bluuebunny/crossref_metadata_2025 huggingface dataset:
Bounds for the continuation of perturbative results to the spectral region
Authors: Ciulli M. , Ciulli S. , Spearman T. D.
Published: March 2003

The problem of analytic continuation to the boundary of the holomorphy domain from both continuous and discrete interior sets has recently been the subject of detailed analyses. This problem is important in phenomenological applications but is also of interest in theoretical calculations, e.g., in attempting to evaluate the parameters of resonances or other nonperturbative effects in QCD. Because of the inherent instability of the continuation problem it is necessary to introduce additional criteria—which should be physically based—to select the right continuation function. In this paper, the results thus obtained for continuation from a continuum are examined for stability, and bounds are derived for the errors on the boundary in terms of the uncertainty of the input data. The procedure is shown to be stable in the sense that these bounds tend to zero as the data errors go to zero.
An Sp(3,R)×O(N−1) basis for the nuclear shell model
Authors: Ogura H. , Rowe D. J.
Published: March 2003

An Sp(3,R)×O(N−1) basis of wave functions is constructed for the nuclear shell model. Such a basis is important because Sp(3,R) is the dynamical group and O(N−1) the symmetry group for a unified independent particle-collective model of the nucleus. It is needed for the diagonalization of a microscopic shell model Hamiltonian and the interpretation of the collective content of its eigenstates.
Electrons moving in a crystal weakly coupled to a random reservoir
Authors: Nogueira Arnaldo C. R.
Published: March 2003

We present here an illustration of the difference between static and temporal disorders. We consider a model which is modification of one previously introduced by Martin and Emch, to discuss the mechanism of the long-time, weak-coupling limit in statistical mechanics. It consists of an electron moving in a crystal where impurities are randomly scattered. We introduce a stochastic time disorder in the potential and prove that this new stochastic dynamics converges to a semigroup law without the limitations occurring in the work of Martin and Emch, i.e., the short time restriction and in any space dimension.
On the solutions to a class of nonlinear integral equations arising in transport theory
Authors: Spiga G. , Bowden R. L. , Boffi V. C.
Published: March 2003

Existence and uniqueness for the solutions to a class of nonlinear equations arising in transport theory are investigated in terms of a real parameter α which can take on positive and negative values. On the basis of contraction mapping and positivity properties of the relevant nonlinear operator, iteration schemes are proposed, and their convergence, either pointwise or in norm, is studied.
Properties of Poincaré generating functions for polynomial covariants (tensors)
Authors: Jarić Marko V.
Published: March 2003

We show that irreducible polynomial covariants (tensors) based on a given irreducible representation of a finite group must have a definite p-phase, i.e., degree modulo p, where p is the order of the center of the image of the group. We also show that the numerator of the Poincaré function is often a polynomial symmetric around a given degree and we derive several interesting properties of the Poincaré function.
On an extension of the classical Thirring model
Authors: David Daniel
Published: March 2003

A new class of classical field theories, in 1+1 dimensions, is introduced, of the form iγμΨ, μ−mΨ−Ψ̄γμ(g1+g2γ5) ×ΨγμΨ−Ψ̄(g3+g4γ5)ΨΨ=0. It is shown that these theories are relativistically invariant; they do not, however, preserve parity in general, and thus could be used to describe the dynamics of weak interaction processes. The prolongation structure method is used to investigate the existence of pseudopotentials. When the coupling constants g3 and g4 are zero, the corresponding theory is then characterized by an infinite family of conservation laws and is thus completely integrable. For this very case, the Bäcklund map (pseudopotential) furnishes the equivalent of a Lax pair of operators as well as a nontrivial Bäcklund transformation and solutions of soliton type.
Landau–Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations
Authors: Kundu A.
Published: March 2003

New Landau–Lifshitz (LL) and higher-order nonlinear systems gauge generated from nonlinear Schrödinger (NS) type equations are presented. The consequences of gauge equivalence between different dynamical systems are discussed. The gauge connections among various LL and NS equations are found and depicted through a schematic representation.
Polynomial constants of motion in flat space
Authors: Thompson Gerard
Published: March 2003

Some general results on commuting integrals for a Hamiltonian system are given. The question of the existence of integrals which are polynomial in the momenta is investigated and the results applied to a variety of mechanical systems.
A viewpoint of Kaluza–Klein type in elasticity theory
Authors: Obata Tsunehiro , Chiba Jiro
Published: March 2003

An N-dimensional anisotropic elastic body without the interior gravity is, under some conditions concerning the Nth dimension, equivalent to an (N−1)-dimensional isotropic elastic body under the influence of the interior gravity. According to this theorem, our method of solving the equation of free motion of anisotropic elastic bodies includes Bromwich’s method of solving the equation of motion of incompressible isotropic elastic bodies under the influence of the interior gravity.
Bound state energy eigenvalues for a general class of one-dimensional problems on the whole axis (−∞, ∞) via the Prüfer transformation
Authors: Úlehla I. , Adamová D.
Published: March 2003

