bluuebunny/crossref_metadata_2025 huggingface dataset:
Gauge and Bäcklund transformations for the variable coefficient higher-order modified Korteweg–de Vries equation
Authors: Zheng Yu-kun , Chan W. L.
Published: July 2002

A family of higher-order modified Korteweg–de Vries equations with variable coefficients (t-ho-mKdV) is introduced. A one-to-one correspondence between a real solution of these equations and a complex solution of the variable coefficient higher-order Korteweg–de Vries (t-ho-KdV) equations is established through a complex Miura transformation. An auto-Bäcklund transformation for these t-ho-mKdV equations is derived from that of the t-ho-KdV equations. The associated gauge transformations of the corresponding AKNS systems are presented. They enable one to construct a hierarchy of solutions of the t-ho-mKdV equations from a known hierarchy without solving the differential equations for the wave functions except the first one. A new family of higher-order evolution equations with an auto-Bäcklund transformation is also derived in connection with the gauge transformation of the t-ho-mKdV equations.
Translating the spin-boson model into a classical system
Authors: Fannes M. , Nachtergaele B.
Published: July 2002

It is shown rigorously how to translate the ground state energy problem for some quantum systems into an equilibrium problem for an associated one-dimensional classical system. The case of the spin-boson model for which the connection is established with a previously obtained Ising model over R is explicitly treated.
Superspace first-order partial differential equations through the Cartan–Kähler integration theorem
Authors: Cianci Roberto
Published: July 2002

In the paper, first-order partial differential equations are studied on superspace; the key point is the use of a suitable generalization of the Cartan–Kähler integration theorem on superspace. By means of this result, it is possible to investigate the characteristic fields and the structure of the solutions.
Exact solutions of the Einstein field equations for a topologically nontrivial metric
Authors: Harriott Tina A. , Williams J. G.
Published: July 2002

Two exact solutions of the Einstein field equations are presented, each having a Finkelstein–Misner kink. The first of these has a perfect fluid interior and a vacuum exterior. The equation of state is ρ=−p=C (where C is a constant), which is the same as that found in inflationary models.
Supersymmetry, parastatistics, and operator realizations of a Lie algebra
Authors: Biswas S. N. , Soni S. K.
Published: July 2002

The algebraic structure of parastatistics has been generalized and it is found to be consistent with supersymmetric quantum mechanics with supercharges constructed out of the generalized para-Bose and para-Fermi operators. It is further shown that the operator algebra of generalized parastatistics offers a realization of the (graded) orthosymplectic group similar to that of orthogonal and symplectic groups using conventional parastatistics.
Spin-connection generalized Yang–Mills fields on double-dual generalized Einstein–Cartan backgrounds
Authors: O’Brien G. M. , Tchrakian D. H.
Published: July 2002

In every even dimension, a modification of the generalized Yang–Mills systems (modGYM) is introduced. It is shown that spin-connection modGYM fields, which are self-dual on a double-self-dual background of generalized Einstein–Cartan (GEC) gravity, can be constructed—this generalizes the constructions of Charap and Duff [Phys. Lett. B 69, 445 (1977)] in four dimensions, to all even dimensions. Additional duality constraints are also given that must be satisfied by the gravitational fields, if these constructions are to apply also to the full GYM systems. Applications to compactification, as well as relevant physical criteria, are briefly discussed.
Lagrangian formalism and retarded classical electrodynamics
Authors: Jaen X. , Llosa J. , Molina A.
Published: July 2002

Unlike the 1/c2 approximation, where classical electrodynamics is described by the Darwin Lagrangian, here there is no Lagrangian to describe retarded (resp., advanced) classical electrodynamics up to 1/c3 for two-point charges with different masses.
Gauge dependences of the covariant effective action in QED
Authors: Nachbagauer Herbert , Kraemmer Ulrike , Rebhan Anton
Published: July 2002

A recent computation of the (nonlocal) covariant effective action of QED in weak constant external electromagnetic fields is generalized to general Lorentz gauges and its gauge dependence is displayed, and it is then removed by the prescription for a gauge and parametrization independent effective action according to Vilkovisky. The geometry, which in this framework is ascribed to the field configuration space of QED, is made explicit, and it is shown that Vilkovisky’s effective action coincides with the conventional Landau gauge case.
The Riemann–Hilbert transformation for an approach to a representation of the Virasoro group
Authors: Li Wei , Hou Bo-yu
Published: July 2002

In this paper, it is the intent to apply the Riemann–Hilbert transformation developed by Hauser and Ernst [J. Math. Phys. 21, 1126, 1418 (1980)] in providing a new representation of the Virasoro group. It is found that the Geroch group that acts on the solution space of the Einstein field equations is extended to the semidirect product of the Virasoro and Kac–Moody groups; also, the relationship between the infinitesimal transformation given previously [B. Y. Hou and W. Li, Lett. Math. Phys. 13, 1 (1987); J. Phys. A 20, L897 (1987); W. Li, Phys. Lett. A 129, 301 (1988)] and the infinitesimal Riemann–Hilbert transformation is pointed out. Finally, it is shown that the well-known Neugebauer–Backlund transformation can be derived from the Riemann–Hilbert transformation.
A Newlander–Nirenberg theorem for supermanifolds
Authors: McHugh Andrew
Published: July 2002

