifford algebra. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 65
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5944-5959 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A new approach for the analysis of partial differential equations is developed which is characterized by a simultaneous use of higher and conditional symmetries. Higher symmetries of the Schrödinger equation with an arbitrary potential are investigated. Nonlinear determining equations for potentials are solved using reductions to Weierstrass, Painlevé, and Riccati forms. Algebraic properties of higher order symmetry operators are analyzed. Combinations of higher and conditional symmetries are used to generate families of exact solutions of linear and nonlinear Schrödinger equations. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 66
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5960-5967 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An R-matrix pair (R,Z) solving a system of Yang–Baxter-type equations is needed to define a quantized braided (matrix) group [L. Hlavaty, J. Math. Phys. 35, 2560 (1994)]. It is found that a series of such kind of R-matrix pairs (R(n),Z) (n=0,±1,±2,...) can be constructed from a known pair (R,Z), and a series of realizations of the quantized braided (matrix) bialgebras A(R(n),Z) in V(R(n+1))⊗V*(R(n)) can be obtained. Some covariant quantized braided linear algebras and their transformation properties under the braided coactions of the quantized braided group A(R,Z) are considered. Some examples are presented. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 67
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5976-5990 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We give a general method to construct a complete set of linearly independent Casimir operators of a Lie algebra with rank N. For a Casimir operator of degree p, this will be provided by an explicit calculation of its symmetric coefficients gA1,A2,...,Ap. It is seen that these coefficients can be described by some rational polynomials of rank N. These polynomials are also multilinear in Cartan sub-algebra indices taking values from the set I0≡{1,2,...,N}. The crucial point here is that for each degree one needs, in general, more than one polynomial. This in fact is related to an observation that the whole set of symmetric coefficients gA1,A2,...,Ap is decomposed into some sub-sets which are in one-to-one correspondence with these polynomials. We call these sub-sets clusters and introduce some indicators with which we specify different clusters. These indicators determine all the clusters whatever the numerical values of coefficients gA1,A2,...,Ap are. For any degree p, the number of clusters is independent of rank N. This hence allows us to generalize our results to any value of rank N. To specify the general framework, explicit contructions of fourth and fifth order Casimir operators of AN Lie algebras are studied and all the polynomials which specify the numerical value of their coefficients are given explicitly. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 68
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6018-6039 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We define some new algebraic structures, termed colored Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set H, corresponding to some parameter set Q, with the transformations of an algebra isomorphism group G, herein called color group. Such transformations are labeled by some color parameters, taking values in a color set C. We show that various classes of Hopf algebras, such as almost cocommutative, coboundary, quasitriangular, and triangular ones, can be extended into corresponding colored algebraic structures, and that colored quasitriangular Hopf algebras, in particular, are characterized by the existence of a colored universal R-matrix, satisfying the colored Yang–Baxter equation. The present definitions extend those previously introduced by Ohtsuki, which correspond to some substructures in those cases where the color group is Abelian. We apply the new concepts to construct colored quantum universal enveloping algebras of both semisimple and nonsemisimple Lie algebras, considering several examples with fixed or varying parameters. As a by-product, some of the matrix representations of colored universal R-matrices, derived in the present paper, provide new solutions of the colored Yang–Baxter equation, which might be of interest in the context of integrable models. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 69
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4900-4908 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: For a wide class of purely attractive potentials, we obtain a new sufficient condition for the existence of bound states for any angular momentum. Applied to some exactly soluble cases, the condition gives good results as compared to exact results. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 70
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4887-4899 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Quantum mechanical anharmonic oscillators and Hamiltonians for particles in external magnetic fields are related to representations of nilpotent groups. Using this connection the eigenfunctions of the quartic anharmonic oscillator with potential Vα(x)=(α+(x2/2))2 can be used to determine the eigenfunctions of a charged particle in a nonconstant magnetic field, of the form Bz=β2+β3x. The quartic anharmonic oscillator eigenvalues for low-lying states are obtained numerically and a function which interpolates between α(very-much-less-than)0 (a double harmonic oscillator) and α(very-much-greater-than)0 (a harmonic oscillator) is shown to give a good fit to the numerical data. Approximate expressions for the quartic anharmonic oscillator eigenfunctions are then used to get the eigenfunctions for the magnetic field Hamiltonian. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 71
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4914-4928 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A family of hypercomplex numbers is introduced in which multiplication is commutative and members can have up to eight components. In particular, the eight basis elements {E} contain those for ordinary complex numbers, E**=E, as well as new elements where E**=−E; the operation * being the generalization of complex conjugation. This family lends itself to the description of quantum mechanical spin states in that it offers a simple treatment of time reversal, representations with the same conjugation properties as underlying operators, and explicit continuous-angle spherical harmonic functions Zsm(θ,φ) analogous to the Ylm(θ,φ) for orbital angular momentum. The new elements are especially well suited for half-integral spin states, whereas conventional complex numbers remain useful for integral spin states. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 72