An extension of the Prüfer phase function method for the bound state energy calculation is presented. It is applicable to one-dimensional problems described by the Schrödingere quation on the whole axis (−∞,∞) with a general class of potentials. Theorems are given which are a generalization of the analogous ones concerning the half-axis (0,∞) problems that have been presented in previous papers. The method is suitable especially for numerical calculations of the bound state energy eignevalues.
Axially symmetric gravitational radiation from isolated sources
Authors: Hobill David W.
Published: March 2003

Asymptotically flat, dynamic, axially symmetric space-times are considered from the point of view of the characteristic initial value problem and the expansion of solutions in powers of r−1. Imposing conditions such that the system initially be exactly static and nonradiative finally, a news function is constructed which governs the dynamics of such a space-time and which yields a finite, nonvanishing total loss of the Bondi mass. Furthermore, the Riemann tensor (to order r−3) is known explicitly for all time since an expression for the mass aspect is also determined. It is also shown that the total change in the asymptotic shear is related to the total change in the Bondi mass. Finally the implications concerning transitions between two exactly stationary states are discussed.
Group theory of the dipole ghost
Authors: Heidenreich W.
Published: March 2003

The conformal representation carried by the dipole ghost ⧠⧠φ=0 is described in a discrete basis; it has dimension zero and contains the constant solution as an irreducible subspace. A free quantum field operator is constructed. The representation is decomposed with respect to the (3.2) de Sitter and the Poincaré groups. A model for coupling relativistically to an external source is given, in which only unitary mass 0 helicity 0 modes propagate.
General irreducibility condition for vector and projective corepresentations of antiunitary groups
Authors: Kim Shoon K.
Published: March 2003

A general condition for irreducibility of vector and projective corepresentations of an antiunitary group is presented. It depends only on the characters of the unitary halving subgroup of the covering group. It reduces to the well known type criterion of corepresentations when it is specialized to the three types of corepresentations.
Singular solutions of the axially symmetric Bogomolny equations
Authors: Morris Hedley C. , Dodd Roger K.
Published: March 2003

A singular Bäcklund transformation is constructed for the Ernst equation and used to construct singular solutions to the axially symmetric Bogomolny equations.
The J-matrix reproducing kernel: Numerical weights at the Harris energy eigenvalues
Authors: Yamani Hashim A.
Published: March 2003

The restriction of the J-matrix scattering wave function to the subspace where the potential is nonzero is used to define a reproducing kernel in the energy parameters. The values of the kernel at the positive Harris energy eigenvalues are shown to be related to the numerical weights at these eigenvalues.
Unification of generalized electromagnetic and gravitational fields
Authors: Rajput B. S.
Published: March 2003

Structural symmetry between generalized gravitational field (gravito-Heavisidian field) and the generalized electromagnetic field associated with dyons has been demonsttrated, and the field equations, equation of motion, and the quantization condition for angular momentum operators for both these fields have been unified.
Stochastic processes driven by dichotomous Markov noise: Some exact dynamical results
Authors: Sancho J. M.
Published: March 2003

Stochastic processes defined by a general Langevin equation of motion where the noise is the non-Gaussian dichotomous Markov noise are studied. A non-Fokker–Planck master differential equation is deduced for the probability density of these processes. Two different models are exactly solved. In the second one, a nonequilibrium bimodal distribution induced by the noise is observed for a critical value of its correlation time. Critical slowing down does not appear in this point but in another one.
On the survival of primordial tachyons up to the present epoch
Authors: Srivastava Sushil K.
Published: March 2003

In the present paper, a spinless primordial tachyon is considered in the background of Robertson–Walker (RW) cosmology. Various physical parameters, such as probability density, energy, and dissipation of energy are investigated in open, flat, and closed RW models. For this purpose, the Klein–Gordon equation, generalized to curved space-time and having a term proportional to the scalar curvature of the space-time, is solved for the spacelike scalar field ψ(t,r,θ,φ). It is speculated that if a primordial spinless tachyon survives up to the present epoch, its metamass would be less than 2.447×10−93 g.
The direct correlation function for the hard-core potentials
Authors: Mazuruk Konstanty
Published: March 2003

The Ornstein–Zernicke relation is examined for the class of intermolecular potentials with a hard-core term. The nonlinear integral equation relating the direct correlation function outside the hard-core region with the inside one is proposed. A class of analytical solutions is obtained.
On some family of congruences of null strings
Authors: Robinson Ivor , Rózga Krzysztof
Published: March 2003

A definition of a special family of congruences of null strings is given, and a link between its existence and ‘‘projective extensions of heavens’’ is provided. Next the integrability conditions of the problem are studied, and a subclass of all ‘‘heavens’’ admitting these special congruences is described in terms of one function of three variables subject to a nonlinear, differential second-order constraint.
A projective constrained variational principle for a classical particle with spin
Authors: Amorim R.
Published: March 2003

A geometric approach for variational principles with constraints is applied to obtain the equations of motion of a classical charged point particle with magnetic moment interacting with an external eletromagnetic field.
Explicit evaluation of group-invariant measure as by-product of path integration over Yang–Mills fields
Authors: Teitelboim Claudio
Published: March 2003

