bluuebunny/crossref_metadata_2025 huggingface dataset:
Irreducible representations of the osp(2,1) and spl(2,1) graded Lie algebras
Authors: Scheunert M. , Nahm W. , Rittenberg V.
Published: March 2003

We illustrate through the examples of the osp(2,1) and spl(2,1) algebras the differences between the properties of the irreducible representations of simple graded Lie algebras and simple Lie algebras.
Coherent states associated with the continuous spectrum of noncompact groups
Authors: Hongoh M.
Published: March 2003

A new, explicit formula is obtained for the coherent states associated with a continuous spectrum of the noncompact group SU(1,1). The method is based on a simple and unified algebraic approach. We briefly discuss its relations to the generalized coherent states of Barut and Girardello, and of Perelomov.
The interaction function and lattice duals
Authors: Greenberg William
Published: March 2003

An interaction function is defined for lattice models in statistical mechanics. A correlation function expansion is derived, giving a direct proof of the duality relations for correlation functions.
Extensions of Lie-graded algebras
Authors: Tilgner Hans
Published: March 2003

For Lie-graded algebras which are generalizations of Lie algebras with respect to a graduation, used recently in physics for the classification of elementary particles, and extension G of F by T, i.e., a short exact sequence T≳→G→≳F can be described by a Lie-graded composition on T⊕F, which is formulated in terms of a pair of mappings ∂:F→derT and Δ:F×F→T. The congruence of two extensions of F by T, i. e., the equivalence of the corresponding short exact sequences, is related to an equivalence relation on the set Z2(F,T) of such 2-cocycles (∂,Δ) such that there exists a bijection between the set of congruence classes of extensions of F by T and the set H2(F,T) of classes in Z2(F,T). This generalizes Lie algebraical results which are also known for groups. Examples for two special cases are given: the semidirect sums with Δ trivial and the almost direct sums with ∂ trivial. Both generalize the concepts of tangent and cotangent algebras of Lie algebras and their central extensions with R, the latter being used in the Bargmann theory of ray representations of these semidirect sums.
Invariant integrals in nonmetric supersymmetry spaces
Authors: Kannenberg L.
Published: March 2003

Definitions are given for the exterior product, infinitesimal extension of a cell, Levi-Civita symbol, and generalized Kronecker delta in order to identify invariant integrals in spaces with both Fermi and Bose dimensions. Stokes’ and Green’s theorems for such spaces are constructed as a preliminary to defining a generalized action principle in supersymmetry spaces not necessarily equipped with a metric or a connection.
The equivalence of a one-dimensional turbulence problem and the one-dimensional Coulomb gas
Authors: Chui S. T. , Frisch H. L.
Published: March 2003

We show that Burger’s equation subject to initial conditions which are governed by a canonical (Gaussian) distribution in the kinetic energy can be related to the properties of a one-dimensional Coulomb gas in a certain limit. Some consequences of this are worked out.
Ground state properties and lower bounds for energy levels of a particle in a uniform magnetic field and external potential
Authors: Lavine Richard , O’Carroll Michael
Published: March 2003

The Hamiltonian H (B), for a particle of mass μ and charge e in a uniform magnetic field of strength B in the z direction and an external axially symmetric potential V, is a direct sum of operators H (m,B) acting in the subspace of eigenvalue m of the z component of angular momentum Lz. Let λ (B) [λ (m,B)] denote the smallest eigenvalue of H (B) [H (m,B)]. For V=−e2/r (r=‖x‖), the attractive Coulomb potential, we obtain lower bounds l (m,B), for the spectrum of H (m,B) such that l (0,B) ≳l (0,0) =λ (0,0) for B≳0, l (m,B) ≳l (0,B) for m≠0, and l (‖m‖,B)−l (−‖m‖,B) =eB‖m‖/μ, l (m′,B) ≳l (m,B) if m′<m?0. We show at least for an interval [0,B′≳0] of B that the ground state of H (B) is the lowest eigenvalue, λ (0,B), of H (0,B) and is an almost everywhere positive function. If V=A/r2+r2 for B=0, λ (0) =λ (0,0) and the ground state wavefunction is an almost everywhere positive function with Lz eigenvalue zero. However, for large A, we prove that for an interval of B away from B=0, the lowest eigenvalue, λ (−1,B), of H (−1,B) is below the lowest eigenvalue, λ (0,B), of H (0,B) and that the ground state of H (B) is not an almost everywhere positive function.
On Schwinger functionals—positive extensions, moment problems, and representations
Authors: Challifour John L. , Slinker Steven P.
Published: March 2003

