bluuebunny/crossref_metadata_2025 huggingface dataset:
Yang–Mills cohomology in four dimensions
Authors: Bandelloni Giuseppe
Published: July 2002

The local polynomial cohomology space of the Yang–Mills BRS operator in four dimensions is computed. In order to simplify the analysis, without omitting the physically interesting cases, the investigation is limited to polynomials whose Fadeev–Popov charge and UV naive dimensions have upper bounds. Furthermore the results are used to compute, á la Stora, the local functional Yang–Mills anomalies, from which the uniqueness of the Adler–Bardeen–Jackiw anomaly follows.
On the generation of equivalent Hamiltonians
Authors: Espindola Oslim , Teixeira Nelson L. , Espindola Maria L.
Published: July 2002

A new approach to the equivalence problem (in phase space) is presented. Given a Hamiltonian describing a system of particles with two degrees of freedom (and the corresponding Hamilton–Jacobi equation), it is shown how to find the most general family of Hamiltonian functions that generates a new Hamilton–Jacobi equation with the following (and essential) characteristic, here defined as equivalence: Every new solution is also a solution of the original Hamilton–Jacobi equation and vice versa.
On Geroch’s limit of space-times and its relation to a new topology in the space of Lie groups
Authors: Schmidt Hans-Jürgen
Published: July 2002

In the space Gn of n-dimensional Lie algebras a new non-Hausdorff topology τ is defined. Here (Gn, τ) is a compact connected T0 space. The closed one-point sets in the noncommutative part of Gn are called atoms. For each n≥3 there exist two atoms. Geroch’s limit defines a topology σ in the space Nn of local homogeneous Riemannian manifolds of dimension n. A natural relation of the Nn to the spaces Gn is given by the Lie algebra corresponding to the isometry group of the elements of Nn. It has nice σ–τ-continuity properties, e.g., the atoms are exactly those elements of Gn that correspond to closed nonempty subsets in the nonflat part of Nn. Applying to cosmology, especially for cosmological models with intrinsically homogeneous slices t=const, a complete answer to the question of how the isometry group of the spacelike hypersurfaces may depend on time is given: The slices are σ-continuous and their isometry groups are τ-continuous functions of time t. Applications of σ and τ to other problems are sketched.
Construction of space-time by gauge translations
Authors: Smrz P. K.
Published: July 2002

The following procedure is described: Starting with a connection in a principal fiber bundle P(M,G), where G is either the Poincaré group or one of the de Sitter groups, a connection in the bundle of linear frames of a submanifold N of M is constructed by using the translational components of the original connection for frame identification. The dimension of N is gauge dependent, and the flat four-dimensional Minkowski space-time may appear of dimension less than 4 when certain gauges are used. It is shown that in the case of a de Sitter group, the minimum dimension to which the flat four-dimensional space-time can be reduced is 1, while the number is 0 for the Poincaré group. The gauge transformation that achieves the maximum dimension reduction in the de Sitter case is constant and leads to infinite strings as a result. Variable continuous gauge transformations that can reduce the dimension over a finite region of the base manifold are also considered.
On the thermodynamic solution of the Boltzmann equation and nonlinear irreversible thermodynamics
Authors: Chen M.
Published: July 2002

Based on the results of a previous paper on the thermodynamic solution of the Boltzmann equation, some important questions in nonlinear irreversible thermodynamics are reexamined; specifically, the Gibbs relations, the Onsager relations, and the relationship between thermodynamic stability in terms of the entropy balance equation and the dynamical stability of the hydrodynamic equations.
Spectral properties of the Kronig–Penney Hamiltonian with a localized impurity
Authors: Fassari Silvestro
Published: July 2002

It is shown that there exist bound states of the operator H±λ=−(d2/dx2) +∑m∈Zδ(⋅−(2m+1)π)±λW, W being an L1(−∞,+∞) non-negative function, in every sufficiently far gap of the spectrum of H0=−d2/dx2 +∑m∈Zδ(⋅−(2m+1)π). Such an operator represents the Schrödinger Hamiltonian of a Kronig–Penney-type crystal with a localized impurity. The analyticity of the greatest (resp. lowest) eigenvalue of Hλ (resp. H−λ) occurring in a spectral gap as a function of the coupling constant λ when W is assumed to have an exponential decay is also proven.
Relations between spherical functions of compact groups
Authors: Klimyk A. U. , Vilenkin N. Ja.
Published: July 2002

The associated spherical functions of the homogeneous spaces SO(n)/SO(n−1), U(n)/U(n−1), and Sp(n)/Sp(n−1) are found in different coordinate systems: They are matrix elements of representation operators, right invariant with respect to the subgroups SO(n−1), U(n−1), and Sp(n−1), respectively. The left index of these matrix elements corresponds to the reductions onto the subgroups SO(p)×SO(q); U(p)×U(q); and Sp(p)×Sp(q), p+q=n. The relations between these spherical functions are derived. These relations lead to the formulas connecting the Clebsch–Gordan coefficients for the groups SO(n), U(n), and Sp(n).
Parastatistics and conformal field theories in two dimensions
Authors: Mansouri Freydoon , Wu Xizeng
Published: July 2002