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4971-4979 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In thermal field dynamics, thermal states are obtained from restrictions of vacuum states on a doubled field algebra. It is shown that the suitably doubled Fock representations of the Heisenberg algebra do not need to be introduced by hand but can be canonically handed down from deformations of the extended Heisenberg bialgebra. No artificial redefinitions of fields are necessary to obtain the thermal representations and the case of arbitrary dimension is considered from the beginning. Our results support a possibly fundamental role of bialgebra structures in defining a general framework for thermal field dynamics. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 73
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4980-5009 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We define N operators as operators that are already normally ordered with respect to the Friedan–Martinec–Shenker spinor operator. With the help of thus defined N operators, we can give the generating functional of physical vertex operators (GFPVO) of fermionic particles (i.e., in the Ramond sector of the superstring). We also propose GFPVO of bosonic particles (i.e., in the Neveu–Schwarz sector of the superstring), which is simply obtained by supergeneralizing GFPVO in the bosonic string. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 74
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 946-980 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Two-dimensional gravity with torsion is considered assuming Euclidean signature of the metric. A general solution of the Euler–Lagrange equations is found in the conformal gauge. Extremals and geodesics are found and analyzed. All global Euclidean solutions are explicitly constructed and classified. Besides the constant curvature Riemann surfaces of arbitrary genus there are a large number of compact and noncompact surfaces of nonconstant curvature and non-trivial torsion possessing conical singularities. The relation between Lorentz and Euclidean global solutions is analyzed. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 75
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 989-999 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The irreducible, finite-dimensional representations of the graded algebras osp(j,2) (j=1,2,3) are expressed in terms of differential operators. Some quantum deformations of these algebras are shown to admit similar kinds of representations. These are formulated in terms of finite difference operators. The results are discussed in the framework of the quasi-exactly solvable equations. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 76
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6061-6071 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We have expanded the Schrödinger hydrogen-like wave functions ψnlm of the discrete spectrum, with respect to the inverse principal quantum number n−1, for fixed values of the quantum numbers l,m. The Laguerre polynomials Lnα(x/n) are expanded with respect to n−1 into a sum of Bessel functions multiplied by powers rk of the distance from the origin. The coefficients of the expansion are a family of polynomials sq,k(l) of the variable l, which can be computed with a recursion formula. The development, which converges rapidly, can be truncated after a few terms, even for low levels n. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 77
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5143-5152 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study a model of polymers with random charges; the possible shapes of the polymer are represented by the sample paths of a Brownian motion, and the cumulative charge distribution along a polymer is modeled by a realization of a Brownian bridge. Charges interact through a general positive-definite two-body potential. We study the infinite volume free energy density for a fixed realization of the Brownian motion; this is not self-averaging, but shows on the contrary a sample dependence through the local time of the Brownian motion. We obtain an explicit series representation for the free energy density; this has a finite radius of convergence, but the free energy is nevertheless analytic in the inverse temperature in the physical domain. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 78
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5167-5182 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: This paper focuses a relation between Adler–Kostant–Symes (AKS) theory applied to Fordy–Kulish scheme and bi-Hamiltonian manifolds. The spirit of this paper is closely related to Casati–Magri–Pedroni work on Hamiltonian formulation of the KP equation. Here the KdV equation is deduced via the superposition of the Fordy–Kulish scheme and AKS construction on the underlying current algebra C∞(S1,g⊗C[[λ]]). This method is different from the Drinfeld–Sokolov reduction method. It is known that AKS construction is endowed with bi-Hamiltonian structure. In this paper we show that if one applies the Fordy–Kulish construction in the Adler–Kostant–Symes scheme to construct an integrable equation associated with symmetric spaces then this superposition method becomes closer to Casati–Magri–Pedroni's bi-Hamiltonian method of the KP equation. We also add a self-contained Appendix, where we establish a direct relation between AKS scheme and bi-Hamiltonian methods. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 79
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6214-6229 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The low energy effective theory of planar QED with a non-local four-fermion interaction including Gross–Neveu and Thirring terms is shown to be equivalent to a Chern–Simons–Higgs model of special characteristics. We study the restrictions imposed by self-duality and supersymmetry, finding in both cases a plethora of (some new) topological and non-topological solitons. The non-relativistic limit of our model generalizes the effective Ginzburg–Landau theory for the fractional quantum Hall effect such that our solitons would be the relativistic version of quasi-particle and quasi-hole excitations. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 80
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6265-6280 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A consistent procedure for regularization of divergences and for subsequent renormalization of the string tension is proposed in the framework of the one-loop calculation of the interquark potential generated by the Polyakov–Kleinert string. In this way, a justification of the formal treatment of divergences by analytic continuation of the Riemann and Epstein–Hurwitz zeta functions is given. A spectral representation for the renormalized string energy at zero temperature is derived, which enables one to find the Casimir energy in this string model at nonzero temperature very easy. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 81