We construct extensions for a class of Schwinger functions at noncoincident arguments to symmetric states on the Borchers algebra. Conditions are given for these states to be strongly positive. For strongly positive states the relation between uniqueness of the Euclidean measure, polynomial density, and self-adjointness for the Euclidean field is examined.
On the evolution equations for Killing fields
Authors: Coll Bartolomé
Published: March 2003

The problem of finding necessary and sufficient conditions on the Cauchy data for Einstein equations which insure the existence of Killing fields in a neighborhood of an initial hypersurface has been considered recently by Berezdivin, Coll, and Moncrief. Nevertheless, it can be shown that the evolution equations obtained in all these cases are of nonstrictly hyperbolic type, and, thus, the Cauchy data must belong to a special class of functions. We prove here that, for the vacuum and Einstein–Maxwell space–times and in a coordinate independent way, one can always choose, as evolution equations for the Killing fields, a strictly hyperbolic system: The above theorems can be thus extended to all Cauchy data for which the Einstein evolution problem has been proved to be well set.
Geometric aspects of supergauge theory
Authors: Lloyd-Evans D. J. R.
Published: March 2003

It is shown that the Wess–Zumino supergauge algebra can be obtained from the theory of automorphisms of a complex structure on spacetime, and that this is related to a formal geometric scheme of quantization. The geometric interpretation requires h/ to be proportional to the square of the basic unit of length.
Correlations near phase transition in a simple fluid
Authors: Ramanathan G. V.
Published: March 2003

Correlations in a system with a weak, long-ranged attractive potential are studied. Using a natural small parameter, the asymptotic orders of all correlations are established. Explicit leading order solutions are obtained for all correlations when the system is away from phase change As it approaches transition, It is shown that the many-body correlations, even though still small, develop very long range and that they are shown extremely slowly varying functions over space. As a results all the correlations contribut equally significantly to the computation of the pair correlation. In an asymptotic ragion near transition, a hierarchy is derived in which each corelation is expressed in terms of its immediate predecessor, its immediate successor and the pair correlation. The pair potential does not appear in these equations. Instead the correlations are expressed in terms of a Yukawa potential whose strength and range are related to the density and other parameters but not to the detailed form of the potential. In the leading approximation, the pair correlation is proportional to this Yukawa function.
Structure of the Azzarelli–Collas representation for the scattering amplitude and generalization to the Rice representation and the Euler–Pochhammer representation
Authors: Wu Alfred C. T.
Published: March 2003

The Azzarelli–Collas integral representation for the scattering amplitude is extended to the Rice representation. The latter representation in turn is viewed as an example of the Euler–Pochhammer representation.
On the accidental degeneracy of the n-dimensional anisotropic harmonic oscillator. II
Authors: Major M. E.
Published: March 2003

In an earlier paper, a group, G, associated with the n-dimensional anisotropic harmonic oscillator was shown to be embedded in a semidirect product, L, of the Weyl group N and the symplectic group Sp(2n,R). A particular representation Rv of L, when restricted to G, was proved to be unitarily equivalent to ⊕sdω,s UGv,−(sgnv)s), where dω,s is the degeneracy of the energy level Eω,s of the n-dimensional anisotropic harmonic oscillator with frequencies (ω1,ω2,...,ωn) =ω, UGv,−(sgnv)s is an irreducible representation of G and s may be regarded as indexing all distinct energy levels of the system. In the present paper, the representation Rv of L is shown to be unitarily equivalent to the representation UNvW⊕? of L, where UNv is an irreducible representation of N, W is the projective representation of Sp(2n,R) which intertwines the representations UNv and SUNv of N [where S ε Sp(2n,R)], and ? is the complex conjugate of W. This alternative form for the representation Rv of L enables it to be decomposed, into two irreducible representations.
A Green’s function for a linear equation associated with solitons
Authors: Keener J. P. , McLaughlin D. W.
Published: March 2003

A linear equation associated with nonlinear wave equations which support solitons is analyzed. A complete set of solutions of this linear equation is described through the techniques of scattering theory. This set is used to construct an explicit representation of a Green’s function for perturbation theory. The cases of the nonlinear Schrödinger and sine-Gordon equations are discussed in some detail.
Path structures on manifolds
Authors: Ehlers Jürgen , Köhler Egon
Published: March 2003