The relation between parafermion field theories of order Q and the corresponding fermion field theories with SO(Q) symmetry is studied. It is shown that these theories are related but not identical. The explicit relation between the states and the observables of the two classes of theories are given without using the Klein transformations. The formalism is applied to the free conformally invariant parafermion theories in two dimensions. Their Virasoro algebra and SO(N) Kac–Moody algebra are given. The equivalence of their canonical form of the energy-momentum tensor with the Sugawara–Sommerfield form is also elucidated.
On the symmetric representations of SU(5). Matrix elements of the generators in the SO(3) basis
Authors: Vanthournout J. , De Meyer H. , Vanden Berghe G.
Published: July 2002

By making use of the results of a previous paper [J. Math. Phys. 29, 1958 (1988)], in which the matrix elements of the SU(5) generators were found in closed form for symmetric representations and in an SO(4) labeled state basis, it is shown how the matrix elements of the generators can also be derived in the physical SO(3) state basis. The main step consists in studying the action of the SU(5) generators upon a particular subset of so-called intrinsic SU(2)×SU(2) states out of which the physical SO(3) states are projected by means of the Hill–Wheeler technique.
On the log-normal diffusion process
Authors: Lehnigk Siegfried H.
Published: July 2002

The log-normal conditional density function is the delta function initial condition solution of a four-parameter Fokker–Planck equation. It defines a diffusion process over the open first quadrant of the (x,t) plane. This process reaches a nonzero steady state as t increases indefinitely if the drift parameter is positive. The process may be monotonic or by expansion and contraction (breathing). If the drift parameter is negative the process goes to zero by expansion and contraction towards x=0 as t increases indefinitely.
A nonlinear eigenvalue problem in astrophysical magnetohydrodynamics: Some properties of the spectrum
Authors: Adam John A.
Published: July 2002

The equations of ideal magnetohydrodynamics (MHD) with an external gravitational potential—a ‘‘magnetoatmosphere’’—are examined in detail as a singular nonlinear eigenvalue problem. Properties of the spectrum are discussed with specific emphasis on two systems relevant to solar magnetohydrodynamics. In the absence of a gravitational potential, the system reduces to that of importance in MHD and plasma physics, albeit in a different geometry. This further reduces to a form isomorphic to that derived in the study of plasma oscillations in a cold plasma, Alfvén wave propagation in an inhomogeneous medium, and MHD waves in a sheet pinch. In cylindrical geometry, the relevant model equations are those for a diffuse linear pinch. The full system, including gravity, has been applied to the study of flare-induced coronal waves, running penumbral waves in sunspots, and linear wave coupling in a highly inhomogeneous medium. The structure of the so-called MHD critical layer and its contribution to the continuous spectrum is examined in detail for a model magnetoatmosphere, based on properties of the hypergeometric differential operator. The relationship of this singular region to critical layers in classical linear hydrodynamic stability theory is also discussed in the light of a specific model (in the Appendix).
Generalized Skyrme model on higher-dimensional Riemannian manifolds
Authors: Yang Yisong
Published: July 2002

The Skyrme model is generalized to higher-dimensional Riemannian manifolds and the geometric conditions under which homothetic maps are absolute or local minimizers of the model are obtained.
Configurational interference in boundary-value problems governed by the Helmholtz equation
Authors: Singh G. S. , Singh S. N.
Published: July 2002

A rigorous approach is discussed for solving the two-dimensional Helmholtz equation in a multiply-connected domain consisting of a ring of N circles distributed symmetrically within a closed space. The outer boundary has been taken to be such that the system as a whole has N-fold rotational symmetry. The Dirichlet boundary condition has been satisfied exactly at the outer as well as at each of the inner edges, using the addition theorems for the cylindrical Bessel functions in conjugation with the Fourier expansions. Numerical results, showing spatial configurational interference, are presented for the lowest cutoff value of the symmetric mode as a function of separation between centers of two inner circles, in the case N=2 with circular outer boundary. The application of the method to various problems of physics and engineering is enunciated.
Multivariable biorthogonal Hahn polynomials
Authors: Tratnik M. V.
Published: July 2002

A multivariable biorthogonal generalization of the discrete Hahn polynomials, a p+1 complex parameter family, where p is the number of variables, is presented. It is shown that the polynomials are orthogonal with respect to subspaces of lower degree and biorthogonal within a given subspace. These properties are over the discrete simplex 0≤x1+x2+⋅⋅⋅+xp≤Δ, where x1, x2,...,xp and Δ are non-negative integers. Some further properties of the closely related multivariable continuous Hahn polynomials are also discussed.
Linear perturbations of plane polarized plane waves. I. The absence of purely incoming perturbations
Authors: Xanthopoulos Basilis C.
Published: July 2002

The linearized perturbations of plane polarized plane gravitational waves coupled with electromagnetic waves are studied. The dependence of the perturbations on the two spatial directions spanning the planar wave fronts and on advanced time is analyzed in normal modes (since the background depends only on retarded time). The linearized Newman–Penrose equations (Ricci and Bianchi identities, commutation relations, and Maxwell equations) are written explicitly for the general perturbations and without imposing any gauge condition. Then, making the assumption that there are no outgoing perturbations—i.e., that the perturbations do not depend on advanced time—the surprising result that there are no nontrivial purely incoming perturbations is obtained.
Extended Schrödinger equations leading to critical phenomena
Authors: Baseia B.
Published: July 2002

