bluuebunny/crossref_metadata_2025 huggingface dataset:
Classes of exactly solvable nonlinear evolution equations for Grassmann variables: The normal form method
Authors: Elphick Christian
Published: July 2002

A systematic procedure is presented to solve analytically differential equations for Grassmann variables with the most general nonlinearity. The method consists in the reduction of the original equation to its simplest form (normal form). The classes of solvable normal forms are determined only by the structure of the linear part of the original equation and are parametrized in terms of the number of critical eigenvalues.
On the spectrum of a third-order SO(3) scalar in the enveloping algebra of SO(6)
Authors: Vanthournout J. , Van der Jeugt J. , De Meyer H. , Vanden Berghe G.
Published: July 2002

With the aid of previously derived expressions for the SO(3) reduced matrix elements of the SO(6) generators, which were obtained by considering an intermediate SO(6)↓SU(2)⊗SU(2) reduction, a method is set up to evaluate analytic expressions for the eigenvalues of a third-order scalar operator belonging to the integrity basis of SO(3) scalar operators in the enveloping algebra of SO(6).
Circle maps and reciprocal winding numbers
Authors: Söderberg B.
Published: July 2002

A construction that relates circle maps of mutually reciprocal winding number, belonging to the same criticality class, is presented. It is explicitly invariant under smooth conjugations of either map, and displays a series of remarkable properties, in spite of its simplicity.
Petrov types D and II perfect-fluid solutions in generalized Kerr–Schild form
Authors: Martín-Pascual F. , Senovilla J. M. M.
Published: July 2002

Petrov types D and II perfect-fluid solutions are obtained starting from conformally flat perfect-fluid metrics and by using a generalized Kerr–Schild ansatz. Most of the Petrov type D metrics obtained have the property that the velocity of the fluid does not lie in the two-space defined by the principal null directions of the Weyl tensor. The properties of the perfect-fluid sources are studied. Finally, a detailed analysis of a new class of spherically symmetric static perfect-fluid metrics is given.
The ground-state energy of a system of identical bosons
Authors: Hall Richard L.
Published: July 2002

A system of N identical bosons is studied, each having mass m, which interact in R3 via attractive central pair potentials and obey nonrelativistic quantum mechanics. A lower energy bound is found by the equivalent two-body method. An upper energy bound established previously on the basis of field theory is now derived by variational methods within conventional quantum mechanics. In the case of the linear potential Vij=γ‖ri−rj‖ the bounds imply that the ground-state energy is given by ℰ=C(N)(N−1)(ℏ2/m)1/3(γN/2)2/3, where 2.3381<C(N)<2.343 52. The energy is therefore determined in this case with error <0.116% for all N≥2. Similar results are given for other power-law potentials.
Geometry of free fall and simultaneity
Authors: Ewen Holger , Schmidt Heinz-Jürgen
Published: July 2002

It is shown that the differentiable, affine, and metric structure of Newton–Cartan space-time is uniquely determined by its projective–conformal–material structure. This means physically, that—similarly as in general relativity—it is also possible in classical gravitation to define operations of parallel transport and measurements of length, time, and mass using only three kinds of world lines: world lines of freely falling test particles, of photons, and of gravitational matter.
Geometric model for gravitational and electroweak interactions
Authors: Rosenbaum M. , D’Olivo J. C. , Nahmad-Achar E. , Bautista R. , Muciño J.
Published: July 2002

A fiber bundle treatment for Kaluza–Klein-type geometric unification of gravitation with the bosonic sector of the standard electroweak theory is presented. The most general G-invariant quadratic Lagrangian is constructed explicitly, and it is shown that the Higgs field sector, including the symmetry-breaking potential, arise naturally from torsion in the fiber through an adequate choice of its transformation properties.
Generalized coherent states for a three-dimensional relativistic model of the oscillator
Authors: Atakishiyev N. M. , Mir-Kasimov R. M.
Published: July 2002

The SU(1,1) coherent states for a relativistic model of the oscillator in the configurational r representation are considered. Classical equations of motion in the generalized phase space are obtained with the help of the path integral for the transition amplitude between SU(1,1) coherent states. It is shown that the use of the semiclassical Bohr–Sommerfeld quantization rule yields the exact expression for the energy levels.
On linear unitary transformations of two canonical variables
Authors: Plebański Jerzy F. , Finley J. D.
Published: July 2002

A useful parametrization of the groups SO(0,3) and SO↑(2,1) is presented that has simple, rational composition laws, albeit that it has a (quasigraded) structure. This ‘‘tangential’’ parametrization is also advantageous in providing a rather simple 1-1 ‘‘picture’’ of the elements of the groups in question. As well, the parametrization allows an explicitly finite result for the composition law needed for the (abstract) Baker–Campbell–Hausdorff formula for exponentials of objects formed from the corresponding Lie algebras. This approach, in turn, allows a useful beginning to the problem of the determination of flows on the group manifold, i.e., the determination of analytic curves given the initial direction of the curve.
A new approach to Bianchi V models
Authors: Bona Carles , Palou Pere
Published: July 2002