A supermanifold version of the Newlander–Nirenberg theorem is proven. The classical Newlander–Nirenberg theorem states the conditions under which an almost complex structure on a differentiable manifold gives rise to a complex structure. A definition is given here of an almost complex structure on a differentiable supermanifold along with the conditions under which this gives rise to a complex structure on the supermanifold.
On the power-series construction of Schrödinger bound states. II. The effective Hill determinants
Authors: Znojil M.
Published: July 2002

For a class of potentials, the radial differential Schrödinger equation for wave functions ψ(r) of bound states may often be replaced by an equivalent matrix equation for coefficients pn in an associated power-series ansatz. In Paper I [J. Math. Phys. 29, 1433 (1988)], a rigorous foundation of such a transition (sometimes called the Hill-determinant method) was presented. Now, it will be shown that and how the Feshbach–Löwdin projection-operator idea may help one to reduce the underlying infinite-dimensional diagonalization to a mere finite-dimensional eigenvalue problem.
The universal current distribution near the end of a tubular antenna
Authors: Shen Hao-Ming , Wu Tai T.
Published: July 2002

An asymptotic solution for the charge density and current near the end of a linear tubular antenna is obtained by means of the Wiener–Hopf technique. It is found that, due to the charge-repulsion effect, the distributions of charge per unit length and of current within a distance of the order of the radius from the end are significantly different from the sinusoidal distributions that are the solutions from approximate theories. Furthermore, the relative distributions are independent of the length of the antenna and of the frequency of operation.
Sequences of point transformations and linear canonical transformations in classical and quantum mechanics
Authors: Leyvraz F. , Seligman T. H.
Published: July 2002

Sequences of point transformations and canonical linear transformations are considered in classical and quantum mechanics. It is shown that the unitary representations of such transformations can be obtained, in general, in the sense that in the limit, classical behavior is retrieved. In the particular case of one point transformation combined with two linear transformations, the results found in this way are exact. A new class of differential equations is thereby solved by quadratures.
De Sitter kinks
Authors: Dunn K. A. , Williams J. G.
Published: July 2002

In this paper a kink solution to the vacuum Einstein equations with cosmological constant Λ>0 is discussed. The solution is well-defined on the whole space-time manifold. An appropriate coordinate transformation shows the solution to be locally the same as the de Sitter solution. Globally, the two are distinct, since the light-cone field for the kink solution is homotopically nontrivial.
U(2) extension of modified Bessel function with two indices
Authors: Tanimura N. , Tanimura O.
Published: July 2002

A new set of functions that are given by the coefficients of the character expansion of the single-link action in the U(2) lattice gauge theory is studied. The set relies on the introduction of the character of the mixed term of the normal and adjoint U(2) variables. From the Schwinger–Dyson variational method the recursion relations among the functions are derived. From the relations the asymptotic behaviors of the function at the inverse coupling →0 and ∞ are derived. Through the combination of the recursion relations and the differentiation the linear differential equation of the fourth order is derived. The properties of the solution are discussed.
Relativistic relaxation models for a simple gas
Authors: Majorana A.
Published: July 2002

A general relativistic time-relaxation model is introduced and compared with the relativistic Boltzmann equation. It is proved that the model has the same features (formal properties of linear operator, positive transport coefficients, etc.) of the Boltzmann equation. It is also shown that the phase speed of infinitesimal disturbances, propagating in a gas described by our model, is less than the speed of light.
Unified models from gauged supergroups. I. Dimensional reduction formalism. Unitary and orthosymplectic series
Authors: Jarvis P. D.
Published: July 2002

Principles are elaborated for constructing consistent grand unified models (GUT’s) plus Higgs sectors from dimensional reduction of gauged supergroups over graded coset spaces. A search of possible GUT groups is made for unitary and orthosymplectic supergroups over a space parametrized by a single pair of Grassmann coordinates.
Parastatistics, supersymmetry and parasupercoherent states
Authors: Beckers J. , Debergh N.
Published: July 2002

Coherent states are constructed in p=2-parasupersymmetric quantum mechanics in connection with the two relative para-Bose and para-Fermi sets of trilinear structure relations. They are called parasupercoherent states. Parasupersymmetric operators [such as the Hamiltonian and (two) annihilation operators] are introduced and discussed. In particular, the parasuperspectrum is determined and compared with the recent results obtained by Rubakov and Spiridonov [Mod. Phys. Lett. A 3, 1337 (1988)]. The superalgebra contents subtended by osp(2/2) and osp(3/2) are analyzed and exploited in order to get constants of motion in both contexts through parallel properties on the supersymmetric harmonic oscillator.
Exact solution of the n-dimensional Dirac–Coulomb equation
Authors: Wong M. K. F.
Published: July 2002

An exact solution of the n-dimensional Dirac–Coulomb equation is obtained with the radial wave function containing only one term of a confluent hypergeometric function. It is of the same form as the solutions to the Schrödinger and Klein–Gordon equations with a Coulomb potential in n dimensions.
A simple derivation of the quantum Clebsch–Gordan coefficients for SU(2)q
Authors: Ruegg H.
Published: July 2002