The role played by integrodifferential Schrödinger equations, as simulating critical phenomena, is investigated.
A family of electrovac colliding wave solutions of Einstein’s equations
Authors: Li Wei , Ernst Frederick J.
Published: July 2002

Beginning with any colliding wave solution of the vacuum Einstein equations, a corresponding electrified colliding wave solution can be generated through the use of a transformation due to Harrison [J. Math. Phys. 9, 1744 (1968)]. The method, long employed in the context of stationary axisymmetric fields, is equally applicable to colliding wave solutions. Here it is applied to a large family of vacuum metrics derived by applying a generalized Ehlers transformation to solutions published recently by Ernst, García, and Hauser (EGH) [J. Math. Phys. 28, 2155, 2951 (1987); 29, 681 (1988)]. Those EGH solutions were themselves a generalization of solutions first derived by Ferrari, Ibañez, and Bruni [Phys. Rev. D 36, 1053 (1987)]. Among the electrovac solutions that are obtained is a charged version of the Nutku–Halil [Phys. Rev. Lett. 39, 1379 (1977)] metric that possesses an arbitrary complex charge parameter.
Space-times admitting special affine conformal vectors
Authors: Coley A. A. , Tupper B. O. J.
Published: July 2002

Space-times admitting a special affine conformal vector (SACV) are shown to be precisely the space-times that admit a special conformal Killing vector. All possible SACV space-times are listed together with the corresponding SACV’s and covariantly constant tensors.
Classical non-Abelian Berry’s phase
Authors: Wu Yihren
Published: July 2002

The classical non-Abelian Berry’s phase is defined for a parameter-dependent dynamical system that is collective with respect to a Hamiltonian G-action when the parameters are fixed. It is shown that the corresponding angular two-form of Berry is given in terms of the momentum mapping of the G-action and is induced naturally by the symplectic form on the phase space. Moreover, this angular two-form can be seen as the correction term in the effective symplectic form on the parameter space, with respect to which the Hamiltonian is to be quantized.
Untenability of a proposed constrained dynamics for the damped harmonic oscillator
Authors: Lemos Nivaldo A.
Published: July 2002

It is argued that the method introduced recently by Wang [J. Phys. A: Math. Gen. 20, 4745 (1987)] to quantize the damped harmonic oscillator is untenable because it does not reproduce the standard results for the quantum oscillator in the limit of arbitrarily small damping. The method is also shown to be inconsistent if the friction coefficient is allowed to take any positive value.
On nonperfect fluid cosmologies evolving towards perfect fluid cosmological models
Authors: Carot J.
Published: July 2002

The problem of entropy production in near-equilibrium situations and their evolution towards a state of thermodynamic equilibrium is considered in the cosmological context. A physically realistic model (i.e., satisfying the energy conditions) describing such a situation is constructed. From a few hypotheses and considerations, it is seen that the metric tensors of the space-time at both equilibrium and nonequilibrium configurations are conformally related. The material content described by the energy-momentum tensor is interpreted as a viscous fluid smoothly evolving into a perfect one.
Spinor solution in a Kasner universe
Authors: Krori K. D. , Borgohain P. , Kar P. , Das (Kar) Dipali
Published: July 2002

In this paper an exact solution of the Dirac equation in an anisotropic Kasner metric is presented.
On the linearization stability of the conformally (anti-) self-dual Einstein equations
Authors: Torre C. G.
Published: July 2002

The Einstein equations with a cosmological constant, when restricted to Euclidean space-times with anti-self-dual Weyl tensor, can be replaced by a quadratic condition on the curvature of an SU(2) (spin) connection. As has been shown elsewhere, when the cosmological constant is positive and the space-time is compact, the moduli space of gauge-inequivalent solutions to this equation is discrete, i.e., zero dimensional; when the cosmological constant is negative, the dimension of the moduli space is essentially controlled by the Atiyah–Singer index theorem provided the field equations are linearization stable. It is shown that linearization instability occurs whenever the unperturbed geometry possesses a Killing vector and/or a ‘‘harmonic Weyl spinor.’’ It is then proven that while there are no Killing vectors on compact conformally anti-self-dual Einstein spaces with a negative cosmological constant, it is possible to have harmonic Weyl spinors. Therefore, the conformally anti-self-dual Einstein equations on a compact Euclidean manifold are linearization stable when the cosmological constant is negative provided the unperturbed geometry admits no harmonic Weyl spinors.
The realizations of quantum groups of A
n−1 and C
n types in q-deformed oscillator systems at classical and quantum levels
Authors: Chang Zhe , Wang Jian-Xiong , Yan Hong
Published: July 2002

In the classical q-deformed oscillators system, the Poisson bracket realizations of the quantum enveloping algebras of An−1 and Cn types are given in the symplectic space (V,Ω) (without deformation). When the oscillators system is canonically quantized, the Lie bracket realizations of the quantum enveloping algebras of An−1 and Cn types are obtained. The Hopf structures of these quantum enveloping algebras are supplied.
Partially invariant solutions of nonlinear Klein–Gordon and Laplace equations
Authors: Martina L. , Winternitz P.
Published: July 2002

The concept of partially invariant solutions is discussed in the framework of the group analysis of systems of partial differential equations. Using a general and systematic approach based on subgroup classification methods, nontrivial partially invariant solutions for specific equations are explicitly obtained, belonging to the NLKGE and NLLE classes in two dimensions. It is proven that the obtained partially invariant solutions are distinct from the invariant ones and from solutions obtained by other methods of reducing PDEs to ODEs.
On a geometrical formulation of the Nambu dynamics
Authors: Fecko Marián
Published: July 2002