Spatially homogeneous perfect fluid space-times pertaining to the Bianchi V class are considered from the point of view of the evolution (3+1) formalism of general relativity. It is shown that the metric can be written in diagonal form in the nontilted case. The necessary and sufficient condition for the metric of a Bianchi V model to be diagonalizable is given.
Symmetries in the Lagrangian formalism
Authors: Grigore D. R.
Published: July 2002

The analysis of Levy-Leblond [Commun. Math. Phys. 12, 64 (1969)] is generalized for Lagrangian systems with symmetry. It is proved that this analysis goes through practically unchanged, and then some examples are analyzed in detail.
Stationary axisymmetric fluid solutions of the Einstein–Born–Infeld equations
Authors: Bretón B. Nora
Published: July 2002

A new class of Einstein’s field equations with the energy-momentum tensor of a perfect fluid with nonlinear electromagnetic field aligned along the Debever–Penrose directions is determined. The solution obtained is a nonlinear electromagnetic generalization of the fluid NUT-B̃(+) [Newman–Unti–Tamburino and Carter B(+)] solution.
Classification of star and grade-star representations of C(n+1)
Authors: Zhang R. B. , Gould M. D.
Published: July 2002

The two types of * and grade-* representations of the Lie superalgebra C(n+1) are classified. A type (1) irreducible *-representation is characterized by the single condition (Λ,αs)≥0, Λ and αs being the highest weight and the odd simple root, respectively, while the type (2) *-representations are duals of type (1) *-representations. For n>1, only the identity and vector representations of C(n+1) are shown to be grade -*. The superalgebra C(2) proves to be an exception and admits several classes of nontrivial irreducible grade -* representations.
Wavelet analysis on the circle
Authors: Holschneider Matthias
Published: July 2002

The construction of a wavelet analysis over the circle is presented. The spaces of infinitely times differentiable functions, tempered distributions, and square integrable functions over the circle are analyzed by means of the wavelet transform.
Space-time geometry of relativistic particles
Authors: Kim Y. S. , Wigner E. P.
Published: July 2002

A three-dimensional space-time geometry of relativistic particles is constructed within the framework of the little groups of the Poincaré group. Since the little group for a massive particle is the three-dimensional rotation group, its relevant geometry is a sphere. For massless particles and massive particles in the infinite-momentum limit, it is shown that the geometry is that of a cylinder and a two-dimensional plane. The geometry of a massive particle continuously becomes that of a massless particle as the momentum/mass becomes large. The geometry of relativistic extended particles is also considered. It is shown that the cylindrical geometry leads to the concept of gauge transformations, while the two-dimensional Euclidean geometry leads to a deeper understanding of the Lorentz condition.
On the complete system of observables in quantum mechanics
Authors: de Oliveira César R.
Published: July 2002

This paper contains a series of remarks about the concept of Complete System of Observables (CSO) in quantum mechanics and a discussion of two definitions of CSO, one given by Jauch [Helv. Phys. Acta 33, 711 (1960)] and the other by Prugovecki [Can. J. Phys. 47, 1083 (1968)].
Applications of the differentiability of eigenvectors and eigenvalues to a perturbed harmonic oscillator
Authors: Ifantis E. K. , Panagopoulos P. N.
Published: July 2002

The potential interaction λx2/(1+gx2), g>0, of the harmonic oscillator H0=−d2/dx2+x2 considered as an operator in the space L2(−∞, ∞) is bounded. This together with the nondegeneracy of the eigenvalues implies that the eigenvectors of the perturbed harmonic oscillator as functions of the parameters λ and g are strongly differentiable. The eigenvalues are therefore differentiable functions for every real λ and every real g>0. In particular, the first eigenvalue E1(λ) as a function of λ is strictly concave (E″1(λ)<0). This paper, exploiting the above properties, aims at several inequalities for the eigenvalues of H0+λx2/(1+gx2), g>0. Emphasis is given to the inequality that follows from the strict concavity of the function E1(λ).
Curvature-squared cosmology in the first-order formalism
Authors: Shahid-Saless Bahman
Published: July 2002

Variation of the R+αR2 action with respect to independent metric and connection fields is shown to be equivalent to the metric-compatible fourth-order gravity coupled to a vector defined as a function of the trace of the energy-momentum tensor. The field equations are second order. The Friedmann cosmology based on this model is studied and it is shown to include nonsingular solutions at t=0.
Infrared singularities and breaking of the Poincaré group: The massless dipole field
Authors: Moschella Ugo
Published: July 2002

A four-dimensional quantum field theory model is studied that exhibits infrared singularities expected to occur in realistic models of confinement. The Fock–Hilbert–Krein structure associated with the model in a local and covariant formulation is constructed and its unconventional features, like the existence of translationally invariant field operators and states (other than the vacuum), the implementation of the symmetries, etc., are discussed. Also, a canonical quantization of the model which improves the existing ones is derived. Finally, it is shown that the infrared singularities are responsible of the breaking of the Poincaré group in every nontrivial physical space; two explicit examples of possible physical spaces are constructed and it is shown that they have the same gauge invariant content.
The Feynman integrand as a Hida distribution
Authors: de Faria M. , Potthoff J. , Streit L.
Published: July 2002