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 6281-6286 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study supersymmetric quantum mechanics on SO(n) to examine Witten's Morse theory concretely. We give a simple instanton picture of the de Rham cohomology of SO(n). We show how the reflection symmetries of the theory select the true vacuums. The number of selected vacuums agrees with the de Rham cohomology of SO(n), at least for n≤5. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 82
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 226-246 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The MKdV equation of normal dispersion with non-vanishing boundary value is solved by the inverse scattering transform method. An affine parameter is introduced to avoid double-valued functions of the usual spectral parameter. In terms of it the inverse scattering transform is performed and the inverse scattering equation of Zakharov–Shabat form as well as of Marchenko form is derived. Dark multi-soliton solutions are found formally by means of the Binet–Cauchy formula. The asymptotic behaviors in the limits of |t|→∞ are derived as expected. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 83
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 247-254 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The choice of a finitely supported distribution is viewed as a degenerate bilinear form on the polynomials in the spectral parameter z and the matrix representing multiplication by z in terms of an orthogonal basis is constructed. It is then shown that the same induced time dependence for finitely supported distributions which gives the ith KP flow under the dual isomorphism induces the ith flow of the Toda hierarchy on the matrix. The corresponding solution is an N particle, finite, nonperiodic Toda solution where N is the cardinality of the support of c plus the sum of the orders of the highest derivative taken at each point. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 84
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 267-282 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The concentration p(x,y) of particles moving by diffusion and advection or drift is analyzed. The motion is impeded by an impenetrable strip that is parallel to the z axis. It is assumed that p satisfies the linear advection-diffusion equation with a boundary condition on the strip. It is also assumed that p=1 at infinity. This problem is solved asymptotically for vL/D(very-much-greater-than)1, where v is the drift velocity, D is the diffusion coefficient, and 2L is the strip width. It is found that p is large on the side of the strip facing the incident flow, that p is small in the shadow behind the strip, and that p is nearly constant elsewhere. The case of a strip normal to the incident flow is rather different from that of a strip oblique to the flow. Methods of asymptotic analysis are used. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 85
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 321-329 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The separation of variables for some constrained flows of soliton hierarchies are shown. The Lax matrix and r-matrix (either constant or dynamical type) are used to construct the separation variables and separation equation for the constrained flows. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 86
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 30-38 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We study the topological mass generation in the 4 dimensional non-Abelian gauge theory, which is the extension of Allen et al.'s work in the Abelian theory. It is crucial to introduce a one form auxiliary field in constructing the gauge invariant non-Abelian action which contains both the one form vector gauge field A and the two form antisymmetric tensor field B. As in the Abelian case, the topological coupling mB∧F, where F is the field strength of A, makes the transmutation among A and B possible, and consequently we see that the gauge field becomes massive. We find the BRST/anti-BRST transformation rule using the horizontality condition, and construct a BRST/anti-BRST invariant quantum action. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 87
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 350-368 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A complete description of dynamics of compact locally homogeneous universes is given, which, in particular, includes explicit calculations of Teichmüller deformations and careful counting of dynamical degrees of freedom. We regard each of the universes as a simply connected four-dimensional space–time with identifications by the action of a discrete subgroup of the isometry group. We then reduce the identifications defined by the space–time isometries to ones in a homogeneous section, and find a condition that such spatial identifications must satisfy. This is essential for explicit construction of compact homogeneous universes. Some examples are demonstrated for Bianchi II, VI0, VII0, and I universal covers. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 88
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 39-48 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: The high-energy-limit of the scattering operator for multidimensional relativistic dynamics, including a Dirac particle in an electromagnetic field, is investigated by using time-dependent, geometrical methods. This yields a reconstruction formula, by which the field can be obtained uniquely from scattering data. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 89
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 411-433 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We apply the method of the central extensions introduced by Reshetikhin and Semenov–Tian–Shansky to the case of the Perk–Shultz model. By using the method proposed by Frenkel–Ding, we establish the Drinfeld constructions of the quantum affine superalgebra Uq(gl(m(circumflex)/n)). © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 90
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 466-475 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of the new algebra for the statistics of quanta are analyzed and discussed. The concept of statistical transmutation between bosons and fermions is introduced. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 91
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 524-534 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We define noncommutative Krein algebras and extend the classical Krein duality for compact groups to compact quantum groups. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 92
