bluuebunny/crossref_metadata_2025 huggingface dataset:
On singularity theorems and curvature growth
Authors: Szabados L. B.
Published: July 2002

It is shown that the proofs of a series of classical singularity theorems of general relativity can be modified such that these theorems also state the maximality of the incomplete nonspacelike geodesics. Since along maximal incomplete nonspacelike geodesics with affine parameter u certain parts of the tidal curvature cannot blow up faster than (ū−u)−2, where ū is the parameter value until which the geodesics cannot be extended, the classical singularity theorems do restrict the behavior of the curvature.
The Dirac equation in a non-Riemannian manifold. I. An analysis using the complex algebra
Authors: Marques S.
Published: July 2002

The Dirac wave equation is obtained in the non-Riemannian manifold of the Einstein–Schrödinger nonsymmetric theory. A new internal connection is determined in terms of complex vierbeins, which shows the coupling of the electromagnetic potential with gravity in the presence of a spin- 1/2 field.
Global anomalies and algebraic topology
Authors: Lundell Albert T. , Tosa Yasunari
Published: July 2002

The algebraic topology aspect of the global pure gauge anomaly calculation is investigated. In particular, the use of a cohomology sequence clarifies the method initiated by Witten [Nucl. Phys. 223, 422, 433 (1983)] and Elitzur and Nair [Nucl. Phys. B 243, 205 (1984)]. Examples in SU(N), Sp(N), and SO(N) are discussed.
Multivariable continuous Hahn polynomials
Authors: Tratnik M. V.
Published: July 2002

A multivariable generalization of the continuous Hahn polynomials is presented; it is a (4p+4)-parameter family, where p is the number of variables. It is shown that they are orthogonal with respect to subspaces of equal degree and biorthogonal within a given subspace. In the simplest case the multivariable weight function takes the form sech[π(x1+x2+⋅⋅⋅+xp)]sech(πx1) sech(πx2)⋅⋅⋅sech(πxp).
On the harmonic radius and the capacity of an inverse ellipsoid
Authors: Dassios George
Published: July 2002

It is shown that the capacity of a body, obtained by Kelvin inversion, is equal to the inverse of the harmonic radius of the image domain with respect to the center of inversion. Using the monotonicity of the harmonic radius and an appropriate isoperimetric inequality, lower and upper estimates for the capacity of an inverse ellipsoid are obtained.
Infinite number of conserved quantities and extended conformal algebra in the Thirring model
Authors: Inoue Kazuhiko , Odaka Kazuhiko , Omote Minoru
Published: July 2002

It is shown that the Thirring model has an infinite number of local conserved quantities, explicit forms of which are presented. These quantities are shown to be expressed in terms of scattering parameters. It will be shown that in this model there exists an extended symmetry algebra that includes the Virasoro algebra as its subalgebra.
Noncanonical groups of transformations, anomalies, and cohomology
Authors: Cariñena J. F. , Ibort Luis A.
Published: July 2002

Two cohomology classes associated to groups of transformations (symplectic or not) of Hamiltonian and Lagrangian systems are studied. A geometrical interpretation of the family of cocycles arising from a class of nonsymplectic actions is given in terms of the Poisson structure of the phase space of the system. These ideas are used to study nongauge (i.e., anomalous) groups of transformations of (locally or globally defined) Lagrangian systems. In particular, well-known results about the magnetic monopole system are described in this context and some hints relating Yang–Mills anomalies with nonsymplectic groups of transformations are given.
Algebraic construction of partition functions for c<1 minimal conformal field theories
Authors: Suranyi P.
Published: July 2002

Partition functions with periodic and twisted boundary conditions are constructed for c<1 minimal conformal field theories using the modular transformation properties of the characters of the Virasoro algebra alone. The construction helps to clarify the connection between twisted partition functions of c<1 and periodic Gaussian conformal field theories.
A general representation for the effective dielectric constant of a composite
Authors: Dell’Antonio G. F. , Nesi V.
Published: July 2002

In its dependence on the dielectric constants εk of its homogeneous components, the effective dielectric constant ε* of a composite is a function analytic in a domain Ω. Some relevant results about the effective dielectric constant are collected, including the form of Ω, and then a general representation of ε* as an analytic function is given. In this representation, the dependence on the geometry is separated from the dependence on the ε′k’s.
A simple model of asymmetry in Wien dissociation of a weak electrolyte
Authors: McIlroy Douglas K.
Published: July 2002

A simple model of Wien dissociation of a weak electrolyte is proposed in which the relative increase in the dissociation constant, K(X)/K(0), where X is the uniform applied electric field, is asymmetric with respect to the direction of X. The model assumes that one ionic species of the electrolyte is mobile but that the other is fixed in a crystal or liquid crystal lattice. The asymmetry of K(X)/K(0) is shown to arise because of the resulting asymmetry in the boundary condition on the distribution function describing pairs of associated ions of the electrolyte at the distance of closest approach of the ions. Solutions for the association rate constant A and K(X)/K(0) of the model electrolyte are obtained by solving the partial differential equation governing the streamfunctions that describe the two ionic states of the electrolyte.
Affine collineations in space-time
Authors: Hall G. S. , da Costa J.
Published: July 2002