It is shown that Feynman integrals are weighted averages over Brownian paths, with suitable Hida distributions as (complex) weights. For simple cases, the construction of these distributions is be performed explicitly, for a much larger class of interactions, their existence is shown.
The three-dimensional real Lie algebras and their contractions
Authors: Weimar-Woods Evelyn
Published: July 2002

In this paper, the general contractions of the three-dimensional real Lie algebras are determined. A short summary will be given of the history, definitions, properties, examples, and applications of contractions of Lie algebras. So far, mostly simple or generalized Inönü–Wigner contractions have been used. The three-dimensional real Lie algebras are classified in such a way that their general contractions can be easily read off. All these contractions can be realized by generalized Inönü–Wigner contractions, which supports the argument that these are the interesting objects to study.
Quantum Ř matrix for E7 and F4 groups
Authors: Kim J. D. , Koh I. G. , Ma Zhong-Qi
Published: July 2002

The quantum Ř matrix for E7 and F4 are explicitly constructed for the defining representations 56 and 26 of E7 and F4, respectively. For these, Skein relations, link polynomials, and spectral parameter-dependent solutions of Yang–Baxter equation are obtained. The Ř matrix for the matrix elements related by the Weyl reflection has different values surprisingly.
Curvature and torsion of the world curve in the action of the relativistic particle
Authors: Nesterenko V. V.
Published: July 2002

A generalization of the relativistic particle action is considered. It contains, in addition to the length of the world trajectory, the integrals along the world curve of its curvature and torsion. The generalized Hamiltonian formalism for this model in the D-dimensional space-time is constructed. A complete set of the constraints in the phase space is obtained and their division into the first-class and the second-class constraints is accomplished. On this basis the canonical quantization of the model is fulfilled. For D=3 the mass spectrum is obtained in the sector without tachyonic states, the mass of the state being dependent on its spin. It is shown that in the framework of this model when D=3 we have the possibility to describe the states with integral, half-odd-integral and continuous spins. Interaction with an external Abelian gauge field is introduced in the geometrical way.
An introduction to the semiclassical limit of Euclidean quantum mechanics
Authors: Kolsrud Torbjörn , Zambrini Jean-Claude
Published: July 2002

A new class of Gaussian (‘‘Bernstein’’) diffusion processes associated with semiclassical quantum dynamics is introduced and studied according to a new Euclidean strategy for the quantization of systems of particles in a potential (‘‘Euclidean quantum mechanics’’). All the measures known by other means, up to now, are included as particular cases of the present framework. It is shown that the theory may be regarded as a well-defined probabilistic version of Feynman’s space-time approach distinct, in particular, from the one due to Kac, and with much closer relations with classical Lagrangian dynamics. Many explicit examples are considered.
On the completeness of geodesics obtained as a limit
Authors: Romero Alfonso , Sánchez Miguel
Published: July 2002

The process to obtain a geodesic as a limit from a sequence of geodesics in a Lorentzian manifold is analyzed in detail. It is found that the limit of incomplete geodesics in a compact manifold is not incomplete in general. A new class of incomplete compact Lorentzian manifolds, one of them showing this anomalous behavior, is constructed. Thus, a counterexample to the proof, given by U. Yurtsever [J. Math. Phys. 33, 1295 (1992)] to the result originally proven by Y. Carrière [Invent. Math. 95, 615 (1989)] (in a quite different way) is given. That proof should imply that an incomplete compact Lorentzian manifold must be null incomplete. It is not known if this assertion is true, and, hence, remains as an open question.
Electromagnetic radiation in multiply connected Robertson–Walker cosmologies
Authors: Tomaschitz Roman
Published: July 2002

Maxwell’s equations on a topologically nontrivial cosmological background are studied. The cosmology is locally determined by a Robertson–Walker line element, but the spacelike slices are open hyperbolic manifolds, whose topology and geometry may vary in time. In this context the spectral resolution of Maxwell’s equations in terms of horospherical elementary waves generated at infinity of hyperbolic space is given. The wave fronts are orthogonal to bundles of unstable geodesic rays, and the eikonal of geometric optics appears just as the phase of the horospherical waves. This fact is used to attach to the unstable geodesic rays a quantum mechanical momentum. In doing so the quantized energy-momentum tensor of the radiation field is constructed in a geometrically and dynamically transparent way, without appealing to the intricacies of the second quantization. In particular Planck’s radiation formula, and the bearing of the multiply connected topology on the fluctuations in the temperature of the background radiation is discussed.
(2,0) Super-Beltrami parametrization and superconformal structures
Authors: Kachkachi M. , Lhallabi T.
Published: July 2002

The superconformal structure of the (2,0) supergeometry of two-dimensional superspace is characterized by the Beltrami differentials. The superdiffeomorphism transformations of the Beltrami variables are given and the superfields with arbitrary conformal weights are studied.
Analysis of the Green’s function approach to one-dimensional inverse problems. I. One parameter reconstruction
Authors: He Sailing , Kabanikhin Sergei I. , Romanov Vladimir G. , Ström Staffan
Published: July 2002

An analysis of a Green’s function approach (based on wave splitting) to the one-dimensional electromagnetic inverse problem is given. The Green’s functions refer to split components of the fundamental solution. The linear system of equations for the Green’s functions is shown to be well-posed for the inverse problem and stability estimates, theorems on existence, uniqueness, local correctness, and convergence are given.
Transmission and reflection coefficients from the tunneling equation with absorption in the complex z plane
Authors: Swanson D. G. , Shvets V. F.
Published: July 2002