A geometrical formulation of the N-triplet Nambu dynamics is given. It enables one to treat some general issues of the latter, including integral invariants and canonical transformations in a simple way. A possible underlying geometrical structure is discussed.
The R-matrix theory and the reduction of Poisson manifolds
Authors: Morosi C.
Published: July 2002

The relation between the R-matrix approach to the construction of bi-Hamiltonian structures and the reduction of Poisson manifolds is discussed. The crucial role of the reduction process is emphasized by showing, on the basis of specific examples, that the knowledge of a R matrix may not be sufficient. The reduction of the Poisson structures related with R from the entire algebra to the Lax submanifold may become an obstruction in constructing the bi-Hamiltonian structures of a specific hierarchy of integrable equations.
A comment on the generalized Kirchhoff–d’Adhémar formula for massless free fields in Minkowski space-time
Authors: Kerrick D. M.
Published: July 2002

A ‘‘spin-reduction’’ argument is used to obtain the generalized Kirchhoff–d’Adhémar formula for spin≳0 massless free fields in Minkowski space-time from the corresponding expression for a scalar field satisfying D’Alembert’s equation. A similar result is obtained for the Newman–Penrose constants in flat space-time.
Neutrino in the presence of gravitational fields: Exact solutions
Authors: Shishkin German V. , Villalba Víctor M.
Published: July 2002

The present paper is a further development of our previous paper [G. V. Shishkin and V. M. Villalba, J. Math. Phys. 33, 2093 (1992)]. Using the algebraic method of separation of variables, the structure of the metric functions is obtained in the presence of gravitational fields associated with a diagonal metric, which permits separation of variables in the Dirac equation. Applying the results obtained in a previous paper, we study the possibilities of finding exact solutions in the Dirac equation for massless neutrinos.
Diffeomorphism algebras and the Nahm and Ward equations
Authors: Chakravarty Sarbarish , Kent Steven , Newman Ezra T.
Published: July 2002

The question is investigated as to what equations arise from the reduction of the anti-self-dual Yang–Mills equations by the imposition of three (space-time) translational symmetries and by the choice of the connection coefficients having values in the infinite-dimensional Lie algebras associated with one- and two-dimensional diffeomorphism groups on one- and two-dimensional auxiliary manifolds. Special cases of this reduction yield the incompressible Euler equations for fluid flow in two spatial dimensions, the membrane equations in 4+1 dimensions, the continuous version of the Heisenberg spin-chain equations for antiferromagnets, as well as the Toda lattice and Liouville equations.
Eigenfunctions and heat kernels of super Maass Laplacians on the super Poincaré upper half-plane
Authors: Oshima Kazuto
Published: July 2002

Heat kernels of ‘‘super Maass Laplacians’’ are explicitly constructed on super Poincaré upper half-plane by a serious treatment of a complete set of eigenfunctions. By component decomposition an explicit treatment can be done for arbitrary weight and a knowledge of classical Maass Laplacians becomes helpful. The result coincides with that of Aoki [Commun. Math. Phys. 117, 405 (1988)] which was obtained by solving differential equations.
Roots of unity: Representations for symplectic and orthogonal quantum groups
Authors: Schnizer W. A.
Published: July 2002

Representations for quantum groups at q an Nth root of 1 with a structure resembling the algebraic structure in the theory of the chiral Potts models are constructed in the Uq(sp(2n,C)), Uq(so(2n+1,C)), and Uq(so(2n,C)) cases. The dimensions of the given representations and their number of free parameters are N(1/2)(dim g-rank g), dim g, respectively.
Superadiabatic evolution and adiabatic transition probability between two nondegenerate levels isolated in the spectrum
Authors: Joye Alain , Pfister Charles-Edouard
Published: July 2002

The Schrödinger equation in the adiabatic limit when the Hamiltonian depends analytically on time and possesses for any fixed time two nondegenerate eigenvalues e1(t) and e2(t) bounded away from the rest of the spectrum is considered herein. An approximation of the evolution called superadiabatic evolution is constructed and studied. Then a solution of the equation which is asymptotically an eigenfunction of energy e1(t) when t→−∞ is considered. Using superadiabatic evolution, an explicit formula for the transition probability to the eigenstate of energy e2(t) when t→+∞, provided the two eigenvalues are sufficiently isolated in the spectrum, is derived. The end result is a decreasing exponential in the adiabaticity parameter times a geometrical prefactor.
Evolution equations invariant under two-dimensional space–time Schrödinger group
Authors: Rideau G. , Winternitz P.
Published: July 2002

The most general second order evolution equation ψt+F(x,t,ψψ*,ψx,ψx*,ψxx, ψxx*)=0, invariant under the Galilei, Galilei-similitude, and Schrödinger groups in two dimensions, is constructed. A preliminary step is a classification of all possible realizations of the corresponding Lie algebras of vector fields in ℛ2×𝒞 parametrized by x, t, ψ, and ψ*. Applications of this study include the investigation of nonlinear alternatives to quantum mechanics and nonrelativistic classical field theories. Among the Schrödinger invariant equations, in particular, are found integrable equations, linearizable by contact transformations.
On quantum characteristic exponents
Authors: Majewski W. A. , Kuna M.
Published: July 2002