To SU(2)q, the quantum deformation of SU(2), the van der Waerden method for calculating the Clebsch–Gordan (CG) coefficients is genaralized. The polynomial basis for irreducible representations of SU(2)q, the relevant polynomial invariants, and the deduction of the q analog of the CG coefficients are given.
Anomalies from geometric quantization of fermionic field theories
Authors: Schaller P. , Schwarz G.
Published: July 2002

Geometric quantization on (infinite-dimensional) graded symplectic manifolds is elaborated for a restricted class of phase spaces. The formalism includes the treatment of Fermionic field theories. The chiral anomaly [U(1)-anomaly] as well as the non-Abelian (covariant) anomaly of D-dimensional non-Abelian gauge theories is calculated in this framework.
Highest weight irreducible unitary representations of Lie algebras of infinite matrices. I. The algebra gl(∞)
Authors: Palev Tchavdar D.
Published: July 2002

Two classes of irreducible highest weight modules of the general linear Lie algebra gl(∞), corresponding to two different Borel subalgebras, are constructed. Both classes contain all unitary representations. Within each module a basis is introduced. Expressions for the transformation of the basis under the action of the algebra are written down.
Introduction to a covariant theory of special functions of mathematical physics
Authors: Lucquiaud J. C.
Published: July 2002

Using harmonic analysis techniquies, the covariant expression of Jacobi and Hermite polynomials on an n-dimensional space endowed with a metric g of signature (p+, q−) is given. The properties of these polynomials are studied and their relations with the hypergeometric function are given.
The functional Ito formula in quantum stochastic calculus
Authors: Ekhaguere G. O. S.
Published: July 2002

Using an Op-*-algebraic approach, noncommutative analogs of the Ito formula of classical stochastic calculus within the framework of the Hudson–Parthasarathy formulation of Boson quantum stochastic calculus are proven.
A posterior Schrödinger equation for continuous nondemolition measurement
Authors: Belavkin V. P.
Published: July 2002

A continuous model for a nondemolition observation of an atom is given. An equation for the corresponding instrument is found and a stochastic dissipative Schrödinger equation for the unnormalized posterior wave function of the atom is derived. It is shown that the continuously observed isolated atom relaxes to the ground state without mixing.
Semiclassical structure of trace formulas
Authors: Littlejohn Robert G.
Published: July 2002

Trace formulas provide the only general relations known connecting quantum mechanics with classical mechanics in the case that the classical motion is chaotic. In particular, they connect quantal objects such as the density of states with classical periodic orbits. In this paper, several trace formulas, including those of Gutzwiller, Balian and Bloch, Tabor, and Berry, are examined from a geometrical standpoint. New forms of the amplitude determinant in asymptotic theory are developed as tools for this examination. The meaning of caustics in these formulas is revealed in terms of intersections of Lagrangian manifolds in phase space. The periodic orbits themselves appear as caustics of an unstable kind, lying on the intersection of two Lagrangian manifolds in the appropriate phase space. New insight is obtained into the Weyl correspondence and the Wigner function, especially their caustic structures.
Equilibrium properties of a multi-urn model
Authors: Gaveau B. , Schulman L. S.
Published: July 2002

Equilibrium properties of the following model are studied: A system is formed of urns (or droplets, or clusters), each containing a number of atoms. That number is governed by an occupation-dependent energy and a chemical potential per atom. An effective interaction between clusters arises from a global constraint on total cluster number and occupation. The system phase diagram exhibits various kinds of transitions. The microscopic structure of the thermodynamic state is also examined (cluster occupation probabilities, etc.) and surprising simplifications relating it to the single-urn model are found. In general, the system is intermediate in its complexity between the single-urn model and the Fisher–Felderhof droplet model. The ultimate purpose in defining this model is to study its dynamical properties and, in particular, its metastable phases. The cluster size distributions are anticipated to be of particular importance for this issue.
Vector coherent state constructions of U(3) symmetric tensors and their SU(3)⊇SU(2)×U(1) Wigner coefficients
Authors: Hecht K. T. , Biedenharn L. C.
Published: July 2002

Generalized vector coherent state constructions of totally symmetric U(3) tensors are used to gain new expressions for the SU(3)⊇SU(2)×U(1) Wigner coefficients for the coupling (λ1μ1)×(λ20)→(λ3μ3). These expressions show how the extremely simple formulas of Le Blanc and Biedenharn, involving a single 9-j coefficient, arise as special cases of a general result that involves 12-j coefficients. A simpler general result involving only 9-j coefficients and K-normalization factors is derived in a way that can, in principle, be generalized to the generic coupling with multiplicity.
Local realizations of kinematical groups with a constant electromagnetic field. II. The nonrelativistic case
Authors: Negro Javier , del Olmo Mariano A.
Published: July 2002

In this paper, nonrelativistic elementary physical systems interacting with constant external electromagnetic fields are studied. The method is to construct a special kind of realizations of the Galilei group, which depend on the electromagnetic field. The linearization of this problem, which consists in obtaining these local realizations via the linear representations of another group, leads to a new representation group: the nonrelativistic Maxwell group. The study of the representations of this group and the related invariant equations completes this work.
Stationarity of time correlation functions for globally linear classical systems and its consequences
Authors: Wassam W. A. , Balderas-López J. A. , Torres-Vega Go.
Published: July 2002