We study collections of paths—i.e., unparametrized curves—on a manifold such that through every point and every direction at that point there passes exactly one path. Among such path structures we characterize, analytically and in terms of symmetries, those which consist of geodesics of a linear connection. Examples of nongeodesic path structures are given, and some of the results are interpreted physically.
On the combined Dirac–Einstein–Maxwell field equations
Authors: Hamilton M. J. , Das A.
Published: March 2003

This paper discusses the combined Dirac–Einstein–Maxwell equations in general relativity. The combined equations are derived from a variational principle which involves the variation of tetrad fields. A class of exact, self-consistent solutions is found where the metric is static, the electromagnetic field is just electrostatic, and the spinor field is stationary in the wave mechanical sense. These solutions are analogous to Dirac’s plane wave solutions which propagate along the x3 axis and are not square integrable. It is shown that under reasonable physical conditions there do not exist solutions with finite total charge. It seems that the static electro-gravitational background is not compatible with localizable matter fields possessing intrinsic spin.
The N-quantum approximation in the Bronzan–Lee extended-source static model
Authors: Scarfone Leonard M. , Burns James A.
Published: March 2003

The Bronzan–Lee model of a soluble field theory with vertex function is analyzed from the viewpoint of the N-quantum approximation. Determination of the Heisenberg field expansions in the single-source one- and two-meson sectors of the model yields three scattering amplitudes, a production amplitude, and the renormalization constants in agreement with other derivations. The solutions to one algebraic and three linear integral equations, the mathematical complexity of which is reminiscent of the Tamm–Dancoff eigenvalue approach in the Lee model with two nontrivial sources, are required for this purpose. Finite results compatible with the conventional renormalization program are obtained from the field expansions and the equations of motion by prescribing that each normal-ordered product of in-fields in an expansion have the same quantum numbers as its Heisenberg field and, so that all relevant terms are included for a sector, all possible combinations of in-fields consistent with the quantum numbers of the sector must occur. In general, this recipe is substituted in place of power counting, which evidently is inappropriate in higher sectors of the Lee model. The investigation of one- and two-meson exchange interactions of two sources in the Lee model via the N-quantum approximation has been carried out, and similar work is contemplated in charged scalar theory and the classic Chew–Low model.
Spectral properties of completely monotonic operators
Authors: Bonora L. , Pasti P.
Published: March 2003

We introduce a special class of j-dependent analytic operator valued functions, the completely monotonic operators, and find the general properties of their spectrum and of their resolvent. Next we study an important and wide subclass of such operators, for which it is possible to reach more detailed information about the leading singularity of the resolvent in the j plane, and in some cases to completely determine it.
A note on the range of the applicability of the Ornstein–Zernike theory in the van der Waals model
Authors: Napiórkowski Marek
Published: March 2003

We show that the condition determining the range of the applicability of the Ornstein–Zernike theory obtained previously by Hemmer for the van der Waals model is too strong. The weaker condition obtained by us is in agreement with the existing results for different physical systems, and it requires the temperature to satisfy the following inequality: (T−Tc)/Tc≫ (γd)6, where γd denotes the ratio of the short-range part of the potential to the range of the long-range part and Tc is the critical temperature predicted in the van der Waals model.
Sequences of transformations for particle-field Hamiltonians
Authors: Gross Eugene P.
Published: March 2003

The nonrelativistic Hamiltonian for a particle interacting with a scalar field is studied by a method that involves a product of unitary transforms. We use intermediate coupling transforms for finite particle momenta to treat the interaction with oscillators with a range of wave vectors. Elimination of the oscillators in the range leads to a new Hamiltonian of the identical operator structure but with a modified interaction and mass. We show that with any finite number of divisions the self energy is always lower than the intermediate coupling result. In the limit of infinitely many divisions differential equations are derived for the interaction and effective mass as a function of the smallest wave vector of the oscillators that have been removed.
K matrix for the Woods–Saxon potential
Authors: Talukdar B. , Ray M. N. Sinha
Published: March 2003

The s-wave part of the off-shell K matrix elements for the Woods–Saxon potential has been obtained in terms of elementary transcendental functions by using the differential equation approach to off-shell scattering.
Stability, equilibrium and KMS for an infinite classical system
Authors: Pulvirenti M.
Published: March 2003