The definition of quantum characteristic exponents for a general quantum dynamical map is given. The basic properties of this notion and illustrative models are presented.
Interpolation in multidimensions, a convenient finite-dimensional matrix representation of the (partial) differential operators, and some applications
Authors: Calogero F.
Published: July 2002

An extension to multidimensions of (a generalized notion of) Lagrangian interpolation is used to introduce finite-dimensional matrix representations of the (partial) differential operators. This makes it possible to extend to a multidimensional environment various results which were obtained in the past by exploiting such a representation in a one-dimensional context. Some such applications are outlined: the construction of remarkable matrices, convenient techniques to solve numerically eigenvalue problems and differential equations in multidimensions, and the manufacture of solvable ‘‘many-body’’ dynamical systems in multidimensional spaces (some instances of such systems are exhibited).
The bi-Hamiltonian structure for the restricted flows of the Boussinesq and the modified Boussinesq equation
Authors: Zeng Yunbo
Published: July 2002

The methods of previous articles are extended herein, using the Miura-type transformation between two soliton equations and the gauge transformation between two associated eigenvalue problems, and a bi-Hamiltonian structure and involutive integrals of motion for x- and t-finite-dimensional integrable Hamiltonian systems (FDIHS) obtained from the decomposition of the Boussinesq equation and the modified Boussinesq equation are computed, respectively. This decomposition provides a way to obtain a certain kind of solution for the later two equations through solving two commuting FDIHS’s. The methods are also applied to the FDIHS’s related to the higher-order constraints.
Third-order bounds on the conductivity of a random stacking of cubes
Authors: Helsing Johan
Published: July 2002

Third-order bounds on the conductivity of a random stacking of cubes are constructed. Since a random stacking of cubes is a symmetric cell material the bounds are determined by a Miller parameter G [J. Math. Phys. 10, 1988 (1969)] that is independent of volume fractions. This parameter is evaluated with a boundary integral technique to G=0.1375164293203.
Deformations of nilpotent parts of the Neveu–Schwarz and Ramond superalgebras
Authors: van den Hijligenberg N.
Published: July 2002

Deformations of nilpotent parts of the Neveu–Schwarz superalgebra and of the Ramond superalgebra are studied herein. This study consists of the computation of the second cohomology space with coefficients in the adjoint representation by means of spectral sequences, the explicit construction of infinitesimal deformations, the extension of these infinitesimal deformations to one-parameter deformations, the realization of these deformations, and the construction of multiparameter deformations.
An n-dimensional interpretation of the δ -expansion for the Thomas–Fermi equation
Authors: Morales Daniel A.
Published: July 2002

The recent success of the δ-expansion in the solution of the Thomas–Fermi equation is interpreted to be due to the selection of an expansion parameter that interpolates between the dimension of interest, n=3, and the dimension where the problem is exactly soluble, n=2.
Resonance theory of elastic head waves in layered media. I. A fluid layer bottomed by an infinite solid
Authors: Yu Shoumian , Yu Tian , Liu Yinbin
Published: July 2002

In the conventional theory of elastic wave in layered media, the head wave is believed to be the ‘‘critically refracted arrival.’’ However, there are many difficulties which remain unsettled. In order to clarify these questions, the corresponding boundary value problem is re-treated by the standing wave method, in which the path of integration in the wave-number plane is uniquely determined by the boundary conditions. It is found that the critical refraction does not exist. The physical mechanism of the head wave is shown to be a mode of resonance, and is a nonlinear effect of the elastic wave equation. The property of the head wave is discussed in detail. Some predictions are compared with observations.
Deformations preserving Huygens’ principle
Authors: Berest Yuri Yu.
Published: July 2002

A new kind of deformation related to the Korteweg–de Vries hierarchy and its master symmetries is studied. The algebra of deformations is generated by trivial (point) transformations via a special recursion operator and proved to preserve Huygens’ principle for a certain family of hyperbolic linear equations. The corresponding evolution flows for Hadamard coefficients are presented explicitly. The connections with spectral deformations and Darboux transformations as well as recent works on the bispectral problem for a Schrödinger operator are discussed.
Phase space structure of non-Abelian Chern–Simmons particles
Authors: Kim Myung Ho , Oh Phillial
Published: July 2002

The classical phase space structure of N SU(n+1) non-Abelian Chern-Simons (NACS) particles is investigated by first constructing the product space of associated SU(n+1) bundle with CPn as the fiber. The Poisson bracket is calculated using the symplectic structure on the associated bundle and it is found that the minimal substitution in the presence of external gauge fields is equivalent to the modification of symplectic structure by the addition of field strength two form. Then, a direct product of the associated bundle is taken by the space of all connections and a specific connection is chosen by the condition of vanishing momentum map corresponding to the gauge transformation, thus recovering the quantum mechanical model of NACS particles in Lee and Oh [Phys. Rev. Lett. 72, 1141 (1994)].
The Calogero bound for nonzero angular momentum
Authors: Chadan K. , Martin A. , Stubbe J.
Published: July 2002