A method is presented for explicitly evaluating the invariant measure over a Lie group, for any parametrization in which a generic group element is written as a product of exponentials of elements of the Lie algebra. The measure is expressed as a transition amplitude associated with the quantum mechanical evolution operator of the ‘‘ghost fields’’ which appear in the path integral over Yang–Mills fields. As an illustration of the method, the measure is evaluated in two cases: (i) in canonical coordinates, for an arbitrary Lie group which admits them; (ii) in terms of Euler angles, for the group of rotations in three-dimensional space.
Green’s functions at zero viscosity
Authors: Fried H. M. , Tessendorf J.
Published: March 2003

Fradkin-type propagator representations are written for solutions to Navier–Stokes and related equations, for arbitrary dimension D and arbitrary source geometry. In the limit of very small viscosity, velocity/vorticity solutions are given in terms of Cauchy position coordinates q of a particle advected by the velocity flow v, using a set of coupled equations for q and v. For localized point vortices in two dimensions, the vectors q become the time-dependent position coordinates of interacting vortices, and our equations reduce to those of the familiar, coupled vortex problem. The formalism is, however, able to discuss three-dimensional vortex motion, discrete or continuous, including the effects of vortex stretching. The mathematical structure of vortex stretching in a D-dimensional fluid without boundaries is conveniently described in terms of an SU(D) representation of these equations. Several simple examples are given in two dimensions, to anchor the method in the context of previously known, exact solutions. In three dimensions, vortex stretching effects are approximated using a previous ‘‘strong coupling’’ technique of particle physics, enabling one to build a crude model of the intermittent growth of enstrophy, which may signal the onset of turbulence. For isotropic turbulence, the possibility of a singularity in the inviscid enstrophy at a finite time is related to the behavior of a single function characterizing the intermittency.
Matrix elements for indecomposable representations of complex su(2)
Authors: Gruber Bruno , Klimyk A. U.
Published: March 2003

Indecomposable representations of the simple complex Lie algebra A1 are investigated in this article from a general point of view. First a ‘‘master representation’’ is obtained which is defined on the space of the universal enveloping algebra Ω of A1. Then, from this master representation other indecomposable representations are derived which are induced on quotient spaces or subduced on invariant subspaces. Finally, it is shown that the familiar finite-dimensional and infinite-dimensional irreducible representations of su(2) and su(1,1) are closely related to certain of the indecomposable representations. Indecomposable representations of A1 [su(2), su(1,1)] have found increased applications in physical problems, including the unusual ‘‘finite multiplicity’’ indecomposable representations. Emphasis is placed in this article on an analysis of the more unfamiliar indecomposable representations. The matrix elements are obtained in explicit form for all representations which are discussed in this article. The methods used are purely algebraic.
On Lie algebras built from SO(3) tensor operators
Authors: Vanden Berghe G. , De Meyer H.
Published: March 2003

Concerning the Lie algebras generated by certain linear combinations of SO(3) tensor operators two theorems are given which disprove some widely accepted results in the standard literature.
Diffusion processes, quantum dynamical semigroups, and the classical KMS condition
Authors: Frigerio Alberto , Gorini Vittorio
Published: March 2003

We study some properties of the generator of a diffusion process describing the reduced dynamics of a classical system weakly coupled to an external reservoir. We show that such processes may be equivalently obtained as classical limits of quantum dynamical semigroups derived in the weak coupling limit. We prove that the stationary state is independent of the coupling if and only if the reservoir is in a state of thermal equilibrium.
A mechanical system with a ‘‘wild’’ horseshoe
Authors: Koiller Jair
Published: March 2003

We consider a gyrostat in its simplest form, namely, a rigid body with a flywheel attached. It is well known that, although the motions are coupled, when the rotor is symmetric, the full system is completely integrable in terms of elliptic functions. The Euler equations for the angular momentum components with respect to the rigid body now depend on the parameter I=angular momentum of the flywheel (a constant of motion) and the phase portrait of the system undergoes several bifurcations. Analytical formulas, in terms of elementary functions, can be given for the separatrices. A small imperfection in the flywheel breaks the S1 symmetry; as a result, the separatrices split with transversal intersection, producing horseshoes. We applied the techniques of Holmes and Marsden to write down the Melnikov function of the system. The integral is computed by the method of residues, in the limit case I→0−. Somewhat surprisingly, the amplitude of the Melnikov function diverges. We propose an explanation for this ‘‘paradox.’’
Solutions of a fourth-order differential equation describing mode conversion in a magnetized plasma
Authors: Maggs J. E. , Baños Alfredo , Morales G. J.
Published: March 2003