The existence of affine collineations in space-time is discussed and the types of space-time admitting proper affine collineations is displayed. The close connection between such space-times and their holonomy structure and local decomposability is established. Affine collineations with fixed points are also considered as is the problem of extending local affine collineations to the whole of space-time.
Birkhoff and Taub theorems generalized to metrics with conformal symmetries
Authors: zhi-quan Kuang , can-bin Liang
Published: July 2002

The Birkhoff theorem for spherically symmetric vacuum solutions and the Taub theorem for plane-symmetric vacuum solutions are both generalized to vacuum solutions with conformal symmetries, i.e., it is proved in this paper that any conformally spherically (resp. plane-) symmetric vacuum solution to Einstein equations must be the Schwarzschild (resp. either Taub–Kasner or flat) solution.
Integral-spin fields on (3+2)-de Sitter space
Authors: Gazeau Jean-Pierre , Hans Michel
Published: July 2002

Nowadays, (3+2)-de Sitter (or anti-de Sitter space) appears as a very attractive possibility at several levels of theoretical physics. The Wigner definition of an elementary system as associated to a unitary irreducible representation of the Poincaré group may be extended to the de Sitter group SO(3,2) [or ∼(SO(3,2))] without great difficulty. The constant curvature, as small as it can be, is a natural candidate to play the role of a regularization parameter with respect to the flat-space limit. Massless particles in (3+2)-de Sitter theory are composite (singletons). On the other hand, supergravity theories necessitate a (large) constant curvature. The content of this paper is group theoretical. It attempts to continue the ‘‘à la Wigner’’ program for SO(3,2), already largely broached by Fronsdal. Three recurrence formulas are presented. They permit one to build up the carrier states for representations with arbitrary integral spin. Two of them are valid for the ‘‘massive’’ representations whereas the third one is applicable to the indecomposable massless representations. In addition, other presumably indecomposable, though nonphysical, representations are studied, in relation to the existence of ‘‘generalized’’ gauge fields and divergences. The recurrence formulas also allow one to build up the invariant two-point functions or homogeneous propagators. Hence it becomes possible to examine the problems of light-cone propagation and ‘‘reverberation’’ into the light cone and to make the following assertion: for a certain choice of the gauge-fixing parameters, the massless states with arbitrary spin propagate only on the light cone and whatever gauge one chooses their physical parts propagate on the light cone.
Analysis and solution of a nonlinear second-order differential equation through rescaling and through a dynamical point of view
Authors: Leach P. G. L. , Feix M. R. , Bouquet S.
Published: July 2002

The solutions of the equation ÿ+yẏ+βy3=0, where β is a free parameter, are investigated. For β= (1)/(9) the equation is linearizable through an eight-parameter symmetry group and is completely integrable. For β≠ (1)/(9) only two symmetries subsist, but through a dynamical description the analytical asymptotic solutions and their behavior are given according to the value of β and according to the initial conditions.
A generalization of manifolds as space-time models
Authors: Gruszczak J. , Heller M. , Multarzyński P.
Published: July 2002

A smooth manifold can be defined as the pair (M, C), where C is a family of functions on a set M, satisfying suitable axioms. The manifold concept can be easily generalized by dropping the axiom ensuring the manifold to be locally diffeomorphic to Rn. The resulting concept, the so-called d-space, turns out to be a geometrically workable structure. The existence of the pseudo-Riemannian structure (both Riemannian and Lorentz) on d-spaces is discussed. It is proposed to model the physical space-time by a d-space rather than by a manifold. In some quantum gravity situations space-time may still be a d-space but already not a manifold.
Infinitesimal operators of group representations in noncanonical bases
Authors: Klimyk A. U. , Kachurik I. I.
Published: July 2002

Explicit expressions are obtained for the action of the infinitesimal operators of some classes of representations of the groups U(p+q), SO(p+q), SU(n), Sp(n), SL(n,R), and GL(n,C) in the bases that differ from the Gel’fand-Zetlin ones.
On the power-series construction of bound states. I. The energies as zeros of the infinite Hill determinants
Authors: Znojil M.
Published: July 2002

For a broad class of potentials, we show that the nonvariational (so-called Hill-determinant) intuitive identification of binding energies with zeros of certain infinite determinants may be given a rigorous mathematical foundation. The essence of the construction lies in an appropriate restriction of the class of the admissible Ansätze. This eliminates the undesirable confluence of the physical and unphysical components of ψ(r) that may take place in the general case.
Spin-3/2 perturbations of algebraically special solutions of the Einstein–Maxwell equations
Authors: Torres del Castillo G. F.
Published: July 2002

The equations for the spin- (3)/(2) perturbations of the solutions of the Einstein–Maxwell equations given by the linearized O(2) extended supergravity are considered. It is shown that for each geodetic and shear-free principal null direction of the background electromagnetic field there exists a gauge-invariant quantity made out of the spin- (3)/(2) field that satisfies a decoupled equation. In the case of type-D solutions with a nonsingular aligned electromagnetic field it is explicitly shown that the decoupled equations associated with the two principal null directions admit separable solutions and the separated functions obey certain differential relations.
Multivariable Wilson polynomials
Authors: Tratnik M. V.
Published: July 2002

A multivariable biorthogonal generalization of the Wilson polynomials is presented. These are four distinct families, which in a special case occur in two complex conjugate pairs, that satisfy four biorthogonality relations among them. An interesting limit case is the multivariable continuous dual Hahn polynomials.
Large-N iterative solution of the Dirac equation
Authors: Atag Satilmis
Published: July 2002