The stability condition as a property which characterizes the thermodynamic equilibrium is studied from an abstract point of view. Furthermore, an application of the main result to the case of an infinite classical harmonic system is given.
Perturbation solution of the Percus–Yevick equation for the square-mound potential
Authors: Fuliński A. , Jȩdrzejek C.
Published: March 2003

The perturbation solution of the Percus–Yevick equation, based on the known solution for hard-sphere interactions, is found for the square-mound potential. The correlation functions are expanded in powers of the parameter α, related to the height of the mound, i.e., describing the deviation of the interactions from the hard-sphere ones. An algorithm for the calculation of subsequent coefficients is given. Numerical calculations show, however, that the series converges slowly and thus a few terms approximate the whole series with sufficient accuracy for small (but still finite) values of α, i.e., for almost hard-sphere interactions, only. For mounds high enough the system behaves very similarly to the hard-sphere system, but it quickly loses its ’’hard’’ characteristics as the mound decreases. This result, in the light of the success of the recent perturbation theory of liquids, seems to suggest that, whereas fairly significant changes of the potential in the outside of the hard core may be treated as small perturbations, even a small change inside the hard core very strongly perturbs the properties of the system.
Functional equations for extended hadrons
Authors: Haba Z.
Published: March 2003

We consider the problem of solution of some functional equations occurring in the theory of extended hadrons. By means of stochastic methods solutions of these equations are obtained in the form of a contractive (Markov) semigroup in Hilbert space. Analytic continuation to a unitary group implementing time evolution is performed. The problem of unitary implementability of Lorentz and gauge symmetries, essential for physical interpretation, remains unsolved.
Quantum counting processes
Authors: Srinivas M. D.
Published: March 2003

It is proposed that counting experiments in quantum physics should be analyzed in terms of point processes (QPP) defined in the framework of quantum probability theory. A coincidence approach is developed for a class QPP called the regular QPP. A counting formula is derived which determines completely the counting statistics of a regular QPP by means of a pair of ’’generators.’’
The gravitational influence of a beam of light of variable flux
Authors: Nackoney Raymond W.
Published: March 2003

An exact solution is obtained for the Einstein field equations of a columnated, time varying beam of light. The beam is circular in cross section, infinite in path length, and is considered in the geometrical limit. The beam is described in a retarded time coordinate system. The flux density is dependent on the radial coordinate and on the retarded time. The solution is sufficiently general so as to describe a single pulse of light traveling through a vacuum. It also allows the description of acceleration fields which propagate in the direction of the beam at the speed of light. Geodesics are considered in order to test the interpretation of the solutions and the stability of the time varying beam.
Fermi–Bose and internal symmetries with universal Clifford algebras
Authors: Dixon Geoffrey
Published: March 2003

Supersymmetry in four-dimensional space–time is approached from the theory of universal Clifford algebras. The representation produced results in a class of new algebras characterized by an index n which indicates the natural appearance of su(2n) ×u(1) as a subalgebra interacting only with the spinor (or odd) parts of the surrounding Fermi–Bose algebra. Finally, a reformulation of the Dirac equation in this formalism is presented which is not plagued with the empirically untenable problem of a continuous range of eigenvalues.
A Lie group framework for soliton equations. I. Path independent case
Authors: Corones James , Markovski B. L. , Rizov V. A.
Published: March 2003

A general Lie group theoretic framework for the study of a class of nonlinear partial differential equations is presented. In two space–time dimensions this class includes soliton equations. The approach is applicable in N⩽2 space–time dimensions. Eigenvalue problems and isospectral flows associated with equations have a natural group theoretic interpretation in this framework. A sequence of nonlocal exact 1-,2-,...,(N−1) -forms are derived in N-dimensional space–time.
The translation kernel in the n-dimensional scattering problem
Authors: Coz Marcel , Rochus Pierre
Published: March 2003

Radial wavefunctions are defined for the n-dimensional scattering problem (n≳1) with spherical symmetry by conditions of regularity at the origin or by conditions of behavior at infinity. The existence of translation kernels can therefore be discussed in both instances. The problem of representing regular solutions appears to be essentially different from that of representing irregular solutions. The essential difference originates from the type of domain used in the representation: It is bounded in the first case and unbounded in the second. If one can still compare the ranges of validity of the two types of representation when one is dealing with a scalar situation, upon proceeding to a matrix situation, a comparison is no longer possible.
Integral theory of radiative heat transfer with anisotropic scattering and general boundary conditions
Authors: Boffi V. C. , Spiga G.
Published: March 2003