It is shown that the ‘‘Calogero’’ bound on the number of bound states in an attractive monotonous potential is not optimal for a strictly positive angular momentum ℓ and a new bound including an extra additive term is proposed. It is Nℓ(V)<(2/π)∫0∞√‖V(r)‖dr+1−√1 +(2/π)2ℓ(ℓ+1). From this new bound it is possible to obtain a bound on the total number of bound states for arbitrary angular momentum. The situation for −1/2≤ℓ<0 is investigated and a bound under the condition that r2V(r) has a single extremum is given. Consequences for zero angular momentum bound states in two dimensions are discussed.
Operator-theoretical analysis of a representation of a supersymmetry algebra in Hilbert space
Authors: Arai Asao
Published: July 2002

Operator-theoretical analysis is made on (unbounded) representations, in Hilbert spaces, of a supersymmetry (SUSY) algebra coming from a supersymmetric quantum field theory in two-dimensional space–time. A basic idea for the analysis is to apply the theory of strongly anticommuting self-adjoint operators. A theorem on integrability of a representation of the SUSY algebra is established. Moreover, it is shown that strong anticommutativity of self-adjoint operators is a natural and suitable concept in analyzing representations of the SUSY algebra in Hilbert space.
A symplectic interpretation of some wave fronts in general relativity
Authors: Liern V. , Olivert J.
Published: July 2002

In order to study the symplectic structures of the elementary relativistic free particles in general relativity, a nonvectorial associated fiber bundle is constructed over the space-time manifold. A foliation in the space-time is achieved which gives rise to the geodesics principle for massive particles and wave fronts for massless particles.
On the algebra generated by two projections
Authors: Borac Silviu
Published: July 2002

The von Neumann algebra generated by a pair of projections on a separable Hilbert space occurs naturally in the study of quantum Hall systems. By a systematic use of Kato’s dual pair of self-adjoint operators corresponding to the two projections, the argument referring to the structure of the algebra can be simplified and the existence of an action of the group SU(2) on the algebra via inner automorphisms can be shown. Also, the algebra can be given an r-structure with respect to which it is r-commutative, and an extension of the classical (commutative) differential calculus becomes possible.
The monopole equations in topological Yang–Mills
Authors: Brooks Roger , Lue Arthur
Published: July 2002

We twist the monopole equations of Seiberg and Witten and show how these equations are realized in topological Yang–Mills theory. A Floer derivative and a Morse functional are found and are used to construct a unitary transformation between the usual Floer cohomologies and those of the monopole equations. Furthermore, these equations are seen to reside in the vanishing self-dual curvature condition of an OSp(1‖2)-bundle. Alternatively, they may be seen arising directly from a vanishing self-dual curvature condition on an SU(2)-bundle in which the fermions are realized as spanning the tangent space for a specific background.
Uniqueness of zero surface gravity SU(2) Einstein–Yang/Mills black holes
Authors: Smoller J. A. , Wasserman A. G.
Published: July 2002

In this paper we prove that the only spherically symmetric black hole solution to the SU(2) Einstein–Yang/Mills equations that has zero temperature at the event horizon is the extreme Reissner–Nordström solution. No assumptions are made on the signs of the metric coefficients, save that the metric has Lorentz signature.
Complete sets of non-self-adjoint observables: An unbounded approach
Authors: Epifanio Giuseppina , Todorov Todor S. , Trapani Camillo
Published: July 2002

The notion of completeness of a set 𝒮 of compatible observables represented by maximal symmetric operators is discussed directly in terms of unbounded operators. In contrast with what happens for self-adjoint observables, the present framework forces us to involve some partial algebraic structures such as the partial GW*-algebra generated by 𝒮. In this way the previous approaches based on von Neumann algebras and on O*-algebras are generalized.
Essential spectrum of the Dirac Hamiltonian for a spin 1/2 neutral particle with an anomalous magnetic moment in an asymptotically constant magnetic field
Authors: Ogurisu Osamu
Published: July 2002

The both lower and upper estimates of the lower bound λ20 of the essential spectrum σess(H2) of the square of the Dirac Hamiltonian H for a spin 1/2 neutral particle with an anomalous magnetic moment in an asymptotically constant magnetic field are obtained. It is found that in a restricted case, λ20≤m2, where m is the mass of the particle. Moreover, it is proven that σess(H2)=[λ20,∞). In particular, in the case where the space dimension d is odd and d≥3, σess(H)=(−∞,−λ0]∪[λ0,∞). In the case where d=2 and 3, σess(H) is exactly identified.
Non-standard thermal statistics with q-entropies
Authors: Guerberoff Gustavo R. , Pury Pedro A. , Raggio Guido A.
Published: July 2002

We consider the quantum thermal statistics à la Gibbs–Shannon–Szilard–Jaynes based on q-entropies Sq[ρ]=(q−1)−1(1−tr(ρq)) (0<q≠1) and the non-standard ‘‘internal energy’’ functionals Uq[ρ]=tr(ρqH) proposed by C. Tsallis [J. Stat. Phys. 52, 479–487 (1988)].
Geometries of relativistic strings and other p-branes
Authors: Jensen Bjo/rn
Published: July 2002

We discuss the geometric structure outside an infinitely long and straight relativistic bosonic string in various space–time dimensions. This structure should, in particular, be a good model for the geometry outside a gauge cosmic string in four dimensions. We study a new such geometry in some depth. A discussion of a possible internal geometry of a gauge cosmic string is also given. We show that space–time is flat outside a relativistic string only in four space–time dimensions. This is connected to the lack of a proper Newtonian limit of Einstein’s theory inside any source for the string geometry in four dimensions. On this background we discuss some features of the geometries induced by other p-branes in various dimensions. We also provide a study of the creation of a gauge cosmic string in the full Einstein theory in four dimensions, with results that differ considerably from similar earlier considerations.
A factorization of a special type S matrix into Jost matrices
Authors: Krutov A. F. , Muravyev D. I. , Troitsky V. E.
Published: July 2002