The large-N iterative technique proposed recently by Chatterjee [J. Math. Phys. 27, 2331 (1986)] is employed to solve the Dirac equation for a spherically symmetric potential. It is shown that the exact results are obtained in the case of the Coulomb potential.
Integrable dynamical systems with hierarchy. I. Formulation
Authors: Okubo Susumu
Published: July 2002

It is shown that any model with the zero (generalized) Nijenhuis tensor, under some additional assumptions, will automatically satisfy the hierarchy equation with an infinite number of conserved quantities in involution. Especially, if there is a dual symplectic structure with zero Nijenhuis tensor, then there exist infinite numbers of Poisson brackets and of Lagrangians giving the same equation of motion. Toda lattice is one such example
On the recurrence relations, summations, and integrations of finite rotation matrix elements
Authors: Lai Shan-Tao , Chiu Ying-Nan
Published: July 2002

In this work a number of recurrence relations of rotation matrix elements are derived and a method is proposed to evaluate some useful summations and integrations involving rotation matrix elements. Examples of applications of these in molecular spectroscopy and in chemical physics are also presented.
Classical solutions of a nonrelativistic model exhibiting spontaneous symmetry breakdown
Authors: Spehler D. , Marques G. C.
Published: July 2002

The inverse scattering method is employed in order to obtain solutions of a nonrelativistic and nonlinear model exhibiting spontaneous breakdown of symmetry. Explicit expressions for multiple-soliton solutions are developed. The one-soliton solution exhibits some interesting properties. In particular, they interpolate between two different vacua of the theory differing by a phase related to the soliton velocity.
Covariant factor ordering of gauge systems using ghost variables. I. Constraint rescaling
Authors: McMullan D. , Paterson J.
Published: July 2002

A dynamical consequence of local gauge invariance is the existence of first class constraints that are linear in momenta. By studying finite-dimensional systems with this constraint structure one finds that, in order to quantize such theories, it is not enough to find a consistent factor ordering, rather, one must also maintain covariance under rescaling of the constraints, point transformations, and weak changes to the observables. Within the standard Dirac constraint formalism, covariance under these symmetries obstructs a full Hilbert space description. It is shown how this difficulty may be overcome by the use of ghost variables. In the present paper, I, an analysis of the Becchi–Rouet–Stora–Tyutin (BRST) structure of such systems is presented. The constraint rescaling is shown to be implemented by a canonical transformation on the super phase space that can be evaluated to a unitary transformation on a suitably defined state space. In the following paper, II [J. Math. Phys. 30, xxx (1989)] these techniques are used to solve the constraint factor ordering problem.
Covariant factor ordering of gauge systems using ghost variables. II. States and observables
Authors: McMullan D. , Paterson J.
Published: July 2002

The aim of any constraint quantization procedure is to be able to recover the physical content of a system after quantizing on the extended state space (which will include both physical and unphysical configurations). Within the Dirac approach to such problems there is no guarantee that the resulting quantum theory will be equivalent to the quantized physical theory and one has to be content with a case by case analysis of its applicability. In this paper it is shown that for finite-dimensional systems with first class constraints linear in momenta, invariance under constraint rescaling and point transformations is sufficient to ensure a consistent quantization. As discussed in the preceding paper [J. Math. Phys. 30, XXX (1989)], in order to become a manifest symmetry, constraint rescaling requires ghost variables. It is now shown how the associated BRST charge is constructed and how it is used to describe the physical states and observables in the constrained system. The extension of this construction to more general constrained systems is also discussed.
Supersymmetric embedding of a model of a quantum harmonic oscillator interacting with infinitely many bosons
Authors: Arai Asao
Published: July 2002

A mathematically rigorous analysis is given on supersymmetric embedding of a model of a one-dimensional quantum harmonic oscillator interacting with infinitely many bosons moving in the s-dimensional space Rs. The model is exactly soluble. By a rigorous explicit construction of supersymmetric quantum field theories, it was proven that the Hamiltonian of the model is supersymmetrically embeddable if it is non-negative. The index of the Dirac–Kähler-type operators associated with the supercharges of the supersymmetric quantum field theories is computed.
Fierz identities in ten-dimensional superspace
Authors: Naito Seichi , Nishimoto Masahiro , Hirokane Tohru
Published: July 2002

All SO(1,9)-irreducible bases composed of tensors and tensor–spinors, which span the whole space up to 16th-order polynomials in θ, θj ( j=1–16) being Majorana–Weyl spinors of SO(1,9), are explicitly constructed. Any superfield φ(xm,θ) in ten-dimensional superspace can be expanded by these bases, expansion coefficients being ordinary tensor and tensor–spinor fields. Then explicit formulas are given for φ(x,θ)Φ(x,θ) (Φ being another superfield) up to sixth order in θ in terms of ordinary fields, while those for (∂/∂θ̄)φ(x,θ) and Γmθ ∂mφ(x,θ) are given up to eighth order in θ.
Baker–Campbell–Hausdorff relations for the orthosymplectic group OSP(1/2)
Authors: Fatyga B. W. , Kostelecký V. Alan , Truax D. Rodney
Published: July 2002

Baker–Campbell–Hausdorff relations are presented for the connected supergroup associated with the orthosymplectic algebra osp(1/2).
Classical relativistic spinning particles
Authors: Rivas Martín
Published: July 2002