A necessary and sufficient condition for the stationarity of all time correlation functions associated with a given globally linear classical dynamical system is rigorously established from basic principles. Since stationarity of time correlation functions is a physical requirement that must be satisfied, the necessary and sufficient condition obtained for its realization represents a universal dynamical constraint on globally linear classical dynamical models intended to describe the execution of spontaneous fluctuations about a stationary state. This dynamical constraint is shown to (i) impose restrictions on the symmetry properties of the transition operator appearing in the global propagator for a system; (ii) represent a universal operator relation that embodies detailed balance and microscopic reversibility, giving rise to their traditional formulations; and (iii) imply the existence of certain generalized symmetry relations for time correlation functions and their Laplace and Fourier transforms. Apart from elucidating some fundamental symmetries of classical dynamical systems, the reported theory has the advantage of providing a simple model independent framework for treating classical time correlation functions via the extraction and utilization of dynamically embedded information. This is demonstrated in a concrete way by exploiting the mathematical apparatus of dual Lanczos transformation theory to determine the advanced and retarded components of the elements of the correlation matrices for first and second moment coordinate and momentum fluctuations for the Brownian harmonic oscillator. The Laplace transforms of the retarded components of the time correlation functions and the Fourier transforms of the full-time correlation functions are also obtained.
Multiparameter deformations of GL(N) and Jordan–Schwinger constructions
Authors: Vokos Stamatis P.
Published: July 2002

The covariant differential calculus on the quantum hyperplane acted on by GLX;qij(N) is interpreted as a deformed Heisenberg algebra (holomorphically realized on a polynomial basis) and the corresponding quantum algebra is constructed through the Jordan–Schwinger construction. For N≥3 this quantum algebra is shown to give quadratic constraints among the generators. However, for N=2 this construction is elevated to a Hopf algebra by finding simple comultiplication rules. This is seen to be equivalent to the Woronowicz-type two-parameter deformation of Schirrmacher et al. [Z. Phys. C 49, 317 (1991)] as well as the Drinfeld–Jimbo deformation V. G. Drinfeld, in Proceedings of the International Congress of Mathematicians, Berkeley, 1986 (Academic, New York), Vol. 1, pp. 798–820; M. Jimbo, Lett. Math. Phys. 10, 63 (1985); M. Jimbo, Lett. Math. Phys. 11, 247 (1986)].
Plane walls interacting with gravitational waves and matter fields
Authors: Wang Anzhong
Published: July 2002

Plane walls with reflection symmetry are studied. A method for generating such solutions to the Einstein equations is developed. It is found that plane wall solutions require very strong restrictions on the metric coefficients and on their derivatives. Using the generalized Bianchi identities, the interaction of plane walls with gravitational waves and matter fields is investigated. In particular, it is shown that a plane wall, in general, interacts with both gravitational plane waves and matter fields. But, a plane domain wall interacts only with matter fields. No matter whether the space-time out of the wall is curved or not, a plane domain wall is always repulsive.
Einstein universe as a moving fluid cosmology
Authors: Rebouças M. J. , Teixeira A. F. F.
Published: July 2002

The combination of Synge’s approach to Einstein’s equations with energy conditions and the Segré classification of the energy-momentum tensor is used in the examination of Einstein’s space-time. An alternative physical interpretation for the Einstein static model is discussed. An Einstein-type moving fluid universe is presented. The meaning of both static space-time and static cosmological models are discussed.
q-oscillator realizations of the metaplectic representation of quantum osp(3,2)
Authors: D’Hoker Eric , Floreanini Roberto , Vinet Luc
Published: July 2002

q-oscillator representations of the quantum superalgebra ospq(3,2) are discussed. It is pointed out that the metaplectic representation of ospq(3,2) can be equivalently realized either in terms of one q-boson and one q-fermion or with one q-boson and two q-fermions.
Some notes on periodic Beltrami fields in Cartesian geometry
Authors: McLaughlin D. , Pironneau O.
Published: July 2002

Some mathematical facts about Beltrami fields, which are time-independent solutions of the three-dimensional incompressible Euler equations with nontrivial helicity, are assembled. The linearization about an arbitrary, fixed Beltrami field is studied in a Hamiltonian framework. A factorization of this linearization is introduced and used to characterize null spaces for Beltrami fields with ergodic streamlines. An interesting property of unstable modes is noticed and its consequences concerning the nature of potential instabilities are discussed.
Orthogonalization coefficients for the Elliott–Draayer states of the two parametric irreps of SU(n)⊇SO(n)
Authors: Ališauskas Sigitas
Published: July 2002

Explicit algebraic-polynomial expressions for the direct and inverse orthogonalization coefficients of the projected (Elliott–Draayer) basis states of SU(n)⊇SO(n) are constructed in the case of two parametric irreducible representation (irreps). They cover the general SU(3)⊇SO(3) case as well as the two parametric covariant irreps of SU(4) restricted to the SU(2)×SU(2) subgroup of spin and isospin. The obtained orthonormal bases are equivalent to those constructed by means of the ordered Gram–Schmidt process. The orthogonalization coefficients are expressed, up to explicitly given elementary factors, in terms of the numerator and denominator polynomials related with those that appeared in the orthogonalization coefficients of the paracanonical coupling coefficients (isofactors) of SU(3) and with Aλ functions of Louck, Biedenharn, and Lohe.
The Lorentz operator revisited
Authors: van Wyk C. B.
Published: July 2002