While exact analytic expressions for the scattering parameters have been obtained from the tunneling equation without absorption, which describes wave propagation through a tunneling region with back-to-back resonance and cutoff layers, no exact analytic results were known with absorption. While emission from absorbing regions has traditionally been calculated from the opacity, which depends on the transmission coefficient, it is proved here that transmission is independent of absorption, so that opacity must be redefined. This has been accomplished by examining the analytic continuation of the solutions into the complex z plane, where the evaluation of certain contour integrals exactly prove that the transmission coefficient is precisely the same with and without absorption and that there is no reflection from the side which encounters the resonance first. These results are general for a broad class of localized absorption functions.
Vector-coherent-state representations of so(5) in an so(3) basis
Authors: Rowe D. J.
Published: July 2002

Vector coherent state theory is used to give an algorithm for constructing the so(5) irreps of type [N,0] and [N,N] in the physical so(3) basis. The construction is remarkably simple and permits the matrices of the so(5) operators, for irreps of low-dimension and/or small multiplicities, to be computed by hand. The construction is applied to the [2,0] and [2,2] irreps to illustrate the process.
q-deformed relativistic wave equations
Authors: Pillin Mathias
Published: July 2002

Based on the representation theory of the q-deformed Lorentz and Poincaré symmetries q-deformed relativistic wave equation are constructed. The most important cases of the Dirac, Proca, Rarita–Schwinger, and Maxwell equations are treated explicitly. The q-deformed wave operators look structurally like the undeformed ones but they consist of the generators of a noncommutative Minkowski space. The existence of the q-deformed wave equations together with previous results on the representation theory of the q-deformed Poincaré symmetry solve the q-deformed relativistic one particle problem.
Symmetry scattering for SU(2,2) with applications
Authors: Wehrhahn R. F. , Barut A. O.
Published: July 2002

In the framework of symmetry scattering, SU(2,2)-invariant differential equations on the homogeneous space X=SU(2,2)/S(U(2)⊗U(2)) are studied. The radial Schrödinger equation for a family of one or two dimensional potentials or for two particles arise. From the asymptotic behavior of the solutions exact partial wave scattering amplitudes are derived.
Note on a solution of the algebraically special perturbation of the Schwarzschild black hole
Authors: Chee Gouying
Published: July 2002

An algebraically special solution of the Regge–Wheeler–Zerilli equation that has not been noticed is examined. This solution is proved to be related to Chandrasekhar’s solution but has a simpler analytical expression.
Group theoretical symmetries and generalized Bäcklund transformations for integrable systems
Authors: Haak Guido
Published: July 2002

A notion of symmetry for 1+1-dimensional integrable systems is presented which is consistent with their group theoretic description. It is shown how a group symmetry may be used together with a dynamical reduction to produce new generalizations of the Bäcklund transformation for the Korteweg–de Vries equation to its SL(n,C) generalization. An additional application to the relativistic invariance of the Leznov–Saveliev systems is given.
Local automorphism invariance: Gauge boson mass without a Higgs particle
Authors: Crawford James P.
Published: July 2002

The consequences of the assumption of invariance of a spinor theory under local automorphism transformations of the Clifford algebra basis elements are explored. This invariance is equivalent to allowing the orthonormal basis spinors of the spinor space to be chosen arbitrarily at each point in space–time and is analogous to the situation in general relativity where the orthonormal basis vectors of the tangent space are allowed to be chosen arbitrarily at each point in space–time. This invariance then dictates that the Clifford algebra generators be functions of space–time and is implemented by introducing new fields, the drehbeins (‘‘spin legs’’), which are somewhat akin to the vielbeins introduced in general relativity to invoke the concept of local Lorentz invariance. However, in contrast to general relativity, the covariant derivatives of the Clifford algebra generators do not vanish. The dynamical variables of the theory are then the spinors, the gauge fields of the automorphism group, and the drehbeins. The invariant Lagrangian density and the concomitant field equations for this theory are discussed. Interestingly, the ‘‘kinetic’’ Lagrangian density term for the drehbein fields induces a gauge invariant mass term for the gauge fields. This constitutes a new mass generation mechanism, of different character and complementary to the familiar Higgs mechanism. Although the idea of local automorphism invariance is a natural generalization of the principle of equivalence, herein attention is restricted to the case of nondynamic flat space–time.
Sub-Hopf-algebra-induced twists of quantum enveloping algebras
Authors: Engeldinger Ralf A. , Kempf Achim
Published: July 2002

It is shown that a quasitriangular Hopf algebra can be twisted by the universal R-matrix of any quasitriangular sub-Hopf algebra and examples are given of R-matrices of quantum groups obtained this way.
Geometric quantization of Neumann-type completely integrable Hamiltonian systems
Authors: Mykytiuk I. V. , Prykarpatsky A. K. , Andrushkiw R. I. , Samoilenko V. Hr.
Published: July 2002

The procedure of geometric quantization is developed for completely integrable dynamical systems on manifolds with exact symplectic structure. These results are applied to Neumann’s nonharmonic oscillatory system on two-dimensional sphere S2.
Quantum measurements and quantum logics
Authors: Pulmannová Sylvia
Published: July 2002