An elementary particle is defined as a mechanical system whose kinematical space is a homogeneous space of the Poincaré group. Lagrangians for describing these systems depend on higher-order derivatives and some of them are analyzed. For bradyons the Lagrangian depends on the acceleration and angular velocity of the particle and is characterized by two parameters m and s, the rest mass and absolute value of spin, respectively. In general the spin is of kinematical nature, related to the rotation and internal orbital motion of the system. Two different kinds of bradyons appear according to the spin structure. One has a spin related to the generalized acceleration. Photons are massless particles with spin lying along the direction of motion and energy hν, where ν is the frequency of its rotational motion. Particles moving in circles with velocity c in their center of mass frame are also predicted, showing a Dirac-type Hamiltonian. There also appear particles with tachyonic orbital motion whose center of mass is bradyonic motion. Transformation properties under space and time reversal are also analyzed.
Shear-free normal cosmological models
Authors: Krasiński Andrzej
Published: July 2002

Shear-free normal cosmological models are the perfect fluid solutions of Einstein’s equations in which rotation and shear vanish, and which are not static [they were all found by A. Barnes, Gen. Relativ. Gravit. 4, 105 (1973)]. They are either spherically, plane, or hyperbolically symmetric. Their symmetries are discussed in various coordinate systems and related to the conformal group of the three-dimensional flat space. A coordinate representation is introduced which unites all three cases into a single two-parameter family. The limiting transitions to the Friedman–Lemaitre–Robertson–Walker (FLRW) models and to the Schwarzschild–de Sitter-like solutions are presented.
Teukolsky–Starobinsky identities for arbitrary spin
Authors: Kalnins E. G. , Miller W. , Williams G. C.
Published: July 2002

The Teukolsky–Starobinsky identities are proven for arbitrary spin s. A pair of covariant equations are given that admit solutions in terms of Teukolsky functions for general s. The method of proof is shown to extend to the general class of space-times considered by Torres del Castillo [J. Math. Phys. 29, 2078 (1988)].
Generating relations for reducing matrices. IV. Subduced representations
Authors: Kotzev J. N. , Peev M. K. , Aroyo M. I. , Dirl R. , Kasperkovitz P.
Published: July 2002

A subduced representation DA↓GB is a (co)representation of the group GB obtained by restricting the (co)representation DA of a supergroup GA to the elements of GB. A systematic and efficient method for calculating the matrices needed for the decomposition of DA↓GB into irreducible constituents is discussed in this paper where the auxiliary group approach developed previously [J. Math. Phys. 27, 37, 2236 (1986); 28, 1947 (1987)] is adopted to the present problem.
Curvature form and solutions of nonlinear models
Authors: Tanaka K.
Published: July 2002

Several equations of motions of bosonic two-dimensional nonlinear models are noted that emerge from the requirement that the curvature two-form Ω=0. This information is used to obtain solutions of these equations.
On the spectra of hypoelliptic operators in R 2
Authors: Brenner Terence
Published: July 2002

Sufficient conditions are given for the spectra and essential spectra of certain classes of operators in R2 to be contained in an interval of the form [d,∞).
Gauge field systems on CPn
Authors: Ma Zhong-Qi , Tchrakian D. H.
Published: July 2002

SU(n)×U(1) gauge fields on CPn are constructed in a gauge where the connection is expressed in so(n−1). The (anti)self-duality relations satisfied by these fields are given, and the 2n-dimensional gauge field systems whose Bogomolnyi bounds are saturated by these are discussed. Other gauge field systems, not endowed with topological lower bounds, are also discussed. The analogy between all these gauge field systems on CPn and S2n is highlighted.
Classification of all star and grade star irreps of gl(n‖1)
Authors: Gould M. D. , Zhang R. B.
Published: July 2002

A method for inducing nondegenerate forms on irreducible gl(m‖n) modules that implies some general results on star and grade star representations is investigated. These results are applied to obtain a complete classification, in terms of highest weights, of the irreducible star and grade star representations of gl(n‖1). It is demonstrated that while gl(n‖1) admits a large class of star representations the irreducible grade star representations are comparatively rare. Moreover, for n≠2 all grade star irreducible representations are also star representations and, for n>2, are atypical. The superalgebra gl(2‖1) proves to be a special case and admits a two-parameter family of four-dimensional typical grade star irreducible representations that are not star representations. In particular, typical grade star irreducible representations of gl(n‖1) exist only for n=1,2.
Adjoint division algebras and SU(3)
Authors: Dixon Geoffrey
Published: July 2002

Adjoint algebras are constructed for the division algebras and their tensor products and for the full tensor product, adjoint idempotents that project lepton and quark color vectors, are also constructed.
A comparison of solution generating techniques for the self-dual Yang–Mills equations. II
Authors: Tafel Jacek
Published: July 2002

It is shown that Bäcklund transformations related to the Yang formulation of the self-dual Yang–Mills equations reduce to Zakharov–Shabat transformations when the gauge group is GL(2,C).
Similarity transformations of irreducible corepresentations in Wigner canonical form
Authors: Kasperkovitz P. , Peev M. K.
Published: July 2002

The general form of the matrices that transform an irreducible corepresentation (coirrep) into an equivalent one, where both representations are assumed to be in the form proposed by Wigner, is analyzed for the three types of coirreps. In addition, the relation of these transformations to inner automorphisms of the corresponding group algebras is clarified.
Bäcklund transformations, soliton solutions and wave functions of Kaup–Newell and Wadati–Konno–Ichikawa systems
Authors: Rangwala Abbas A. , Rao Jyoti A.
Published: July 2002