Some kinematical aspects of the decomposition of the product of two pure Lorentz operators into the product of a third pure Lorentz operator and a pure rotation are discussed. It is shown that a triangle can be associated with such a decomposition and the properties of such a triangle are compared with those of a triangle in the more conventional hyperbolic geometry. The lack of uniqueness in this decomposition is discussed. Finally, a Lorentz operator containing six independent parameters is expressed in terms of the initial and final vectors of the corresponding Lorentz transformation.
Exact solutions for nonpolynomial potentials in N-space dimensions using a factorization method and supersymmetry
Authors: Adhikari R. , Dutt R. , Varshni Y. P.
Published: July 2002

A supersymmetry-inspired factorization method is used to obtain exact analytic solutions for one or a few quantum states of a broad class of nonpolynomial potentials in an arbitrary space dimension under suitable constraints on the potential parameters. For the specific nonpolynomial oscillator potential, V(x)=x2+λx2/(1+gx2), previous analytic results including algebraic and integral type in one and three dimensions are easily obtainable from these compact expressions. Interesting aspects of the existence of pairs of solutions for certain combinations of λ and g are also discussed.
Fluid of multidimensional objects in cosmology
Authors: Maszczyk Roman A.
Published: July 2002

The subject of this paper is a generalized Robertson–Walker model filled with the fluid of multidimensional objects. The solutions are classified according to curvatures of the internal and external spaces, as well as to the qualities of the dynamics of the models. The majority of solutions are singular. The analysis shows, however, that there may also be nonsingular oscillatory solutions.
BRST quantization of the Schwinger model
Authors: Horuzhy S. S. , Voronin A. V.
Published: July 2002

The rigorous construction and study of the BRST formalism for the Schwinger model is performed. The BRST transformation and BRST algebra are defined and the kernel of the BRST charge Q is studied. It is proved that our BRST quantization is physically correct, i.e., ker Q is a non-negative subspace (‘‘no-ghost theorem’’); moreover, the space of the BRST cohomologies ker Q/ran Q is one dimensional up to factors on which Q acts trivially. It is found that the well-known Lowenstein–Swieca solution cannot produce the correct BRST quantization (Theorem 1) and so the formalism is based on the Capri–Ferrari solution [Capri and Ferrari, Nuovo Cimento A 62, 273 (1981)] valid in the arbitrary local covariant gauge (although only the Lorentz gauge is considered here for simplicity reasons). The important by-product of our study is the general construction of the BRST–Fock moduli satisfying the no-ghost theorem. The construction is done with the aid of a special kind of the finite-dimensional approximation, the ‘‘N-cell technique.’’
Addition formulas for q-Bessel functions
Authors: Floreanini Roberto , Vinet Luc
Published: July 2002

The two-dimensional Euclidean algebra provides an algebraic setting for q-Bessel functions. Using a two-variable realization of this algebra, q analogs of the Lommel and Graf addition formulas for the q-Bessel functions are obtained.
Shifted vertex operator algebras and G-elliptic systems
Authors: Tsukada Haruo
Published: July 2002

Shifted vertex operator algebras and superalgebras are defined, both in bosonic and in fermionic pictures. Their isomorphism (Boson–Fermion correspondence) is shown. Partition functions of bosonic shifted vertex operator algebras are realized analytically and are interpreted as string path integrals over elliptic curves. Their modular properties follow, and elliptic systems are constructed based on fermionic shifted vertex operator algebras.
Bounding the remainder in variational calculations of potential scattering
Authors: Darewych J. W. , Schlifer I.
Published: July 2002

Rigorous, calculable bounds to the absolute value of the second-order remainder term, which is usually neglected in variational scattering calculations, are derived for a wide class of potentials.
Wigner analysis and Casimir operators of SA(4,R)
Authors: Lemke Jürgen , Ne Yuval , Pecina-Cruz Jose
Published: July 2002

In theories involving gravity, including QCD-generated gravitylike effects in hadrons, SA(4,R) plays a role. Its single Casimir invariant and that of its SA(2,R) and SA(3,R) subgroups are evaluated. The group orbits are studied and the unitary irreducible representations are classified.
Symmetries of the renormalization group equations
Authors: Jha Pradip K. , Tripathy Kishor C.
Published: July 2002

The invariance of the renormalization group equation under the action of the prolonged Lie field is examined and it is shown that the system exhibits infinite dimensional symmetry. From the characteristics, detailed solutions of the renormalization group equation is derived. As an illustration, the method is applied to QED and QCD.
Models of q-algebra representations: Tensor products of special unitary and oscillator algebras
Authors: Kalnins E. G. , Manocha H. L. , Miller Willard
Published: July 2002

This paper begins a study of one- and two-variable function space models of irreducible representations of q analogs of Lie enveloping algebras, motivated by recurrence relations satisfied by q-hypergeometric functions. The algebras considered are the quantum algebra Uq(su2) and a q analog of the oscillator algebra (not a quantum algebra). In each case a simple one-variable model of the positive discrete series of finite- and infinite-dimensional irreducible representations is used to compute the Clebsch–Gordan coefficients. It is shown that various q analogs of the exponential function can be used to mimic the exponential mapping from a Lie algebra to its Lie group and the corresponding matrix elements of the ‘‘group operators’’ on these representation spaces are computed. It is shown that the matrix elements are polynomials satisfying orthogonality relations analogous to those holding for true irreducible group representations. It is also demonstrated that general q-hypergeometric functions can occur as basis functions in two-variable models, in contrast with the very restricted parameter values for the q-hypergeometric functions arising as matrix elements in the theory of quantum groups.
Renormalized stress tensors on ellipses
Authors: Worden K.
Published: July 2002