Solutions of the equation ε2u(4)+zu(2)+αu(1)+β1u −β22zu=0, where α, β1,  β22 are constants, ε2≪1, and z is the independent variable, are obtained using the Laplace integral technique. This equation describes the propagation of high frequency electrostatic waves near plasma resonance in a magnetized plasma with a longitudinal density gradient and is a generalization of an equation studied by Wasow and by Rabenstein in the context of boundary layer phenomena. The solutions of this fourth-order equation in which the associated second-order equation (i.e., ε2=0) exhibits both a singularity (at z=0) and a turning point (at z=β1/β22) fall readily into two classes. One class resembles Airy functions and exists only for ε2 not equal to zero. In the other class, the solutions are related to confluent hypergeometric functions and can be viewed as solutions of the second-order equation with small corrections proportional to ε2. Using the integral representations of solutions, it is demonstrated that each class of solutions can generate the other when the independent variable crosses the singular point. This is the physical phenomenon of mode conversion. Asymptotic descriptions of both classes of solutions are given and the form of the solutions near the singular point is expressed as a power series.
Determination of point group harmonics for arbitrary j by a projection method. I. Cubic group, quantization along an axis of order 4
Authors: Conte R. , Raynal Jacques , Soulié E.
Published: March 2003

We give a method for systematically building cubic harmonics, i.e., base vectors of irreducible representations of the group of invariance of a cube. Applications include solid state physics, molecular chemistry, spectroscopy, etc. The only necessary operators are Cz4 and Ry, rotation of π/2 around 0y. Projectors on representations are constructed; then their rows are orthogonalized by a Schmidt method and normalized simply by dividing by the square root of a diagonal element.
Quantum harmonic analysis on phase space
Authors: Werner R.
Published: March 2003

Relative to an irreducible representation of the canonical commutation relations, convolutions between quantum mechanical operators and between functions and operators are defined, for which the usual Weyl transform acts as a Fourier transform. Basic properties of these operations are developed in close analogy to harmonic analysis on R2n. Using the quantum version of Wiener’s approximation theorem, a natural one-to-one correspondence between the closed, phase-space translation invariant subspaces of classical and quantum observables is established.
A six-dimensional oscillator basis classified by O(6)⊇S𝒪(2)×S𝒰(3)⊇SO(3)
Authors: Chacón E. , Castaños O. , Frank A.
Published: March 2003

We explicitly construct a complete set of states, useful in three-body problems, both in a boson operator realization and in terms of coordinates which are of interest to microscopic collective models. The states carry the angular momentum quantum number L and, for the classification scheme mentioned in the title, our expressions generalize to arbitrary L the results previously available only for L=0 and 1.
On the relation between classical and quantum-thermodynamic entropy
Authors: Beretta Gian Paolo
Published: March 2003

We discuss the unresolved problem of proving rigorously that in the classical limit ℏ→0, the quantum-thermodynamic entropy functional tends to the classical entropy functional. We state rather restrictive conditions that define the general problem of finding a complete classical phase-space representation of quantum kinematics. Whether the problem admits of solutions remains an unresolved question. We discuss a physically interesting attempt to relate the structure in the classical limit ℏ→0 of the well-known Blokhintzev, Wigner, and Wehrl phase-space functions to the spectral expansion of the quantum state operator.
On the relation between complex manifolds and soliton theoretic constructions for self-dual fields
Authors: Burzlaff Jurgen , Hornos J. E. M.
Published: March 2003

We study the relation between the Atiyah–Drinfeld–Hitchin–Manin construction for self-dual fields, Ward’s twistor method, and the Belavin–Zakharov and Forgacs–Horvath–Palla soliton theoretic methods. Starting from the vector spaces, in terms of which the Atiyah–Drinfeld–Hitchin–Manin construction is formulated, we calculate the transition matrices, in terms of which the twistor method is formulated, for the Belavin–Polyakov–Schwartz–Tyupkin instanton and the Prasad–Sommerfield monopole explicitly. Given the transition matrices, we show how to solve the inverse scattering problem à la Belavin–Zakharov and Forgacs–Horvath–Palla, respectively.
Radiation reaction dynamics in an electromagnetic wave and constant electric field
Authors: Atlee Jackson E.
Published: March 2003

The relativistic motion of a charged particle is studied when it is acted on simultaneously by a constant electric field and a plane electromagnetic wave, propagating in the direction of the electric field (x axis). The dynamics includes the radiation reaction (self-force) on the particle through a standard approximation of the Lorentz–Dirac equation. The interest is to determine the result of the competition between the average acceleration due to the electromagnetic wave (‘‘radiation pressure’’) and the acceleration due to the constant force of the static field. Each of these actions alone of course produce an unbounded particle energy asymptotically in time. However, it is proved first that, when the ‘‘forces’’ are in opposite directions, the particle can never accelerate (on the average) indefinitely in the x direction, regardless how weak the electric field (E0) is compared to the amplitude of the wave (A). It is then proved that all solutions converge to a region of zero area in a suitable velocity phase space and, if there exists a periodic solution [in the phase ξ=ω (t−x/c)] in a specified region of this phase space, then all solutions must converge to this solution asymptotically (ξ→+∞). In the case when (E0A2/ω2) has a specified bound (ω: wave frequency), an iterative method is developed which explicitly yields such a periodic solution, showing that the energy remains bounded. The direction of the average drift is determined in terms of (A,E0,ω). When the parameter (E0A2/ω2) is above this bound, a combination of numerical and analytic results are obtained which indicate that this periodic solution persists. These results indicate that all motions tend to states with bounded energy, regardless of the field strengths.
Explicit evaluation of a path integral with memory kernel
Authors: Brosens F. , Devreese J. T.
Published: March 2003