A quantum logic formulation of quantum measurements is introduced using Boolean powers of orthomodular σ-posets to the description of the coupled system. A comparison with the traditional Hilbert space approach to quantum measurements and a discussion of some important classes of measurements is given.
Matter collineations: The inverse ‘‘symmetry inheritance’’ problem
Authors: Carot J. , da Costa J. , Vaz E. G. L. R.
Published: July 2002

Matter collineations, as a symmetry property of the energy-momentum tensor Tab, are studied from the point of view of the Lie algebra of vector fields generating them. Most attention is given to space–times with a degenerate energy-momentum tensor. Some examples of matter collineations are found for dust fluids (including Szekeres’s space–times), and null fluid space–times.
Contractions of Lie algebras: Generalized Inönü–Wigner contractions versus graded contractions
Authors: Weimar-Woods Evelyn
Published: July 2002

Recently, a new notion of contraction has been introduced, the purely algebraically defined graded contractions that fall into two disjoint classes: continuous and discrete. Our main result is that all continuous graded contractions can be realized by generalized Inönü–Wigner contractions. Furthermore, we give a complete characterization of the discrete graded contractions via certain higher-order identities inherent to the grading group.
Renormalized perturbation series and the semiclassical limit of quantum mechanics
Authors: Fernández Francisco M.
Published: July 2002

The accuracy of the renormalized perturbation series for anharmonic oscillators and other simple quantum-mechanical models increases with the quantum number when the adjustable parameter is determined by a simple variational criterion. In the semiclassical limit of quantum mechanics such an expansion converges towards the result of the Jeffreys–Wentzel–Kramers–Brillouin method to all orders. The hypervirial and Hellmann–Feynman theorems facilitate the derivation of the semiclassical series from Rayleigh–Schrödinger perturbation theory.
The vacuum and Bach equations in terms of light cone cuts
Authors: Mason L. J.
Published: July 2002

Light cone cuts are the intersection of the light cones of space–time events with an initial data surface which is usually taken to be null infinity. These are determined by a ‘‘cut function,’’ a function of the space–time coordinates and the sphere of generators of null infinity. The Bach equations and the conformal vacuum equations are shown to lead to a single scalar ‘‘main’’ equation on the cut function. In simplified cases, i.e., when the Weyl curvature is either small or self-dual, this equation can be integrated to give a simple scalar conformally invariant elliptic equation on the sphere of null directions. It has the remarkable property that the general solution of the Einstein vacuum equations in these cases can be derived from the solution to this auxiliary equation in two dimensions. In general, it will not be possible to reduce it to an auxilliary equation on the sphere. Nevertheless, the main equation is still a necessary condition and it is conjectured that it is also sufficient to imply the Bach equations in general and supporting arguments are given. It is also shown how to extend the Kozameh–Newman framework to the case of light cone cuts of a spacelike Cauchy hypersurface. The analogous procedures for Yang–Mills are also discussed. A conformally invariant formalism for calculations on null infinity is described in an Appendix. This is used for all the calculations which are only described in brief form in the main text.
Induced shift tensors in vector coherent state theory
Authors: Rowe D. J. , Repka J.
Published: July 2002

It is shown that the so-called shift tensors of Biedenharn and Louck have a natural expression within the framework of vector coherent state (VCS) theory. VCS theory was developed to give a systematic construction of the representations of Lie groups and to derive the corresponding matrices representing the elements of their Lie algebras. In this paper there are explicit realizations of shift tensors within the framework of VCS theory for semisimple Lie groups in terms of shift tensors for suitably defined subgroups.
Lanczos potential for some type D space–times
Authors: Torres del Castillo G. F.
Published: July 2002

A Lanczos potential of any non-null orbit type D solution of the Einstein–Maxwell equations with nonsingular aligned electromagnetic field is obtained. In the case of the Kerr–Newman solution the Lanczos potential is also explicitly given.
Topological aspects of spin and statistics in nonlinear sigma models
Authors: Baez John C. , Ody Michael S. , Richter William
Published: July 2002

Spin and statistics for topological solitons in nonlinear sigma models are studied using topological methods based on the classical configuration space. Taking as space the connected d-manifold X, and considering nonlinear sigma models with the connected manifold M as target space, topological solitons are given by elements of πd(M). Any topological soliton α∈πd(M) determines a quotient Statn(X,α) of the group of framed braids with n strands on X, such that a framed braid determines a contractible path in the n-soliton sector of the configuration space if and only if its image in Statn(X,α) is the identity. In particular, when M=S2, as in the O(3) nonlinear sigma model with Hopf term, and α∈π2(S2) is a generator, we compute that Statn(R2,α)=Z, while Statn(S2,α)=Z2n. Thus one expects the phase exp(iθ) for interchanging two solitons of type α on S2 to satisfy the constraint θ=kπ/n, k∈Z, when n such solitons are present.
Solutions of the spherically symmetric wave equation in p+q dimensions
Authors: Bietenholz W. , Giambiagi J. J.
Published: July 2002