An integral formulation of the theory of planar radiative heat transfer with anisotropic scattering and general boundary conditions is proposed in the paper. Explicit expressions for the relevant kernels are obtained, and the correlations between the structure of these kernels and the properties of the bounding surfaces as well as the interaction between the bounding surfaces themselves are investigated for a variety of physical situations. The lines along which exact and approximate analytical solutions can be constructed are indicated and commented upon.
One-dimensional, neighbor-pair degeneracies for dumbbells with distinguishable ends
Authors: McQuistan R. B.
Published: March 2003

Expressions are developed which describe exactly the degeneracies for the various kinds of neighbor pairs that can arise when dumbbells with distinguishable ends are distributed on a one-dimensional lattice. Expectation values and normalization constants are also developed.
Mirror planes in Newtonian stars with stratified flows
Authors: Lindblom Lee
Published: March 2003

This paper shows that a certain class of Newtonian stellar models must possess a plane of mirror symmetry. A corollary of this result is that static Newtonian stars must be spherical. The new features of the results given here are that: (a) The assumptions about the velocity distribution of the fluid are weaker than previous treatments and (b) the method of proof given here does not depend as strongly on the linearity of the gravitational field equations as the previously published treatments. Therefore, this proof may serve as a model for a general relativistic generalization of the mirror plane theorem.
KMS condition for stable states of infinite classical systems
Authors: Pulvirenti M. , Riela G.
Published: March 2003

Using an abstract algebraic approach, we obtain a new derivation of the KMS condition from a stability property of an infinite system via a classical version of the Tomita–Takesaki theorem.
Classical particles with spin. I. The WKBJ approximation
Authors: Stachel John , Plebański Jerzy
Published: March 2003

This is the first of a series of papers developing the classical theory of a spinning particle. The equations of motion will be derived from a Lagrangian, and solutions for the classical trajectory and spin precession in external fields will be given. In this paper an abstract spin vector is introduced to characterize the spin of a classical particle. Lagrangians for the classical trajectories and for the motion of the abstract spin vector are derived from corresponding quantum-mechanical Lagrangians by the WKBJ approximation method for nonrelativistic and relativistic particles. The equations of motion for the trajectory and the abstract spin vector following from the extremalization of these Lagrangians are given. The equations of motion for the precession in an external electromagnetic field of the spin vector (or tensor) in space–time is derived from the equations of motion for the abstract spin vector. In the relativistic case, they are equivalent to the Bargmann–Michel–Telegdi equations [Phys. Rev. Lett. 2, 435 (1959)]. The relationship between the ensemble and single-particle points of view is also elucidated.
Properties of causally continuous closed universes
Authors: Ishikawa Hirohisa
Published: March 2003

We consider the properties of causally continuous space–time with a closed spacelike hypersurface 𝒮, i.e., a closed universe. We show that a closed universe does not collide with other universes.
Klein–Gordon kinks with fourth order derivative self-coupling
Authors: Rañada Antonio F. , Rañada Manuel F.
Published: March 2003

A Klein–Gordon field with a derivative fourth order self-coupling is studied. It is shown that the kinks of the model form singlets, doublets, or triplets of electric charge, according to the values of the coupling constants.
A generalization of the Gel’fand–Levitan equation for the one-dimensional Schrödinger equation
Authors: Moses H. E.
Published: March 2003

The Gel’fand–Levitan equation for the one-dimensional Schrödinger equation is generalized to the case that the unperturbed Hamiltonian contains part of the scattering potential, this part being denoted by V0(x), and that the direct scattering problem has been solved for this Hamiltonian. Hence one knows the reflection coefficient b0(k), the point eigenvalues E0i, and the normalizations of the corresponding eigenfunctions C0i. We are given b1(k), E1i, C1i, which are the corresponding quantities for full potential V1(x) =V0(x)+ΔV (x). A Gel’fand–Levitan equation is set up in terms of b1(k)−b0(k) and the difference in measures for the discrete spectra for V0 and V1, respectively, from which ΔV can be found. One may regard the new algorithm as providing a means to modify a known potential to accommodate prescribed changes in the reflection coefficient and changes in the nature of the discrete spectrum. The generalization has applications to the Korteweg–de Vries equation. It is shown that a kind of ’’superposition’’ principle exists for solutions in that one can add a function of x and t to one solution and obtain a second solution. This principle can be used to separate the soliton part of a solution from the continuous spectrum part.
Multi-soliton-like solutions to the Benjamin–Ono equation
Authors: Joseph R. I.
Published: March 2003