Using the Bargmann–Darboux method, the Bäcklund transformations, n-soliton solutions and corresponding wave functions of the Kaup–Newell and Wadati–Konno–Ichikawa systems are obtained. These results culminate in an algebraic recursive procedure for the determination of multisoliton solutions and their wave functions of the derivative and mixed derivative nonlinear Schrödinger equations iQt+Qxx∓iα(‖Q‖2Q)x ±β‖Q‖2Q=0, α>0, β≥0.
Solution of the multivariate Fokker–Planck equation by using a maximum path entropy principle
Authors: Jumarie Guy
Published: July 2002

This paper proposes an approach via the maximum entropy principle in order to determine the nonstationary solutions of the Fokker–Planck equation with time varying coefficients. The constraints are not the state moments (as usual) but their dynamic equations. The maximum entropy principle herein utilized is a slight extension of Jaynes’ principle, which involves the ‘‘path entropy’’ of the stochastic process.
The potential group approach and hypergeometric differential equations
Authors: Wu J. , Alhassid Y.
Published: July 2002

This paper proposes a generalized realization of the potential groups SO(2,1) and SO(2,2) to describe the confluent hypergeometric and the hypergeometric equations, respectively. It implies that the classes of Schrödinger equations with solvable potentials whose analytical solutions are related to the confluent hypergeometric and the hypergeometric functions can be realized in terms of the above group structure.
Inflation in a spatially closed anisotropic universe
Authors: Ponce de León J.
Published: July 2002

The effects of shear on the occurrence of inflation are studied on the basis of a simple model for a spatially closed universe which enters an inflationary era. It is assumed that the universe enters a vacuum-dominated phase in an abrupt transition that occurs everywhere at the same time. The space-time geometries, before and after the phase transition, are matched to each other via the Lichnerowicz junction conditions. The Einstein field equations are solved exactly for a viscous universe of the Kantowski–Sachs type. It is found that the inclusion of (positive) shear retards the occurrence of the vacuum phase transition. The magnitude of this effect depends on the mass of the universe at the time of the phase transition. For a universe with a mass of about 10 kg (which is a value usually associated with the mass of the region from which our universe originated), it is found that the inclusion of shear does not really have a large effect on the time at which the vacuum phase transition occurs. The generality of the results is also discussed.
Inhomogeneous multidimensional Epstein zeta functions
Authors: Kirsten Klaus
Published: July 2002

The pole structure of the inhomogeneous multidimensional Epstein zeta function, Em2N(s; a1,...,aN)=∑∞n1,...,nN =1 (a1n21+⋅⋅⋅+aNn2N +m2)−s, is determined using heat-kernel techniques. The poles of Em2N(s; a1,...,aN) are found to be s=N/2; (N−1)/2;...; (1)/(2) ; −(2l+1)/2, l∈ 𝒩0. Furthermore, their residues and Em2N(−p; a1,...,aN), p∈ 𝒩0, are given explicitly. These results are used to find the high-temperature expansion of the Helmholtz free-energy of a massive spin-0 and spin- (1)/(2) gas subject to Dirichlet boundary conditions on hypercuboids in a flat n-dimensional space-time.
Contraction of Lie algebra representations
Authors: Weimar-Woods Evelyn
Published: July 2002

Motivated by an example of Inönü and Wigner, a general procedure for the contraction of irreducible unitary representations of semisimple compact Lie algebras is given. In this situation, contractions mean generalized Inönü–Wigner contractions. In particular, this means that by a simple limiting process, one obtains representations of nonsemisimple noncompact Lie algebras. As examples, a general treatment of SO(3) is given as well as some results for SU(3).
Integrable systems associated with the Schrödinger spectral problem in the plane
Authors: Cheng Y.
Published: July 2002

Associated with the Schrödinger spectral problem in the plane, the nonlinear integrable systems are investigated. The commutative properties of equations of the flow and their symmetries and mastersymmetries are derived in spite of the noncanonicality of the related extended recursion operator. By applying the inverse scattering transform, the systems can be solved and then the correspondences between commuting (resp. noncommuting) flows and isospectral (resp. nonisospectral) deformations of the spectral problem are found.
A new q-deformed boson realization of quantum algebra slq(n+1) and nongeneric slq(2) R-matrices
Authors: Sun Chang-Pu , Liu Xu-Feng , Ge Mo-Lin
Published: July 2002

In this paper a new q-deformed boson realization of quantum algebra slq(n+1) is presented for the first time, and its representations are obtained in the nongeneric case that q is a root of unity. A new type of slq(2) R-matrices are systematically constructed through the universal R-matrix.
Meromorphic N=2 Wess–Zumino supersymmetric quantum mechanics
Authors: Arai Asao , Ogurisu Osamu
Published: July 2002

The ordinary (holomorphic) N=2 Wess–Zumino model in supersymmetric quantum mechanics is extended to the case where the superpotential V(z) is a meromorphic function on C■{∞}. The extended model is analyzed in a mathematically rigorous way. Self-adjoint extensions and the essential self-adjointness of the supercharges are discussed. The supersymmetric Hamiltonian defined by one of the self-adjoint extensions of the supercharges has no fermionic zero-energy states (‘‘vanishing theorem’’). It is proven that if V(z) has only one pole at z=0 in C, then the supercharges are essentially self-adjoint on C∞0(R2■{0};C4). The special case where V(z)=λz−p(p∈N,λ∈C■{0}) is analyzed in detail to prove the following facts: (i) the number of the bosonic zero-energy ground state(s) is equal to p−1; (ii) the supercharges are not Fredholm.
Path integral quantization of certain noncentral systems with dynamical symmetries
Authors: Carpio-Bernido M. Victoria
Published: July 2002