Solutions of the spherically symmetric wave equation and Klein–Gordon equation in an arbitrary number of spatial and temporal dimensions are discussed herein. Starting from a given solution, various procedures to generate further solutions in the same or in different dimensions are presented. The transition from odd to even and noninteger dimensions can be performed by fractional derivation or integration. The dimensional shift, however, can also be interpreted simply as a modification of the dynamics. The analytic continuation to arbitrary real powers of the D’Alembert operator is also discussed. There, particular peculiarities in the pole structure show up when p and q are both even. Finally, operators are given which transform a space into a time coordinate and vice versa and they are possibly related to black holes. In this context, a few aspects of the extension of the discussion to a curved metric are described.
Cuspidal coverings for pairs of congruence subgroups
Authors: Gilbert George T. , Richey Matthew P.
Published: July 2002

A formula is developed for the number of cusps in certain congruence subgroups equivalent to a given cusp in certain larger subgroups. In particular, necessary and sufficient conditions for this number to be independent of the particular cusp are given. Applications to statistical mechanics are surveyed.
R-matrix construction of electromagnetic models for the Painlevé transcendents
Authors: Harnad J. , Routhier M.
Published: July 2002

The Painlevé transcendents PI–PV and their representations as isomonodromic deformation equations are derived as nonautonomous Hamiltonian systems from the classical R-matrix Poisson bracket structure on the dual space sl̃R*(2) of the loop algebra sl̃R(2). The Hamiltonians are obtained by composing elements of the Poisson commuting ring of spectral invariant functions on sl̃R*(2) with a time-dependent family of Poisson maps whose images are four-dimensional rational coadjoint orbits in sl̃R*(2). Each system may be interpreted as describing a particle moving on a surface of zero curvature in the presence of a time-varying electromagnetic field. The Painlevé equations follow from reduction of these systems by the Hamiltonian flow generated by a second commuting element in the ring of spectral invariants. © 1995 American Institute of Physics.
Summation of power series by continued exponentials
Authors: Bender Carl M. , Vinson Jade P.
Published: July 2002

It is proposed that a power series may be summed (analytically continued outside its radius of convergence) by converting it to a continued exponential, which is a structure of the form a0 exp(a1z exp(a2zexp (a3z exp(a4z...)))). The continued-exponential coefficients {ai} for a given function f(z) are determined by equating the Taylor coefficients of the continued exponential with those of f(z). (The coefficients {ai} have a combinatoric interpretation; the nth Taylor coefficient enumerates all n+1-vertex tree graphs whose vertex amplitudes are {ai}.) Continued exponentials have remarkable convergence properties. When a power series has a nonzero radius of convergence, the corresponding continued exponential often converges in a heart-shaped region Ω, whose cusp is determined by the nearest zero or singularity of the function being approximated. The convergence region Ω contains and is much larger than the circle of convergence of the power series. Outside Ω, the complex plane is divided up into an elaborate patchwork of regions in which the continued exponential may either diverge or else approach an N-cycle, N=2,3,4,... .
On the dimension of the global attractor for the damped Sine–Gordon equation
Authors: Wang Guanxiang , Zhu Shu
Published: July 2002

This article gives a more precise estimate on the dimension of the global attractor for the damped Sine–Gordon equation. The gained Hausdorff dimension remains small for large damping, which conforms to physics.
Upper limit of the discrete hydrogen-like wave functions: Expansion in the inverse principal quantum number n−1
Authors: Blaive Bruno , Cadilhac Michel
Published: July 2002

We have expanded the Schrödinger hydrogen-like wave functions ψnlm of the discrete spectrum, with respect to the inverse principal quantum number n−1, for fixed values of the quantum numbers l,m. The Laguerre polynomials Lnα(x/n) are expanded with respect to n−1 into a sum of Bessel functions multiplied by powers rk of the distance from the origin. The coefficients of the expansion are a family of polynomials sq,k(l) of the variable l, which can be computed with a recursion formula. The development, which converges rapidly, can be truncated after a few terms, even for low levels n.
Existence of parallel spinors on nonsimply connected Riemannian manifolds
Authors: McInnes Brett
Published: July 2002

It is well known, and important for applications, that Ricci-flat Riemannian manifolds of nongeneric holonomy always admit a parallel (covariant constant) spinor if they are simply connected. The nonsimply connected case is much more subtle, however. We show that a parallel spinor can still be found in this case provided that the (real) dimension is not a multiple of four, and provided that the spin structure is carefully chosen.
Multidimensional classical and quantum cosmology with intersecting p-branes
Authors: Ivashchuk V. D. , Melnikov V. N.
Published: July 2002

A multidimensional cosmological model describing the evolution of (n+1) Einstein spaces in the theory with several scalar fields and forms is considered. When a (electro-magnetic composite) p-brane ansatz is adopted the field equations are reduced to the equations for the Toda-like system. The Wheeler–De Witt equation is obtained. In the case when n “internal” spaces are Ricci-flat, one space M0 has a non-zero curvature, and all p-branes do not “live” in M0; the classical and quantum solutions are obtained if certain orthogonality relations on parameters are imposed. Spherically symmetric solutions with intersecting non-extremal p-branes are singled out. A non-orthogonal generalization of intersection rules corresponding to (open, closed) Toda lattices is obtained. A chain of bosonic D⩾11 models (that may be related to hypothetical higher dimensional supergravities and F-theories) is suggested.
New varieties of Gowdy space–times
Authors: Tanimoto Masayuki
Published: July 2002