An explicit expression is presented for the path integral of an harmonic oscillator interacting with itself in the past. The time dependence of the memory kernel is assumed to be exponential. The relation with the Feynman trial action for the variational calculation of the polaron ground state energy is discussed.
Explicit expressions of the nth gradient of 1/r
Authors: Blaive B. , Metzger J.
Published: March 2003

Explicit expressions of the nth gradient tensor and partial derivatives of the function 1/r are given, in the absolute and in the local bases associated, respectively, with the Cartesian and the spherical coordinates of space. They may be used in various multipolar developments of r−1 interaction energies.
The propagator of the time-dependent forced harmonic oscillator with constant damping
Authors: Cheng Bin Kang
Published: March 2003

The work of Montroll in deriving the propagator of a time-dependent harmonic oscillator is generalized to obtain the propagator of the time-dependent forced harmonic oscillator with constant damping.
Propagation of a Dirac particle. A path integral approach
Authors: Ichinose Takashi , Tamura Hiroshi
Published: March 2003

Rigorous path integral formulas are given which represent, in two space-time dimensions, the fundamental solution of the Cauchy problem for the Dirac equation as well as the retarded and advanced propagators for the Dirac particle. It is also shown that the theory can be applied to a free particle and a particle in a central electric field in four space-time dimensions and reveals some aspects of the path integral. Heuristically discussed is the connection with the phase space path integral or Hamiltonian path integral.
On the path integral quantization of the damped harmonic oscillator
Authors: Gerry Christopher C.
Published: March 2003

A time-dependent canonical transformation is performed in the path integral expression of the propagator for a damped harmonic oscillator to reduce it to a harmonic oscillator with modified frequency. The transformation is carried out in a properly time-symmetrized expression of the lattice space path integral by making expansions about the midpoint of each time interval.
Combined symmetries in curved space-times
Authors: Maia M. D.
Published: March 2003

The exact combination of internal and of geometrical symmetries in curved space-times is discussed. It is seen that it is possible to define locally a Lie group S containing two noninvariant subgroups E and G, such that in the flat limit of the space-time, S decomposes in the product of the Poincaré group resulting from a contraction of E and an internal group with point dependent parameters resulting fom G. Furthermore, E does not have necessarily a nilpotent action on S except in the flat limit. An explicit squared mass-splitting expression for S is derived and its behavior in a local gravitational field and in the flat limit of the space-time is analyzed.
Velocity and density of a two-dimensional acoustic medium from point source surface data
Authors: Coen Shimon , Cheney Margaret , Weglein Arthur
Published: March 2003

An inverse acoustic scattering theory and algorithm is presented for the reconstruction of a two-dimensional inhomogeneous acoustic medium from surface measurements. The measurements of the surface pressure due to a harmonically oscillating surface point source at two arbitrary frequencies allows the separate reconstruction of the density and velocity of the subsurface. This is a first step towards solving the inverse problem of exploration geophyiscs.
Finite rank approximation of wave operators for short-range and Coulomb interactions
Authors: Kröger Helmut
Published: March 2003

For the two-body system wave operators are shown to be strongly approximatable by finite rank operators which are obtained from finite rank approximations of the full and asymptotic Hamiltonian in the sense of strong resolvent convergence. This is demonstrated for short-range potentials plus the Coulomb potential with expansion functions chosen in momentum space as step functions. A generalization to the N-body system is indicated.
The time-dependent inverse source problem for the acoustic and electromagnetic equations in the one- and three-dimensional cases
Authors: Moses Harry E.
Published: March 2003

The object of the time-dependent inverse source problem of electromagnetic theory and acoustics is to find time-dependent sources and currents, which are turned on at a given time and then off to give rise to prescribed radiation fields. In an early paper for the three-dimensional electromagnetic case, the present writer showed that the sources and currents are not unique and gave conditions which make them so. The ideas of that paper are reformulated for the three-dimensional electromagnetic case and extended to the acoustical three-dimensional case and the one-dimensional electromagnetic and acoustic cases. The one-dimensional cases show very explicitly the nature of the ambiguity of the choice of sources and currents. This ambiguity is closely related to one which occurs in inverse scattering theory. The ambiguity in inverse scattering theory arises when one wishes to obtain the off-shell elements of the T matrix from some of the on-shell elements (i.e., from the corresponding elements of the scattering operator). In inverse scattering theory prescribing of the representation in which the potential is to be diagonal removes the ambiguity. For the inverse source problem a partial prescription of the time dependence of the sources and currents removes the ambiguity. The inverse source problem is then solved explicitly for this prescribed time dependence. The direct source problems for the one- and three-dimensional acoustic and electromagnetic cases are also given to provide a contrast with the inverse source problem and for use in later papers. Moreover, the present author’s earlier work on the eigenfunctions of the curl operator is reviewed and used to simplify drastically the three-dimensional direct and inverse source problems for electromagnetic theory by splitting off the radiation field and its currents from the longitudinal field and its sources and currents. Finally, for a prescribed time dependence, the inverse source problem is solved explicitly in closed form. Using methods developed for the inverse source problem for three-dimensional electromagnetic theory, we solve the following important direct problem. Consider a sphere of finite radius and uniform charge density rotating about a fixed axis. Assume that the angular velocity is zero before a certain time, varies in an arbitrary fashion, and then becomes zero again. What is the final electromagnetic field?
Exhaustive integration and a single expression for the general solution of the type D vacuum and electrovac field equations with cosmological constant for a nonsingular aligned Maxwell field
Authors: Debever R. , Kamran N. , McLenaghan R. G.
Published: March 2003