We outline a systematic method of obtaining particular solutions to the nonlinear, integrodifferential equation obtained by Benjamin and Ono in their study of the propagation of finite amplitude waves in fluids of great depth. These solutions have the property of asymptotically breaking up into a series of N spatially localized waves of permanent form; we loosely refer to these as ’’N-soliton’’ solutions. Detailed results for the two-soliton solution are explicitly given.
Vector spherical harmonics of the unit hyperboloid in Minkowski space
Authors: Hostler Levere
Published: March 2003

Vector fields in Minkowski space which are simultaneous eigenfunctions of the operators [Jx]2+[Jy]2 +[Jz]2, [Jz], and −(1/2) LμνLμν are investigated using special tensor methods which exploit the properties of the intrinsic gradient operator ∇ of the unit hyperboloid xμxμ=1. A convenient representation of the simultaneous eigenfunctions is provided by the use of Helmholtz’s theorem for the unit hyperboloid. The utility of this representation arises from the existence of intertwining relations such as Jμν∇=∇Lμν. An addition theorem for the solenoidal vector spherical harmonics of the unit hyperboloid is derived, and the Green’s function of Poisson’s equation on the unit hyperboloid is obtained.
Classical mechanics, the diffusion (heat) equation, and the Schrödinger equation
Authors: Truman Aubrey
Published: March 2003

We consider the limiting case λ→0 of the Cauchy problem ∂uλ/∂t= (λ/2μ) ∇2xuλ +[V (x)/λ]uλ, uλ(x,0) =exp[−S0(x)/λ]T0(x); S0, T0 independent of λ, for both real and pure imaginary λ. We prove two new theorems relating the limiting solution of the above Cauchy problem to the corresponding equations of classical mechanics μ (d2x/dτ2)(τ) =−∇xV[x (τ)], τ∈ (0,t). These relationships include the physical result quantum mechanics → classical mechanics as h/→0.
Proof that the H− ion has only one bound state. Details and extension to finite nuclear mass
Authors: Hill Robert Nyden
Published: March 2003

It is rigorously demonstrated that the H− ion, treated in nonrelativistic approximation with Coulomb interactions only, has only one bound state for the electron to nucleus mass ratio less than 0.21010636. This extends earlier work which had proven the result in the fixed (infinite mass) nucleus approximation. The method used can, if desired, also be used to calculate rigorous lower bounds to the energies of those bound states of two electron atomic systems which do exist.
The generalized Langevin equation with Gaussian fluctuations
Authors: Fox Ronald Forrest
Published: March 2003

It is shown that all statistical properties of the generalized Langevin equation with Gaussian fluctuations are determined by a single, two-point correlation function. The resulting description corresponds with a stationary, Gaussian, non-Markovian process. Fokker–Planck-like equations are discussed, and it is explained how they can lead one to the erroneous conclusion that the process is nonstationary, Gaussian, and Markovian.
N-body quantum scattering theory in two Hilbert spaces. I. The basic equations
Authors: Chandler Colston , Gibson A. G.
Published: March 2003

Derivations are given for some transition and resolvent operator equations for multichannel quantum scattering with short-range potentials. The basic difference between these and previous equations is that the unknown operators act only on the channel subspaces. This is made possible by utilizing, and extending, the two-Hilbert-space formulation previously given by the authors [in J. Math. Phys. 14, 1328 (1973)]. The equations in abstract form are of the Lippmann–Schwinger type, differing only in the appearance of certain injection operators from one Hilbert space to the other. When applied to multichannel quantum scattering, the abstract theory yields a new system of equations for the transition and resolvent operators. Uniqueness of the solution to the equations is proved.
On plane symmetric Einstein–Maxwell fields
Authors: Banerjee A. , Chakrabarty N.
Published: March 2003