Path integral quantization is done for the five classes of potentials appearing in the systematic search for nonrelativistic systems with dynamical symmetries done by Makarov, Smorodinsky, Valiev, and Winternitz [Nuovo Cimento A 52, 1061 (1967)]. By an iterated application of Bateman’s series formula to the polar coordinate path integral, an expansion is obtained of the Feynman kernel or the Green’s function, whichever is possible, in terms of hypergeometric functions of the polar and azimuthal parts and a radial path integral is obtained whose evaluation yields the energy eigenvalues and the normalized wave functions. Special cases include the Hartmann potential and the ring-shaped oscillator.
No Lagrangian? No quantization!
Authors: Hojman Sergio A. , Shepley L. C.
Published: July 2002

This work starts with classical equations of motion and sets very general quantization conditions (commutation relations). It is proved that these conditions imply that the equations of motion are equivalent to the Euler–Lagrange equations of a Lagrangian L. The result is a generalization of work by Feynman, recently reported by Dyson [Am. J. Phys. 58, 209–211 (1990)]. The Lagrangian L need not be unique. Examples are given, including classical equations that do not come from a Lagrangian and therefore cannot be quantized consistently.
Composite nearest-neighbor degeneracies for several kinds of simple particles distributed on two-dimensional, square-cell lattices
Authors: McQuistan R. B. , Hock J. L.
Published: July 2002

A recursion is derived that yields, exactly, the composite nearest-neighbor degeneracies when several kinds of simple particles [indistinguishable within each kind] are distributed on a two-dimensional, square-cell lattice in such a way as to create prescribed numbers of the various possible types of nearest-neighbor pairs.
A Newton–Marchenko equation and generalized optical theorem for elastodynamics
Authors: Budreck David E. , Rose James H.
Published: July 2002

Two new results are derived for the scattering theory of waves in nondissipative elastic media. These results are (1) a Newton–Marchenko equation, and (2) a generalized optical theorem. The Newton–Marchenko equation is an integral equation for the wavefield in terms of scattering amplitude data. It is supposed that it may play an important role in the development of exact inverse scattering methods for elastodynamics. The generalized optical theorem provides explicit relations between the scattering amplitudes, and is expected to be useful in the analysis of both the forward and inverse scattering problem. The results are presented within the context of a localized, possibly anisotropic, inhomogeneity contained in an otherwise uniform isotropic elastic medium of infinite extent in R3.
Partition functions for quantized fields in curved space-times
Authors: Bandyopadhyay N.
Published: July 2002

It is shown that partition functions for quantized fields in arbitrary stationary backgrounds do not contain undetermined regularization constants. A related result is that the trace-anomaly effect for thermal massless fields is absent.
The equivalence problem in torsion theories of gravitation
Authors: Fonseca-Neto J. B. , Rebouças M. J. , Teixeira A. F. F.
Published: July 2002

The basic problem of equivalence of gravitational fields in the framework of torsion theories of gravitation is solved. A coordinate-invariant description of the gravitational field is then presented. Explicit expressions for the dimensions of the group of transformations and its subgroup of isotropy are derived.
Asymptotically exact diffusive boundary conditions in linear kinetic theory
Authors: Malvagi F. , Sammartino M. , Pomraning G. C.
Published: July 2002

In a recent article in this journal, asymptotic considerations were used to define appropriate boundary conditions for diffusive approximations to linear kinetic equations. A variational treatment was invoked to carry out the details of the analysis. Here these details are carried out exactly, and it is shown that the earlier variational results are accurate to a few percent.
Weyl orbits and their expansions in irreducible representations for affine Kac–Moody algebras
Authors: Bégin F. , Sharp R. T.
Published: July 2002

Weyl orbits of affine rank 2 and 3 algebras are obtained analytically, along with the depths of their weights, in terms of an integrity basis consisting of sets of compatible (or adjacent) weights, one from each fundamental orbit. The fundamental orbits and others of the same level and congruence class are then decomposed into irreducible representations (IR). Since the orbit →IR matrix is triangular, it will be easy to invert it to get orbit multiplicities and subalgebra branching rules.
Tensor product of group representations and structural zeros of Racah coefficients
Authors: Van der Jeugt J.
Published: July 2002

It is shown that structural (or nontrivial) zeros of Racah coefficients (6-j symbols) can be related to decompositions of tensor products of group representations reduced to SO(3). This extends a previous relation between structural zeros of 6-j symbols and boson realizations of exceptional Lie groups. In the present case, both classical and exceptional groups may appear, and examples are given for SU(3), SO(7), SO(9), and F4.
The Hamiltonian structures associated with a generalized Lax operator
Authors: Das Ashok , Huang Wen-Jui
Published: July 2002