We present an exhaustive integration of the type D vacuum and electrovac field equations with cosmological constant admitting a nonsingular aligned Maxwell field satisfying the generalized Goldberg–Sachs theorem. We derive a single expression for the general solution from which one may obtain all particular cases known until now in partial versions. We also investigate in detail the separability properties of the Hamilton–Jacobi equation for the charged particle orbits and of the Klein–Gordon equation for a massive charged spin-zero test particle and their corresponding Killing tensors.
‘‘Polynomial constants’’ for the quantized NLS equation
Authors: Case K. M.
Published: March 2003

The classical nonlinear Schrödinger equation (NLS) is known to have an infinite number of polynomial constants. While recursion relations to compute these are available, no general expressions in terms of the fields have been found. However, general expressions have been obtained in terms of the reflection coefficients. When we turn to the quantum case where the fields become operators with conventional commutation relations, the polynomials with suitable ordering are still constants. The classical expression for the constants in terms of the reflection coefficients strongly suggests what the quantum form should be. This conjecture is proved for the repulsive case. The expression is significantly simpler than the classical one. It is In =(1/2π)∫∞−∞(k)nR*(k)R(k)dk.
Conformally invariant wave equations for massless particles
Authors: McLennan James A.
Published: March 2003

The invariance of wave equations for massless particles under conformal transformations of space-time is briefly summarized. Particular attention is given to a recent paper by Bracken and Jessup in which it is claimed that results obtained by the author are in error. Their paper contains several misleading statements based on a misreading of the author’s paper, and in addition an argument of theirs, intended to show error, is itself invalid. Their claims of error on the author’s part are therefore unfounded.
Crystal field effect in an Ising model
Authors: Chatterjee Ibha
Published: March 2003

The crystal field effect has been studied in the linear Ising model which can be solved exactly. For spins S= 1/2 , 1, (3)/(2) it is easy to diagonalize the transfer matrix analytically, but for spins S> (3)/(2) , the transfer matrices are diagonalized numerically. The numerical results are accurate to seven decimal places and can be treated as exact for all practical purposes. Crystal field has no effect on spin- 1/2 systems, its effect has been studied in systems with spins S> (1)/(2) . The ferromagnetic as well as the antiferromagnetic sysceptibilities have been computed for the systems with and without the crystal field. It has been found that, for small crystal fields, the susceptibility behavior is not much different from that in the absence of crystal field. But for large crystal fields, not only the antiferromagnetic susceptibilities but the ferromagnetic susceptibilities also start showing maxima which appear for integer spins only.
Poisson branching point processes
Authors: Matsuo Kuniaki , Teich Malvin Carl , Saleh Bahaa E. A.
Published: March 2003

We investigate the statistical properties of a special branching point process. The initial process is assumed to be a homogeneous Poisson point process (HPP). The initiating events at each branching stage are carried forward to the following stage. In addition, each initiating event independently contributes a nonstationary Poisson point process (whose rate is a specified function) located at that point. The additional contributions from all points of a given stage constitute a doubly stochastic Poisson point process (DSPP) whose rate is a filtered version of the initiating point process at that stage. The process studied is a generalization of a Poisson branching process in which random time delays are permitted in the generation of events. Particular attention is given to the limit in which the number of branching stages is infinite while the average number of added events per event of the previous stage is infinitesimal. In the special case when the branching is instantaneous this limit of continuous branching corresponds to the well-known Yule–Furry process with an initial Poisson population. The Poisson branching point process provides a useful description for many problems in various scientific disciplines, such as the behavior of electron multipliers, neutron chain reactions, and cosmic ray showers.
Integrals of motion for Toda systems with unequal masses
Authors: Dorizzi B. , Grammaticos B. , Padjen R. , Papageorgiou V.
Published: March 2003

We present new integrals of motion for the Toda lattice (chain of particles in one dimension with exponential interaction) for two special cases of boundary conditions: the free-end lattice with three non-equal-mass particles and the fixed-end lattice for two particles. In both cases, we use two distinct approaches in order to identify the integrable cases: direct search of the integral of motion and group theoretical methods. Our results are in agreement with the predictions of Painlevé analysis.
The sine-Gordon equations: Complete and partial integrability
Authors: Weiss John
Published: March 2003