An effective algebraic approach to S-matrix factorization into Jost matrices is developed for the case of a 2×2 S matrix that can be diagonalized by means of a rotation by an angle whose tangent is a rational function of k2. The Jost matrix is given as a solution of the boundary value Riemann–Hilbert problem.
Disconnected forms of the standard group
Authors: McInnes Brett
Published: July 2002

Recent work in quantum gravity has led to a revival of interest in the concept of disconnected gauge groups. Here we explain how to classify all of the (nontrivial) groups which have the same Lie algebra as the “standard group,” SU(3)×SU(2)×U(1), without requiring connectedness. The number of possibilities is surprisingly large. We also discuss the geometry of the “Kiskis effect,” the ambiguity induced by nontrivial space–time topology in such gauge theories.
Automorphisms of sl(2) and dynamical r-matrices
Authors: Tsiganov A. V.
Published: July 2002

Two outer automorphisms of the space of infinite-dimensional representations of sl(2) algebra are considered. The similar constructions for the loop algebras and Yangians are presented. The corresponding linear and quadratic R-brackets include the dynamical r-matrices.
Quantum critical fluctuations in a ferroelectric model: Quasi-average approach
Authors: Joussot Patrice , Zagrebnov Valentin A.
Published: July 2002

We show that critical fluctuations in a quantum ferroelectric model depend not only on the range of harmonic interactions but also on infinitesimal perturbations breaking symmetry of the model. This means that algebra of fluctuation operators is degenerated for (unique) critical equilibrium state.
Analytic regularization of the (ψ̄iψi)D2 model at finite temperature and density
Authors: Añaños G. N. J. , Malbouisson A. P. C. , Svaiter N. F.
Published: July 2002

Simultaneously using the dimensional and analytic regularization methods we reexamine the Gross–Neveu model at finite temperature and density (chemical potential) in a D-dimensional space–time. The regularized effective potential is presented at the 1/N (large N) approximation. It is found that in D=3 the effective potential is finite.
Matrix formulation of Hamiltonian structures of constrained KP hierarchy
Authors: Huang Wen-Jui , Shaw Jiin-Chang , Tu Ming-Hsien
Published: July 2002

We give a matrix formulation of the Hamiltonian structures of constrained KP hierarchy. First, we derive from the matrix formulation the Hamiltonian structure of the one-constraint KP hierarchy, which was originally obtained by Oevel and Strampp. We then generalize the derivation to the multiconstraint case and show that the resulting bracket is actually the second Gelfand–Dickey bracket associated with the corresponding Lax operator. The matrix formulation of the Hamiltonian structure of the one-constraint KP hierarchy in the form introduced in the study of matrix model is also discussed.
Integrable discretizations of the Euler top
Authors: Bobenko A. I. , Lorbeer B. , Suris Yu. B.
Published: July 2002

Discretizations of the Euler top sharing the integrals of motion with the continuous time system are studied. Those of them which are also Poisson with respect to the invariant Poisson bracket of the Euler top are characterized. For all these Poisson discretizations a solution in terms of elliptic functions is found, allowing a direct comparison with the continuous time case. We demonstrate that the Veselov–Moser discretization also belongs to our family, and apply our methods to this particular example.
Quantization of massive vector fields in curved space–time
Authors: Furlani Edward P.
Published: July 2002

We develop a cannonical quantization for massive vector fields on a globally hyperbolic Lorentzian manifold.
On the spectral theory of dispersive N-body Hamiltonians
Authors: Damak Mondher
Published: July 2002

In this work we describe a general class of dispersive N-body Hamiltonians for which we prove the Hunziker, van Winter, and Zislin (HWZ) theorem and a Mourre estimate outside a closed and countable set of energies called thresholds. As a consequence of the Mourre estimate we prove a strong form of the limiting absorption principle, which implies the absence of a singular continuous spectrum and gives criteria of local smoothness.
Nonlocal potentials, isolated states, and Levinson’s theorem
Authors: Weber T. A.
Published: July 2002

A compact expression for the calculation of phase shifts is derived for a potential which is the sum of local and nonlocal parts. Nonlocal potentials can support positive energy bound states, that is, states embedded in the continuous energy spectrum. These states, sometimes referred to as “isolated” states, are not associated with any poles of the S matrix. Some controversy exists in the literature on how such bound states are included in Levinson’s theorem; it is found that the phase shift should be taken continuous at the energy of the bound state rather than taken to have a discontinuity of π. For simplicity, the analysis is restricted to the radial s wave Schrödinger equation and separable nonlocal potentials.
Poisson–Lie structures on infinite-dimensional jet groups and quantum groups related to them
Authors: Stoyanov Ognyan
Published: July 2002