The stress-energy tensor of a conformally invariant field is calculated in a two-dimensional Euclidean space-time with elliptical boundary. The results are expressed in terms of elliptic functions and are displayed.
Algebraic structure of tensor superoperators for the super-rotation algebra. II
Authors: Minnaert Pierre , Mozrzymas Marek
Published: July 2002

It is shown that the sets of tensor superoperators for the super-rotation algebra can be used to build explicit bases for the representations of several superalgebras. The representations built in this way are the fundamental representations of the special linear superalgebras sl(2j+1‖2j) and of the orthosymplectic superalgebras osp(2j+1‖2j) and the (4j+1)-dimensional representations of osp(1‖2) and sl(1‖2) (Stavraki) superalgebras. It is shown that the chain osp(1‖2)⊆osp(2j+1‖2j) or osp(2j‖2j+1) explains the existence of a series of nontrival zeros for the super-rotation 6-j symbol (SR6-j symbols).
Some null solutions of the Yang–Mills equations and Cauchy–Riemann structures
Authors: Nurowski Pawel
Published: July 2002

Some new null solutions of the Yang–Mills equations with congruences of twisting shear-free and null geodesics are obtained. These are test fields. Each of them is defined on a Lorentzian manifold with a metric tensor adapted to the Cauchy–Riemann geometry associated with the congruence. Some examples of solutions on Minkowski space-time are also given. Among them is a solution with a congruence of twisting shear-free and null geodesics different from the Robinson congruence.
Generating relations for Tratnik’s multivariable biorthogonal continuous Hahn polynomials
Authors: Exton Harold
Published: July 2002

Multiple series generating relations for the generalized continuous Hahn polynomials are obtained. Special cases consist of results involving products of several confluent hypergeometric functions.
On the first tangency of stable and unstable manifolds in C
r planar diffeomorphisms
Authors: Yamaguchi Yoshihiro , Tanikawa Kiyotaka
Published: July 2002

Two problems in two-dimensional Cr diffeomorphisms are discussed. In doing this, the intersection and tangency of the stable and unstable manifolds are strictly discriminated and the notion of the first direct and asymptotic tangencies is introduced. The first problem is what happens if neither stable and unstable manifolds transversely nor nontransversely intersect with each other nor are their closures disjoint. It is shown that there are cases in which the existence of homoclinic tangency of the usual sense is inhibited. The second problem is what is expected as a consequence of the first direct homoclinic tangency. Several consequences are shown. Among others, an extension of Palis’s lambda lemma to cases of the first direct tangency is obtained. Finally, the numerical examples on the first asymptotic tangency are given using two maps.
Representations of one-dimensional Hamiltonians in terms of their invariants
Authors: Lewis H. Ralph , Leach P. G. L. , Bouquet Serge , Feix Marc R.
Published: July 2002

A general formalism for representing the Hamiltonian of a system with one degree of freedom in terms of its invariants is developed. Those Hamiltonians H(q,p,t) are derived for which any particular function I(q,p,t) is an invariant. For each of those Hamiltonians, a function canonically conjugate to I(q,p,t) is derived which is also an invariant of H(q,p,t). The formalism is also presented for the case in which I(q,p,t) is expressed as a function of two canonically conjugate functions. The formalism is illustrated by applying it to the case of a particle moving in a time-dependent potential. Some earlier results are recovered and an invariant is found for a new potential. Lines for further study are outlined that may be fruitful for finding more examples of integrable systems.
Strong curvature singularities and causal simplicity
Authors: Królak Andrzej
Published: July 2002

Techniques of differential topology in Lorentzian manifolds developed by Geroch, Hawking, and Penrose are used to rule out a class of locally naked strong curvature singularities in strongly causal space-times. This result yields some support to the validity of Penrose’s strong cosmic censorship hypothesis.
Direct integration of generalized Lie or dynamical symmetries of three degrees of freedom nonlinear Hamiltonian systems: Integrability and separability
Authors: Lakshmanan M. , Senthil Velan M.
Published: July 2002

It is shown that by directly integrating the characteristic equation of the infinitesimals of the generalized Lie or dynamical symmetries associated with three degrees of freedom Hamiltonians, one can almost, by inspection, obtain the required involutive integrals of motion, whenever they exist. The method is illustrated for the coupled quartic and cubic oscillators considered earlier. Further, all the separable coordinates can be obtained by integrating a subset of the characteristic equation associated with the coordinate variables alone.
On the strength of space-time singularities
Authors: Kánnár János , Rácz István
Published: July 2002

New integral conditions are proposed that are sufficient for the existence of conjugate pointpairs along causal geodesics. As to maximal incomplete causal geodesics the upper bound on the rate of possible divergency of the tidal curvature is examined.
Exact solutions of the vacuum Einstein’s equations allowing for two noncommutative killing vectors (Type G2II of Petrov classification)
Authors: Aliev B. N. , Leznov A. N.
Published: July 2002