The sine–Gordon equation in one space-one time dimension is known to possess the Painlevé property and to be completely integrable. It is shown how the method of ‘‘singular manifold’’ analysis obtains the Bäcklund transform and the Lax pair for this equation. A connection with the sequence of higher-order KdV equations is found. The ‘‘modified’’ sine–Gordon equations are defined in terms of the singular manifold. These equations are shown to be identically Painlevé. Also, certain ‘‘rational’’ solutions are constructed iteratively. The double sine–Gordon equation is shown not to possess the Painlevé property. However, if the singular manifold defines an ‘‘affine minimal surface,’’ then the equation has integrable solutions. This restriction is termed ‘‘partial integrability.’’ The sine–Gordon equation in (N+1) variables (N space, 1 time) where N is greater than one is shown not to possess the Painlevé property. The condition of partial integrability requires the singular manifold to be an ‘‘Einstein space with null scalar curvature.’’ The known integrable solutions satisfy this constraint in a trivial manner. Finally, the coupled KdV, or Hirota–Satsuma, equations possess the Painlevé property. The associated ‘‘modified’’ equations are derived and from these the Lax pair is found.
An exact nonghost solution for a plane-symmetric cosmology containing a classical spinor field
Authors: Matzner Richard A. , Ryan Michael P.
Published: March 2003

An exact solution (up to quadratures) of the Einstein–Dirac system is presented for cosmological models that depend only on one temporal and one space coordinate. Four solutions to the Dirac equation, all with zero helicity, are given.
A quantum-mechanical theory of distant correlations
Authors: Vujičić Milan , Herbut Fedor
Published: March 2003

A composite quantum system consisting of two distant subsystems and described by a correlated state vector φ12 is considered. It was shown in a previous work by the authors [Ann. Phys. 96, 382 (1976)] that such a system can be equivalently described in terms of the reduced statistical operators ρ1 and ρ2 of φ12 applying to the subsystems and a correlation operator Ua between them. It is argued that this description has a firm physical foundation for the system considered in view of the fact that, on account of the subsystems being distant, one can only measure pairs of subsystem observables A1, B2 in coincidence. The direct measurement of A1 such that [A1,ρ1]=0 on the ensemble of first subsystems performs distantly (without interaction) an orthogonal decomposition of the ensemble of second subsystems ρ2, that amounts to the measurement of the twin observable A2 (A2≡UaA1U−1aQ2, Q2 being the range projector of ρ2). A number of coincidence experiments have confirmed this claim, and have disproved all attempts (on the quantum and on the subquantum levels) to view this decomposition of ρ2 as being present also before the measurement of A1. Hence, this decomposition into subensembles comes about in the very measurement of A1, and Ua determines them in a simple way. It is demonstrated that Ua is essential for twin observables and twin symmetry operators. A detailed study of these operators is presented from a unified point of view. Puzzling features of quantum correlations described by Ua show up in composite states when the mentioned distant decompositions of ρ2 into subensembles can be incompatible with one another. A general definition of such φEPR12 states (called Einstein–Podolsky–Rosen states) is given in a few equivalent forms, and the nonuniqueness of the Schmidt canonical form of φEPR12 is investigated in order to encourage further theoretical and experimental exploration of distant quantum correlations.
A unified theory of point groups. VI. The projective corepresentations of the magnetic point groups of infinite order
Authors: Kim Shoon K.
Published: March 2003

This paper provides all the p-inequivalent projective irreducible unitary corepresentations of all the magnetic point groups of infinite order with full use of their isomorphisms.
Some geometrical consequences of physical symmetries
Authors: Rzewuski Jan
Published: March 2003

Invariant submanifolds of the linear representation space C4m of the physical symmetry group SU(2,2)×SU(m) and its subgroup 𝒫×SU(m) are studied in some detail. It is shown that there exists only one such manifold admitting unique projection onto Minkowski space. The structure of this manifold is investigated by using proper local coordinate systems.
Fixed symmetry and fixed class generating functions
Authors: Gaskell R. W. , Sharp R. T.
Published: March 2003

A fixed symmetry (or fixed plethysm) generating function enumerates all representations Rb of a compact Lie group G contained in that part of the direct product of p copies of any irreducible representation Ra of G that has a particular exchange symmetry under the symmetric group Sp. Fixed symmetry generating functions are conveniently given as linear combinations of the simpler fixed class generating functions. We give a systematic procedure for their construction and some examples for SU(2), SU(3), and SO(5). For SU(3) the examples include plethysms of up to three boxes; for SO(5) we treat two-box plethysms in general and give the scalar content of three-box plethysms; the SU(2) examples include up to six boxes.
Bound on the Nth order term of the partition function of the massive Schwinger model
Authors: Fry M. P.
Published: March 2003

An upper bound on the vacuum-to-vacuum amplitude of the Schwinger model with massive fermions is obtained.
The cohomology of the generalized Lie algebras
Authors: Mitra Bani , Tripathy K. C.
Published: March 2003