Gowdy space–times are generalized to admit two commuting spatial local Killing vectors, and some new varieties of them are presented, which are all closely related to Thurston’s geometries. Explicit spatial compactifications, as well as the boundary conditions for the metrics, are given in a systematic way. A short comment on an implication of their dynamics toward the initial singularity is made.
Intertwining operators for a degenerate double affine Hecke algebra and multivariable orthogonal polynomials
Authors: Kakei Saburo
Published: July 2002

Several properties of the multivariable Hermite and Laguerre polynomials associated with the quantum Calogero models are investigated by using the operators that intertwine representations of a degenerate version of the double affine Hecke algebra. As applications, raising operators and shift operators for the polynomials are constructed in a unified manner.
Symplectic structure for Gaussian diffusions
Authors: Brandão Augusto
Published: July 2002

Using information exclusively about classical Hamiltonian boundary value problems (with quadratic time-dependent potentials) we construct probability measures providing a symplectic structure associated with some inhomogeneous Gaussian diffusion processes introduced earlier [T. Kolsrod and J. C. Zambrini, J. Math. Phys. 33, 1301 (1992)].
On simulating Liouvillian flow from quantum mechanics via Wigner functions
Authors: Mitra A. N. , Ramanathan R.
Published: July 2002

The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is achieved by first defining a bilocal 4-current and then taking its Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases also lend themselves to a closely parallel treatment provided the Kemmer-Duffin β-matrix formalism is employed for the former. Calculation of WF is carried out in a Lorentz-covariant fashion by standard “trace” techniques. The results are compared with a recent derivation due to Bosanac.
Maximally even sets and the devil’s-staircase phase diagram for the one-dimensional Ising antiferromagnet with arbitrary-range interaction
Authors: Krantz Richard J. , Douthett Jack , Doty Steven D.
Published: July 2002

By extending the formalism of maximally even sets to the one-dimensional antiferromagnetic Ising model with arbitrary-range interaction in an applied magnetic field it is shown that the system exhibits a devil’s-staircase magnetic phase diagram. A “generalized” similarity dimension (a generalization for nonuniform fractals) of the phase diagram is calculated and compared to previous results. It is shown that previous estimates of the dimension of the phase diagram for this system differs from this “generalized” similarity dimension.
Supersymmetric Drinfeld–Sokolov reduction
Authors: Delduc F. , Gallot L.
Published: July 2002

The Drinfeld–Sokolov construction of integrable hierarchies, as well as its generalizations, may be extended to the case of loop superalgebras. A sufficient condition on the algebraic data for the resulting hierarchy to be invariant under supersymmetry transformation is given. The method used is a construction of the hierarchies in superspace, where supersymmetry is manifest. Several examples are discussed.
Direct proof of integrability of Calogero–Moser model
Authors: Gonera Cezary
Published: July 2002

The straightforward proof of involutiveness of the set of integrals of motion for the general Calogero–Moser model is given for the classical as well as the quantum case.
Applications of topological*-algebras of unbounded operators
Authors: Bagarello F.
Published: July 2002

In this paper we discuss some physical applications of topological*-algebras of unbounded operators. The first example is a simple system of free bosons. Then we consider other models related to this one. Finally, we discuss the time evolution of two interacting models of matter and bosons. We show that for all these systems it is possible to build up a common mathematical framework where the existence of the thermodynamical limit of the algebraic dynamics can be conveniently analyzed.
Colliding plane waves in terms of Jacobi functions
Authors: Bretón Nora , Garcı́a Alberto , Macı́as Alfredo , Yáñez Gustavo
Published: July 2002

We present a general class of noncollinear colliding wave solutions of the Einstein–Maxwell equations given in terms of fourth order polynomials, which in turn can be expressed through Jacobi functions depending on generalized advanced and retarded time coordinates. The solutions are characterized by six free parameters. The parameters can be chosen in such a way as to avoid the generic focusing singularity.
Amplitude equations for electrostatic waves: Multiple species
Authors: Crawford John David , Jayaraman Anandhan
Published: July 2002

The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude A(t). In the limit of weak instability, i.e., γ→0+ where γ is the linear growth rate, the nonlinear coefficients are singular and their singularities predict the dependence of A(t) on γ. Generically the scaling |A(t)|=γ5/2r(γt) as γ→0+ is required to cancel the coefficient singularities to all orders. This result predicts the electric field scaling |Ek|∼γ5/2 will hold universally for these instabilities (including beam-plasma and two-stream configurations) throughout the dynamical evolution and in the time-asymptotic state. In exceptional cases, such as infinitely massive ions, the coefficients are less singular and the more familiar trapping scaling |Ek|∼γ2 is recovered.
Integral-difference collision operators: Analytical and numerical spectral analysis
Authors: Melnikov Yu. , Yarevsky E.
Published: July 2002

We analyze spectral properties of a class of integral-difference collision operators arising in some nonequilibrium statistical physics models. We present analytical estimates and numerical results for the operators defined on finite intervals and corresponding to the truncated Gaussian equilibrium distribution function. Some conclusions are drawn about the spectrum of operators on whole axis. Physical limitations for these kinds of models are discussed.
On spectral properties of Harper-like models
Authors: Herrmann D. J. L. , Janssen T.
Published: July 2002