Einstein’s equations are written in the form of covariant gauge theory in two-dimensional space with the binomial solvable gauge group, with respect to two noncommutative Killing vectors. In the one-dimensional case the theory is exactly integrable and in the two-dimensional case, the series of partial exact solutions is constructed.
Nonclassical symmetry reductions for the dispersive wave equations in shallow water
Authors: Lou Sen-yue
Published: July 2002

All (six types of) the similarity reductions of the dispersive wave equations in shallow water are obtained by the direct method. The group explanation of the results is also given. It is pointed out that, in order to find all the results by nonclassical Lie approach, two additional condition equations should be satisfied at the same time together with two original equations. The logarithmic branch points for time t can be included in two types of the similarity solutions, though the model can be cast into the canonical Hamiltonian form.
The presentation and q deformation of special linear Lie superalgebras
Authors: Scheunert M.
Published: July 2002

It is shown that the naive Serre presentation corresponding to the simplest Cartan matrix of the special linear Lie superalgebra sl(m,n) yields, for m,n≥2, a larger Lie superalgebra s(m,n) of which sl(m,n) is a nontrivial quotient. The missing relations are found and the q deformation of the universal enveloping algebra of sl(m,n) is constructed. Some auxiliary results related to associative algebras and ε Lie algebras defined in terms of generators and relations are also included.
Central extensions of sphere groups and their Lie algebras
Authors: Nash Charles , O’Connor Denjoe , Sen Siddhartha
Published: July 2002

This note is a short comment on central extensions of Lie groups of the form Map(X, G) when X=Sn and G is a compact simple Lie group. The cohomology of Map(X, G) is computed and cases where the Lie algebra is extended but the corresponding Lie group extension is trivial are considered.
A convergent lattice approximation for nonlinear electromagnetic fields in four dimensions
Authors: Albeverio S. , Iwata K. , Schmidt M.
Published: July 2002

A discrete version of the quaternionic Cauchy–Riemann equation ∂A=F, where F is Gauss–Poisson white noise, is discussed. On the lattice δZ4 random variables Fδ(δn) and Aδ(δn) are constructed which approximate the corresponding random fields F and A, respectively, in the limit δ→0. In the Gaussian case the random variables Aδ(δn) can be interpreted as the lattice approximation of the free electromagnetic Euclidean potential field whereas in the non-Gaussian case one obtains an approximation of nonlinear interacting electromagnetic quantum fields. Convergence to the continuum limit is proven.
Generalized Schwinger duality in bound state theory
Authors: Chhajlany S. C.
Published: July 2002

It is shown that an exactly solvable bound state problem is the generator of a nonterminable sequence of partially exactly solvable problems. The reversible passage from exact to partial solvability is realized through a class of admissible nonlinear coordinate transformations of which the parabolic Schwinger transformation that relates the Coulomb and oscillator problems is a particular case. Interesting spectral features of a novel set of partially solvable problems that emerge through the present considerations are also pointed out.
Extended kinetic theory
Authors: Grmela Miroslav , Jou David
Published: July 2002

The domain of applicability of one-point kinetic theory is enlarged by admitting two-point distribution functions or some of their moments as extra state variables. Kinetic equations governing the time evolution in the extended state space are introduced as particular realizations of the nonlinear Onsager–Casimir equation. This abstract equation collects the common structure of equations arising in the analysis of compatibility of two levels of description (e.g., kinetic theory and equilibrium thermodynamics or kinetic theory and hydrodynamics). The structure consists of a Poisson bracket and two potentials. The Poisson bracket expresses kinematics, the first potential, called the thermodynamic potential, generates the time evolution and links the theory with thermodynamics. The second potential, called the dissipative potential, introduces dissipation into the time evolution that is compatible with the kinematics and thermodynamics. To find a particular realization of the nonlinear Onsager–Casimir equation means to identify kinematics (Poisson bracket) and the two potentials, that correspond to a particular system and situations under consideration. This way of introducing kinetic equations has two advantages. First, the kinetic equations are guaranteed to be intrinsically consistent and compatible with more macroscopic theories. Second, the clear physical meaning of kinematics and the two potentials, together with the possibility of discussing them separately, allows one to use a broad range of physical insights and considerations to specify them for particular systems and situations of interest.
Quantum group symmetric Bargmann–Fock space: Integral kernels, Green functions, driving forces
Authors: Kempf Achim
Published: July 2002

Raising and lowering operators that transform under the SUq(n)-quantum group get deformed commutation relations. They are represented as adjoint operators on a Hilbert space of noncommutative holomorphic functions. Through the algebraically defined integral on this function space, every operator on the Fock space can also be represented as an integral kernel. The Green function for free harmonic oscillators and spin-1/2’s in a constant magnetic field is given. Further on it is studied how such systems react on the switching on of a driving force. Calculating the vacuum–vacuum transition amplitude, it is found that the deviations from the undeformed case grow with the strength of the driving force. Throughout all calculations the bosonic and the fermionic cases are considered simultaneously.
Tensor product decompositions and branching rules of the N=2 superconformal algebra
Authors: Baker T. H.
Published: July 2002