It is shown that with every Lax operator, which is a pseudodifferential operator of nonzero leading order, is associated a KP hierarchy. For each such operator, we construct the second Gelfand–Dikii bracket associated with the Lax equation and show that it defines a Hamiltonian structure. When the leading order is positive the corresponding compatible first Hamiltonian structure, which turns out, in general, to be different from the naive first Gelfand–Dikii bracket is derived. The corresponding Hamiltonian structures for the constrained Lax operator, where the next to leading-order term vanishes or has a constant coefficient, is discussed.
Generalization of the pseudopotential to an interaction with nonzero range
Authors: Freeman D. Kent
Published: July 2002

The resonance properties of certain arrays of potentials defined by a self-adjoint integral operator of finite rank are studied. It is shown that a uniformly spaced infinite linear array of such potentials can admit zero-width resonances, and that a uniformly spaced circular array can admit resonances whose widths tend to zero exponentially, as the number of potentials tends to infinity while the arc-length spacing remains constant−properties that have previously been studied for the Fermi pseudopotential (point interaction). Additionally, it is demonstrated that the pseudopotential can be derived from such an integral-operator potential as an appropriate limit. The relevance of these calculations to the study of arrays of cylindrical dipoles in classical electromagnetism is discussed.
Green functions of the De Rham Laplacian in maximally symmetric spaces
Authors: Folacci A.
Published: July 2002

The massive p-form two-point functions in maximally symmetric spaces of arbitrary dimension n are obtained.
Comment on ‘‘The matrix representation of U4 in the U2×U2 basis and isoscalar factors for U
p+q⊇U
p×U
q’’ [F. Pan, J. Math. Phys. 31, 1333 (1990)]
Authors: Ališauskas S.
Published: July 2002

Complementary group technique leads to more simple solutions of some problems considered by F. Pan [J. Math. Phys. 31, 1333 (1990)], including special resubducing coefficients and isoscalar factors of unitary groups.
Analysis on the p-adic superspace. I. Generalized functions: Gaussian distribution
Authors: Khrennikov A. Yu.
Published: July 2002

The theory of generalized functions on the p-adic superspace Qn,mp over the (super)commutative Banach superalgebra Λ=Λ0⊕Λ1 with the trivial Λ1 annihilator is proposed. The p-adic Gaussian ‘‘supermeasure’’ is defined as a generalized function on the p-adic superspace. The connection between the p-adic Gaussian integration and the p-adic gamma function of Morita is considered
The Gel’fand–Tsetlin representations of the orthogonal Cayley–Klein algebras
Authors: Gromov N. A.
Published: July 2002

The explicit expressions of the operators of the irreducible representations of the orthogonal Cayley–Klein algebras son+1(j) are obtained from the well-known Gel’fand–Tsetlin representations of son+1. The contractions and the analytic continuations of the representations of so3(j1,j2),so4(j1, j2, j3) are regarded as examples. This approach gives the representations of the contracted and the analytically continued algebras in different bases, for example, in discrete and continuous ones. Possible contractions of the irreducible representations are discussed.
Movable singularities in Sigma and Skyrme models
Authors: Ferreira Erasmo , Neto Jorge Ananias
Published: July 2002

The singularity structure of the solutions of the equations of motion for the Sigma and Skyrme model Lagrangians with the hedgehog ansatz is investigated. In both cases the solutions present superposed a polelike term and a logarithmic branch point. The set of solitonic configurations of the Skyrme model is characterized by the sequence of locations of their singularities on the negative real axis of the dimensionless variable z = (eFπr)2, with an accumulation point at z=0. The first few terms of the Laurent series representing the Skyrme soliton profile are shown to reproduce well the exact values in an interval about the origin. Padé approximants to the residual power series obtained after subtraction of the dominant pole term are modified in order to satisfy the constraints imposed by the asymptotic power series expansion, and approximate representations are built for the Skyrme soliton configuration, which are shown to combine simplicity with accuracy.
Nijenhuis–Bianchi identity and BRST-like operators
Authors: Okubo Susumu
Published: July 2002

Let M be a differentiable manifold with a (1,1) tensor field Sνμ(x). A notion of distorted torsion tensor is introduced that reduces to the ordinary torsion tensor when Sνμ=δνμ. It is then shown that the distorted torsion tensor satisfies a generalization of the first Bianchi identity. The new identity involves the Nijenhuis tensor in contrast to the standard Bianchi identity. Using this generalized formula, BRST-like operators are constructed that satisfy a Lie-super algebra, when both Nijenhuis and Riemann tensors vanish identically.
N=2 conformal supergravity and superconformal anomaly
Authors: Kachkachi M. , Lhallabi T.
Published: July 2002

The differential geometry formalism for N=2 conformal supergravity in harmonic superspace is developed. The N=2 superdiffeomorphisms and local super-Weyl transformations and their BRST-like symmetries are derived. These lead to the formulation of the cohomology problem and the N=2 superconformal anomaly.
Singularity structure analysis of the continuum Heisenberg spin chain with anisotropy and transverse field: Nonintegrability and chaos
Authors: Daniel M. , Kruskal M. D. , Lakshmanan M. , Nakamura K.
Published: July 2002

The integrability aspects of the continuum limit of the one-dimensional anisotropic Heisenberg spin chain in a transverse magnetic field are studied by carrying out a Painlevé singularity structure analysis. The analytic structure of the system exhibits some unusual features and requires expansions that start like a Taylor series. A careful analysis exhibits the presence of a movable logarithmic critical singular manifold in the combined presence of the anisotropy and transverse field, thereby elucidating the nonintegrable nature. Numerical analysis on the static spin configurations of the nonintegrable case shows typically chaotic spatial structures.
Green’s function for crossed time-dependent electric and magnetic fields. Phase-space quantum mechanics approach
Authors: Nieto Luis M.
Published: July 2002