In this paper, we develop the cohomology theory of the generalized Lie algebras. Using the identification of H2φ( g,V) with ExtF( g,h), we discuss some of the extended Lie algebras useful in physics, for instance the supersymmetry, quantized field, and su(2)⊕u(1) algebras. Finally, we show that for a certain class of representations of some generalized Lie algebras, the cohomology is trivial; in so doing, we generalize the result obtained in our earlier investigation.
Tight bounds for the critical screening parameters of the generalized exponential cosine screened Coulomb potential
Authors: Dutt Ranabir , Varshni Y. P.
Published: March 2003

Analytic expressions have been obtained for the lower and upper bounds to the critical screening parameter λc associated with the ground state of the generalized exponential cosine screened Coulomb potential, V(r)=−e−λr cos(ελr)/r employing the methods of Hulthén and Laurikainen and of Hemmer. It is found that the predicted numerical results for the range 0≤ε≤1 for the lower bound for λc are within 0.08% of the exact results, and for the upper bound, within 0.7% of the exact results. It emerges further that the critical screening parameters for the excited s-states can be determined as well in an approximate way. For the static screened Coulomb potential, we obtain λnsc =1.283 664n−2 −0.092 793n−3, where n is the principal quantum number. The predicted λc for various quantum states (n=1 to 9) are in excellent agreement with the values obtained numerically by Rogers et al. [Phys. Rev. A 1, 1577 (1970)].
Kinematics of the CS method for the treatment of molecular collisions
Authors: Hahne G. E.
Published: March 2003

This paper presents the kinematical part of a proposal for founding the CS method (for one definition, see V. Khare and D. J. Kouri [J. Chem. Phys. 72, 2017 (1980)]) for the quantum treatment of molecular collisions on a certain testable physical approximation scheme. That is, let the molecules be rigid diatoms A1A2 and B1B2, with internal angular momentum ja and jb, respectively; with relative position, momentum, and angular momentum r, p, and l=r×p; and with total angular momentum J=ja+jb+l. Then the motivating conjecture is that, in addition to commuting exactly with J, and as a result of dynamical properties not discussed here, the fully off-the-energy-shell T(E) operator approximately commutes with either r, r̂, or J ⋅ r̂=ω=‘‘the r-helicity.’’ The principal results obtained in the paper are these: First, the definitions of, and transformations between, certain complete sets of system basis states in which the r-helicity ω or the p-helicity λ=J ⋅ p̂ is diagonal are established by methods similar to those of Jacob and Wick [Ann. Phys. (N.Y.) 7, 404 (1959)]. Second, it is argued that in several papers in the literature of the CS method an explicitly or presumptively incorrect kinematical law was applied to derive the matrix elements of T(E) operators for atom–molecule collisions in a basis in which ω was said to be diagonal from the fully on-the-energy-shell matrix elements of a given T(E). It is clear from the contexts that the quantities tested for conservation could not have been the r-helicity in a quantum-mechanical sense. Thus, there is no foundation to the corresponding assertions in these papers that, even if the CS method works fairly well, r-helicity conservation is usually badly violated. Third, the Wigner–Mackey theory of induced representations of continuous groups and Schur’s lemma are applied to determine the limitations (analogous to the Wigner–Eckart theorem for single operators invariant under rotations) that commuting with J and with either of the sets of operators r, r̂, or ω, imposes on the matrix of a T(E) in a basis in which r is diagonal. Fourth, and finally, it is shown that the on-the-energy-shell matrix of a T(E) that commutes with J and r has the property that its matrix elements are zero unless the angular momentum transfer j′a+j′b−ja−jb (prime indicates post-, no prime indicates precollision) is perpendicular in a quantum sense to p′−p, a result that corresponds to one obtained for an analogous classical atom–molecule collision by V. Khare et al. [J. Chem. Phys. 74, 2275 (1981)].
Locally attractive normal modes for chemical process
Authors: Fernández Ariel , Sinanoǧlu Oktay
Published: March 2003

It is shown that if along a normal mode of perturbation of a steady state which is far from equilibrium, the mixed second variation of the entropy is a constant of motion, this mode is locally attractive and the system becomes structurally unstable (in the sense of Adronov and Pontriaguin). In general, the existence of such a mode indicates chemical oscillation. In the special case that the mode has also a vanishing imaginary part of the frequency, it leads to the formation of a dissipative spatial structure.
A new method for summation of divergent power series
Authors: Arteca Gustavo A. , Fernández Francisco M. , Castro Eduardo A.
Published: March 2003

A new method for summation of divergent power series is developed. It only requires the knowledge of the form of both the small and large λ-power expansion (λ being the perturbation parameter) and few coefficients of one of them to yield excellent results. Convergence is proved for a simple two-level model, and reasonable arguments are given for more complex and interesting models. The method is quite general and contains some resummation techniques reported previously as particular cases. The anharmonic, mean square, displacement function, the ground-state eigenvalue of the quantum-mechanical anharmonic oscillator, and the ground-state energy of the hydrogen atom in a magnetic field calculated in this way are shown to be of striking accuracy in the whole range of the perturbation parameter.