Tensor product decompositions of the N=2 superconformal algebras are examined to determine when they are finite or multiplicity-free, using various combinatorial identities. Using similar techniques, branching rules for the winding subalgebras of the N=2 superconformal algebras are investigated.
Quantum deformation of Bose parastatistics
Authors: Hadjiivanov Ludmil K.
Published: July 2002

A q-deformation of the transformation of the Chevalley basis to an odd basis of generators of the universal enveloping of the Lie superalgebra 𝒢(n)≡osp(1‖2n) is presented. It is shown that one thus obtains a reasonable quantum deformation of the algebra of n para-Bose oscillators.
Quasiexactly solvable 2×2 matrix equations
Authors: Brihaye Y. , Kosinski P.
Published: July 2002

The conditions under which systems of two differential eigenvalue equations are quasiexactly solvable are investigated. These systems reveal a rich set of algebraic structures. Some of them are explicitly described. An example of a quasiexactly solvable system which provides a direct counterpart of the Lamé equation is studied.
Schwinger–Dyson Becchi–Rouet–Stora–Tyutin symmetry and the Batalin–Vilkovisky Lagrangian quantization of gauge theories with open or reducible gauge algebras
Authors: de Jonghe Frank
Published: July 2002

In this short paper we extend the results of Alfaro and Damgaard on the origin of antifields to theories with a gauge algebra that is open or reducible.
A soluble model for scattering and decay in quaternionic quantum mechanics. II. Scattering
Authors: Horwitz L. P.
Published: July 2002

In a previous article, it was shown that a soluble model can be constructed for the the description of a decaying system in analogy to the Lee–Friedrichs model of complex quantum theory. It is shown here that this model also provides a soluble scattering theory, and therefore constitutes a model for a decay-scattering system. Generalized second resolvent equations are obtained for quaternionic scattering theory. It is shown explicitly for this model, in accordance with a general theorem of Adler, that the scattering matrix is complex subalgebra valued. It is also shown that the method of Adler, using an effective optical potential in the complex sector to describe the effect of the quaternionic interactions, is equivalent to the general method of Green’s functions described here.
Representations of commutation relations in BRST quantization
Authors: Rybkin G. N. , Vernov Yu. S.
Published: July 2002

It is shown that the asymptotic state space in the BRST quantization is a Krein space. The equivalence of the representations, which are realized by the asymptotic fields in such spaces, is proved.
An involutive system and integrable C. Neumann system associated with the modified Korteweg–de Vries hierarchy
Authors: Qiao Zhijun
Published: July 2002

In this article, a system of finite-dimensional involutive functions is presented and proven to be integrable in the Liouville sense. By using the nonlinearization method, the C. Neumann system associated with the modified Korteweg–de Vries (mKdV) hierarchy is obtained. Thus, the C. Neumann system is shown to be completely integrable via a gauge transformation between it and an integrable Hamiltonian system. Finally, the solution of a stationary mKdV equation and the involutive solutions of the mKdV hierarchy are secured. As two examples, the involutive solutions are given for the mKdV equation: vt+1/4vxxx−3/2v2vx=0 and the 5th mKdV equation vt−1/16vxxxxx+5/8v2vxxx +5/2vvxvxx +5/8v3x−3/40v4vx=0.
Finite-dimensional representations of the quantum superalgebra U
q[gl(2/2)]. I. Typical representations at generic q
Authors: Ky Nguyen Anh
Published: July 2002

In the present paper all typical finite-dimensional representations of the quantum Lie superalgebra Uq[gl(2/2)] are constructed at generic deformation parameter q. As in the nondeformed case, the finite-dimensional Uq[gl(2/2)]-module Wq obtained is irreducible and can be decomposed into finite-dimensional irreducible Uq[gl(2)⊕gl(2)]-submodules Vqk.
Noncommutative geometry for arbitrary braidings
Authors: Marcinek Wl/adysl/aw
Published: July 2002

The noncommutative geometry corresponding to arbitrary braidings is studied in a purely algebraical way. The new and original proposal of the geometry is given in terms of the theory of braided monoidal categories. The quantum oscillator is considered as an example of application of our geometry.
A geometrical formulation of Abelian gauge structure in non-Abelian gauge theories and disconnected gauge group
Authors: Sen Krishna , Bandyopadhyay Pratul
Published: July 2002

A geometrical formalism of non-Abelian gauge theory with a topological term is constructed here with special reference to the role of Abelian gauge structures in non-Abelian theories. It is shown that when fermionic currents are written in chiral forms, we can take into account the disconnected gauge group which helps us to formulate a non-Abelian gauge structure so that the theory becomes asymptotically free.
A class of new invariant surfaces under the trace maps for nary Fibonacci lattices
Authors: Iguchi Kazumoto
Published: July 2002

A class of new noncompact surfaces that are invariant under the trace maps for a series of nary Fibonacci lattices is derived herein. When n is fixed the lattice is constructed by a substitution scheme of n letters: A →ABCD...Z,B→A,C→B,D→C,... ,Z→Y, where the trace map is given by an n(n+1)/2-dimensional dynamical map. The invariant surface is of the (n+1)th degree and exists in Rn(n+1)/2. The existence of such surfaces is relevant to prove the universal criticality of the spectrum—whether or not all the states in the system belong to critical states, where the wave function is self-similar or fractal.