In the present paper, the Moyal propagator is obtained for an electron inmersed in a constant uniform magnetic field crossed with a uniform electric field having arbitrary time dependence, using the techniques of phase space quantum mechanics. All the interesting magnitudes can be evaluated from it, and one can make quantum physics remaining in the context of phase space. Making use of these methods, the corresponding Green’s function is also obtained.
Boson–fermion and baryon mapping: Construction of collective subspaces. I. Theory
Authors: Meyer Jutta
Published: July 2002

Recently, the mathematical formalism of the Dyson boson mapping has been extended to a system of 3n fermions, leading to the boson–fermion and the baryon mapping. In the present paper, the case of a restriction to a subset of three-fermion quantum numbers, the collective indices, is discussed. A theory is developed for the representation of fermionic states and operators in a truncated ideal space where only collective boson–fermion pairs or collective ideal baryons are allowed. An exact reproduction of physical properties is proved to be possible provided that the original fermionic problem can be solved in a subspace where all three-fermion subsystems carry collective indices. Examples of simple applications are presented in the two subsequent papers of this series.
Structure of matrices transforming Stokes parameters
Authors: van der Mee C. V. M. , Hovenier J. W.
Published: July 2002

The structure of matrices that represent a linear transformation of the Stokes parameters of a beam of light into the Stokes parameters of another beam of light is investigated by means of the so-called Stokes criterion. This holds that the degree of polarization of a beam of light can never be changed into a number larger than unity. Several general properties are derived for matrices satisfying the Stokes criterion. These are used to establish conditions for the elements of such matrices. Conditions that are either necessary, or sufficient or both are presented. General 4×4 matrices are treated and a number of special cases is worked out analytically. Several applications are pointed out.
Explicit orthogonalization of some biorthogonal bases for SU(n)⊇SO(n) and Sp(4)⊇U(2)
Authors: Ališauskas Sigitas
Published: July 2002

Mutually related explicit algebraic-polynomial expressions of the orthogonalization coefficients are proposed for the biorthogonal [polynomial (Bargmann–Moshinsky), stretched, antistretched, quasistretched, and their dual] bases of the two parametric (mixed tensor and covariant) irreducible representations (irreps) of SU(n) restricted to SO(n), as well as for the projected (Smirnov–Tolstoy) and dual bases of the five-dimensional quasispin. The orthogonalization coefficients of the essentially simplified Gram–Schmidt process are expressed, up to explicitly given elementary factors, in terms of the numerator and denominator polynomials, represented as compositions of the generalized hypergeometric coefficients <3ℱ2(...)‖μ≳ and <1ℱ0(...)‖ν≳ and equivalent in the diagonal (denominator) and boundary cases to the Aλ(cabde) functions of Biedenharn and Louck. The distribution of zeros and the symmetry properties of the introduced polynomials are crucial for the conjectured solutions.
Bicovariant differential calculus on the two-parameter quantum group GLp,q(2)
Authors: Sun Xiao-Dong , Wang Shi-Kun
Published: July 2002

The quantum Lie algebra and quantum de Rham complex of the two-parameter quantum group GLp,q(2) are presented. It is shown that the differential calculus on the two-parameter quantum group GLp,q(2) given in this paper is bicovariant.
Linearization of polynomials
Authors: Fleury N. , Rausch de Traubenberg M.
Published: July 2002

It is well known that the linearization of quadratic forms is accomplished using Dirac matrices. The general problem of linearization of any polynomial of degree n having p variables is considered. First the homogeneous polynomials are considered and it is shown that we only need to study two basic homogeneous forms, namely, the sum and the product one. The sum is linearized using matrices which turn out to be a matrix representation of a generalized Clifford algebra. The homogeneous form is linearized using matrices, the size of which is large for practical use. Some clues are given to reduce their size. Since any polynomial of degree n can be made homogeneous by introducing a supplementary variable, the method proposed is quite general. It constitutes an algorithm for the linearization of any polynomial.
Irreducibility and reducing subspaces for Krein space representations of field algebra
Authors: Jakóbczyk Lech
Published: July 2002

The irreducibility of Krein space representations of a field algebra in terms of the so-called weak Krein commutants and Krein-reducing subspaces are studied. In particular, in this context the properties of Krein self-adjoint representations and Krein space representations similar to Hilbert space representations are analyzed.
Phase space analysis of the identity decompositions
Authors: Fan Qihong
Published: July 2002

The connections between the decompositions of the identity operator on L2(Rn) and the decompositions of the function 1 on the phase space R2n are considered. The phase space properties of various transformations (such as the Fourier transform, Gabor transform, and wavelet transform, etc.) are investigated.
Proper conformal symmetries of space-times with divergence-free Weyl conformal tensor
Authors: Sharma Ramesh
Published: July 2002

It has been shown that a four-dimensional space-time with divergence-free Weyl conformal curvature tensor and admitting a proper conformal symmetry is locally of type O (conformally flat) or N. The latter case has been studied in terms of null sectional curvature. Finally, a physical characterization of general relativistic perfect fluid space-times with divergence-free Weyl conformal tensor has been presented and moreover it is shown that such fluid space-times admitting a proper conformal symmetry are conformally flat.