We study the problem of classifying all Poisson–Lie structures on the group G∞ of formal diffeomorphisms of the real line R1 which leave the origin fixed, as well as the extended group of diffeomorphisms G0∞⊃G∞ whose action on R1 does not necessarily fix the origin. A complete local classification of all Poisson–Lie structures on the groups G∞ and G0∞ is given. This includes a classification of all Lie-bialgebra structures on the Lie algebra G∞ of G∞, which we prove to be all of the coboundary type, and a classification of all Lie-bialgebra strucutures on the Lie algebra G0∞ (the Witt algebra) of G0∞ which also turned out to be all of the coboundary type. A large class of Poisson structures on the space Vλ of λ-densities on the real line is found such that Vλ becomes a homogeneous Poisson space under the action of the Poisson–Lie group G∞. We construct a series of quantum semigroups whose quasiclassical limits are finite-dimensional Poisson–Lie quotient groups of G∞ and G0∞.
On a trace formula of the Buslaev–Faddeev type for a long-range potential
Authors: Rybkin Alexei
Published: July 2002

We propose an approach to obtaining new trace formulas of the Gel’fand–Levitan–Buslaev–Faddeev type, valid for Hilbert–Schmidt perturbations. In this way we obtain a new trace formula for Schrödinger operators on the half-line with long-range potentials.
On a purported local extension of the quantum formalism
Authors: Melia Joseph , Redhead Michael
Published: July 2002

It is widely believed that Bell has proved there can be no consistent local extension of the quantum formalism. Against this, Angelidis has presented a hidden variable theory which, he claims, makes precisely the same predictions as the quantum formalism and which also satisfies locality. In this note, we argue that Angelidis’ theory does not live up to its inventor’s claims.
Solution of a discrete inverse scattering problem and of the Cauchy problem of a class of discrete evolution equations
Authors: Blohm Henning
Published: July 2002

The Cauchy problem of a class of nonlinear evolution equations is solved by finding explicit solutions of a discrete inverse scattering problem that are not restricted to the pure soliton case and implementing appropriate time evolution of the scattering data. This yields operator-valued functions, which are shown to solve a hierarchy of operator evolution equations by applying methods similar to those in Marchenko’s work. In addition the relation to canonical Lax constructions is investigated. Using methods introduced by Aden and Carl and Schiebold, one obtains scalar solutions to corresponding scalar equations, sometimes representable by determinants on operator ideals.
Families of quasi-bi-Hamiltonian systems and separability
Authors: Zeng Yunbo B. , Ma Wen-Xiu
Published: July 2002

It is shown how to construct an infinite number of families of quasi-bi-Hamiltonian (QBH) systems by means of the constrained flows of soliton equations. Three explicit QBH structures are presented for the first three families of the constrained flows. The Nijenhuis coordinates defined by the Nijenhuis tensor for the corresponding families of QBH systems are proved to be exactly the same as the separated variables introduced by mean of the Lax matrices for the constrained flows.
Exact solutions to sourceless charged massive scalar field equation on Kerr–Newman background
Authors: Wu S. Q. , Cai X.
Published: July 2002

The covariant Klein–Gordon equation in the Kerr–Newman black hole geometry is separated into a radial part and an angular part. It is discovered that in the nonextreme case, these two equations belong to a generalized spin-weighted spheroidal wave equation. Then general exact solutions in integral forms and several special solutions with physical interest are given. While in the extreme case, the radial equation can be transformed into a generalized Whittaker–Hill equation. In both cases, five-term recurrence relations between coefficients in power series expansion of general solutions are presented. Finally, the connection between the radial equations in both cases is discussed.
On the number of particles that a curved quantum waveguide can bind
Authors: Exner Pavel , Vugalter Simeon A.
Published: July 2002

We discuss the discrete spectrum of N particles in a curved planar waveguide. If they are neutral fermions, the maximum number of particles that the waveguide can bind is given by a one-particle Birman–Schwinger bound in combination with the Pauli principle. On the other hand, if they are charged, e.g., electrons in a bent quantum wire, the Coulomb repulsion plays a crucial role. We prove a sufficient condition under which the discrete spectrum of such a system is empty.
The semispin groups in string theory
Authors: McInnes Brett
Published: July 2002

In string theory, an important role is played by certain Lie groups which are locally isomorphic to SO(4m), m⩽8. It has long been known that these groups are actually isomorphic not to SO(4m) but rather to the groups for which the half-spin representations are faithful, which we propose to call Semispin(4m). (They are known in the physics literature by the ambiguous name of “Spin(4m)/Z2.”) Recent work on string duality has shown that the distinction between SO(4m) and Semispin(4m) can have a definite physical significance. This work is a survey of the relevant properties of Semispin(4m) and its subgroups.
Time harmonic electromagnetic scattering from a bounded obstacle: An existence theorem and a computational method
Authors: Fatone Lorella , Pignotti Cristina , Recchioni Maria Cristina , Zirilli Francesco
Published: July 2002

Let Ω⊂R3 be a bounded simply connected obstacle with boundary ∂Ω locally Lipschitz, we consider the scattering of a time harmonic electromagnetic wave that hits Ω when ∂Ω is assumed to be perfectly conducting. The scattered electromagnetic field is the solution of an exterior boundary value problem for the vector Helmholtz equation. Under suitable hypotheses we prove the existence and uniqueness of the solution of this boundary value problem and we give a new numerical method to compute this solution. The numerical method proposed is based on a perturbative series and is highly parallelizable. Some numerical results obtained with the numerical method proposed on test problems are presented and discussed from the numerical and the physical point of view.