We study spectral properties of Harper-like models by algebraic and combinatorial methods and derive sufficient conditions for the existence of spectral gaps with qualitative estimates. For this class the Chambers relation holds and we obtain an analytic expression for the representation dependent part. Models corresponding to the rectangular and triangular lattice are studied. In the second case we show that one class of spectral gaps is open for magnetic fields with “rational magnetic flux per unit cell.” A quantitative estimate for the gap widths is given for the anisotropic case and for “irrational magnetic flux” fulfilling some Liouville condition the spectrum is a Cantor set.
Dynamical semigroups for interacting quantum and classical systems
Authors: Olkiewicz R.
Published: July 2002

A mathematical framework for the completely positive semigroup coupling between classical and quantum systems is proposed. The coupling ensures a flow of information from the quantum system to the classical one and the influence of the classics on the dynamics of the quantum system in a dissipative way. The classical evolution on average is modified by the expectation value of some quantum operator. Examples of a classical particle moving along a geodesic line in a curved space interacting with the quantum system, and the coupling of a two state quantum system to all pure states, are discussed.
Arithmetic properties of spectra produced by Farey hierarchies of approximants
Authors: Radulescu O. , Janssen T.
Published: July 2002

We discuss the consequences of the hierarchical nature of series of approximants of aperiodic crystals on their diffraction patterns and spectra of elementary excitations. We show how a linear form defined on Z3 can be used to order Bragg reflections in diffraction patterns according to their amplitudes, and gaps in spectra of elementary excitations according to their widths, for all the structures in the hierarchy. Bragg peaks amplitudes and gap widths are projective functions on P(Z3), recursively defined on 2D Farey sets (generalization of Farey series).
On the anisotropic Manev problem
Authors: Craig Scott , Diacu Florin , Lacomba Ernesto A. , Perez Ernesto
Published: July 2002

We consider the Manev potential, given by the sum between the inverse and the inverse square of the distance, in an anisotropic space, i.e., such that the force acts differently in each direction. Using McGehee coordinates, we blow up the collision singularity, paste a collision manifold to the phase space, study the flow on and near the collision manifold, and find a positive-measure set of collision orbits. Besides frontal homothetic, frontal nonhomothetic, and spiraling collisions and ejections, we put into the evidence the surprising class of oscillatory collision and ejection orbits. Using the infinity manifold, we further tackle capture and escape solutions in the zero-energy case. By finding the connection orbits between equilibria and/or cycles at impact and at infinity, we describe a large class of capture-collision and ejection-escape solutions.
Highest weight irreducible representations of the Lie superalgebra gl(1|∞)
Authors: Palev T. D. , Stoilova N. I.
Published: July 2002

Two classes of irreducible highest weight modules of the general linear Lie superalgebra gl(1|∞) are constructed. Within each module a basis is introduced and the transformation relations of the basis under the action of the algebra generators are written down.
Generalized Lamé functions. II. Hyperbolic and trigonometric specializations
Authors: Ruijsenaars S. N. M.
Published: July 2002

In Part I [J. Math. Phys. 40, 1595 (1999)] we studied eigenfunctions of the quantum dynamics that defines the two-particle relativistic Calogero–Moser system with elliptic interaction. In the present paper we consider the same system with hyperbolic and trigonometric interactions. In these special regimes the eigenfunctions are shown to admit an elementary representation that is far more explicit than the “zero representation” of Part I. In particular, the new representation can be exploited to prove that the hyperbolic eigenfunctions can be chosen to be symmetric under interchanging position and momentum variables (self-duality). In the trigonometric case duality properties are derived, too, and several orthogonality and completeness results are obtained.
Locality in free string field theory
Authors: Dimock J.
Published: July 2002

Free string field operators are constructed for the open bosonic string in the light cone gauge in any dimension. These are naturally localized by the center of mass coordinate. Relative to this localization they are shown to have a causal commutator provided there are no tachyons. For the critical string in d=26 the result still holds if the tachyon is suppressed. We also show a causal commutator relative to the “string light cone.”
Semi-classical study of the origin of quantized Hall conductance in periodic potentials
Authors: Faure Frédéric , Parisse Bernard
Published: July 2002

The semi-classical study of the integer quantum Hall conductivity is investigated for electrons in a biperiodic potential V(x,y). The Hall conductivity is due to the tunnelling effect and we concentrate our study on potentials having three wells in a periodic cell. We show that a nonzero topological conductivity requires special conditions for the positions and shapes of the wells. The results are derived by changing the potential, using the topological nature of Chern indices. Our numerical calculations show that these semi-classical results are still valid for small value of B.
N=2
supercovariant operators and Krichever–Novikov algebra
Authors: Benhamou N. , Lhallabi T.
Published: July 2002

The N=2 superdiffeomorphism anomaly is defined on the compact N=2 super-Riemann surfaces by the inclusion of N=2 superprojective connection. The N=2 supercovariant operators which are superconformally covariant are constructed and the relations with the N=2 super-Poisson operators and the Krichever–Novikov algebra are given.