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 484-500 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Mathematical physicists are familiar with a large set of tools designed for dealing with linear operators, which are so common in both the classical and quantum theories; but many of those tools are useless with nonlinear equations of motion. In this work a general algebra and calculus is developed for working with nonlinear operators: The basic new tool being the "slash product," defined by A(1+εB) =A+εA/B+O(ε2). For a generic time development equation, the propagator is constructed and then there follows the formal version of time dependent perturbation theory, in remarkable similarity to the linear situation. A nonperturbative approximation scheme capable of producing high accuracy computations, previously developed for linear operators, is shown to be applicable as well in the nonlinear domain. A number of auxiliary mathematical properties and examples are given. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 93
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 535-543 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Aspects of the algebraic structure and representation theory of the quantum affine superalgebras with symmetrizable Cartan matrices are studied. The irreducible integrable highest weight representations are classified, and shown to be deformations of their classical counterparts. It is also shown that Jimbo-type quantum affine superalgebras can be obtained by deforming universal enveloping algebras of ordinary (i.e., nongraded) affine algebras supplemented by certain parity operators. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 94
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5739-5755 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: A Lax representation for the equations of the coupled Korteveg–de Vries (cKdV) hierarchy with sources is derived from the energy-dependent Schrödinger spectral problem. It is proved that each stationary flow of the cKdV hierarchy with sources can be reparametrized as a system of Newton equations with velocity-independent forces. These Newton systems have a Lagrangian formulation and are completely integrable. The developed decomposition techniques lead to construction of new infinite families of integrable classical mechanical systems. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 95
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 4951-4970 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Using connection with quantum field theory, the infinitesimal covariant Abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding wave equations shown. Because of the three-dimensional projection operation, these transformation laws are interaction dependent. Simplifications occur for local potentials, which result, in each formal order of perturbation theory, from the infra-red leading effects of multiphoton exchange diagrams. In this case, the finite gauge transformation can explicitly be represented, with a suitable approximation and up to a multiplicative factor, by a momentum dependent unitary operator that acts in x-space as a local dilatation operator. The latter is utilized to reconstruct from the Feynman gauge the potentials in other linear covariant gauges. The resulting effective potential of the final Pauli–Schrödinger type eigenvalue equation has the gauge invariant attractive singularity α2/r2, leading to a gauge invariant critical coupling constant αc=1/2. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 96
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5127-5142 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: An expression is derived for the Casimir free energy of a spherical cavity in a polar dielectric medium at finite temperature. In the process of the derivation the general problem of infinities and their renormalization in calculations of Casimir forces is analyzed. It is shown that the renormalized Casimir free energy has a minimum at a finite mesoscopic value of the cavity radius R=RMinCas, with the repulsion for R〈RMinCas and the attraction for R≥RMinCas. The implications of this result for the explanation of cavitation effects are discussed. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 97
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5153-5166 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper we consider dissipative fluxes as well as the conserved variables as a set of independent variables characterizing the thermodynamic state of a nonequilibrium system. We then generalize the traditional internal energy balance equation so that contributions due to the dissipative fluxes are taken into consideration. On the other hand, the second law is formulated in terms of Caratheodory's inaccessibility condition in conjunction with the assumption that dissipative energy associated with internal work arising from irreversible processes be semipositive definite. We show that the second law formulated in this manner is equivalent to Kelvin's principle and Clausius's principle, as well as Clausius's inequality. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 98
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 5183-5189 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: Hierarchies of evolution equations associated with certain symmetric spaces are presented. Main examples of such symmetric spaces are Hermitian symmetric spaces and the obtained evolution equations include generalized nonlinear Schrödinger equations. Those results are obtained by extending the Lie algebra in the Ablowitz–Kaup–Newell–Segur scheme from sl(2,C) to more general one. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 99
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 283-291 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: We derive solutions of general Wronskian form for the (vector) constrained KP hierarchies. As one explicit example we discuss rational solutions. In order to introduce our method, we give a direct, elementary proof of the existence of Wronskian solutions for the l-modified KP hierarchies (l:0,1,...). © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
  • 100
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    Journal of Mathematical Physics 38 (1997), S. 292-299 
    ISSN: 1089-7658
    Source: AIP Digital Archive
    Topics: Mathematics , Physics
    Notes: In this paper, we investigate the integrability aspects of the (2+1) dimensional coupled long dispersive wave (2LDW) equation introduced recently by Chakravarty, Kent, and Newman and establish its Painlevé (P-) property. We then deduce its bilinear form from the P analysis and use it to construct wave type solutions for the field variables. We then identify line solitons for the composite field variable "qr" which eventually helps to bring out the peculiar localization behavior of the system by generating localized structures (dromions) for the composite field from out of only one ghost soliton driving the boundary. We have then extended this analysis to multidromion solutions. © 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
    Location Call Number Expected Availability
    BibTip Others were also interested in ...
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...