It is shown that the results given by Letelier and Tabensky [J. Math. Phys. 15, 594 (1974)] regarding the solution of Einstein–Maxwell equations for plane symmetry will be modified after suitable correction of an error in their paper. Further appropriate exterior solutions, which satisfy the conditions of fit at the boundaries of plane symmetric charged dust distributions, are obtained. One such exterior nonstatic solution can be transformed to a static one, which is a member of the general class.
Stochastic mechanics and dissipative forces
Authors: Skagerstam Bo-Sture K.
Published: March 2003

We analyze a simple velocity dependent potential in the framework of stochastic mechanics. A nonlinear Schrödinger–Langevin equation is obtained. This equation turns out to have solutions with the remarkable property of giving an approach to stationary quantum states. Information theoretical aspects on the irreversible behavior of the model is also briefly discussed.
Electromagnetic eigenmode perturbations caused by deformation of a plasma core in a spherical cavity resonator
Authors: Steiger Arno D.
Published: March 2003

A perturbation formalism for the electromagnetic eigenmodes of a lossless spherical cavity resonator has been derived from the Boltzmann–Ehrenfest theorem. The perturbations are caused by adiabatic deformations of a plasma core located at the center of the cavity.
Jauch–Piron states
Authors: Rüttimann Gottfried T.
Published: March 2003

We argue that a finite proposition system in the sense of Jauch and Piron that admits a unital set of states is necessarily purely classical. Based on this result, we investigate the extensibility of σ-additive states on projection lattices to all projections of a separable Hilbert space.
Nonuniqueness in the inverse source problem in acoustics and electromagnetics
Authors: Bleistein Norman , Cohen Jack K.
Published: March 2003

A recently developed formulation of the inverse source problem as a Fredholm integral equation of the first kind provides motivation for the development of analytical characterizations of the nonuniqueness in the inverse source problem. Nonradiating sources, i. e., sources for which the field is identically zero outside a finite region, are introduced. It is then shown that the null space of the Fredholm integral equation is exactly the class of nonradiating sources.
Subalgebras of the similitude algebra and their invariants
Authors: Peccia Anthony
Published: March 2003

The subalgebras of the similitude algebra have previously been classified into conjugacy classes; in this article these classes are classified into isomorphism classes. For each conjugacy class of subalgebras, the invariants are also calculated. All the results are summarized in tables.
Systems of imprimitivity and representations of quantum mechanics on fuzzy phase spaces
Authors: Ali S. Twareque , Prugove?ki E.
Published: March 2003

The problem of expressing quantum mechanical expectation values as averages with respect to nonnegative density functions on phase space, by analogy with classical mechanics, is reexamined in the light of some earlier work on fuzzy phase spaces. It is shown that such phase space representations are possible if ordinary phase space is replaced by a so-called fuzzy phase space, on which the usual marginal distribution functions are redefined to conform to the fact that arbitrarily precise simultaneous measurements on position and momentum are not compatible with quantum mechanics. In the process a generalization of Wigner’s theorem on the nonexistence of phase space representations of quantum mechanics, which also satisfy the standard (classical) marginality conditions in position and momentum, is obtained. It is shown that a (continuous) representation of quantum mechanics exists on a given fuzzy phase space if an only if the corresponding confidence functions for position and momentum measurements satisfy the Heisenberg uncertainty relations.
Plane wave solutions in scalar tensor theories and solutions of source-free Einstein–Maxwell theory
Authors: Ray Dipankar
Published: March 2003

Vacuum solutions of the field equations that satisfy the original notion of the plane wave, namely gμν=gμν(Z), Z=Σμaμxμ, aμ’s being constants and gμνZ,μZ,ν=0, are sought for both Brans–Dicke scalar–tensor theory and the more recent scalar–tensor theory due to Sen and Dunn. (Here Greek letters range from 1 to 4 and Latin letters from 1 to 3.) A complete set of solutions are obtained for both cases. Although not required at the outset, it turns out that, in both cases, the scalar field is also function of Z alone. As a by-product, one gets the complete set of solutions of the Einstein–Maxwell equations for the null electromagnetic field for the cases when gμν satisfies the above-mentioned requirement.
Group theoretic aspects of conservation laws of nonlinear dispersive waves: KdV type equations and nonlinear Schrödinger equations
Authors: Kumei Sukeyuki
Published: March 2003

Group theoretic properties of nonlinear time evolution equations have been studied from the standpoint of a generalized Lie transformation. It has been found that with each constant of motion of the KdV type equation fxxx+a (f) fx+ft=0 and of the coupled nonlinear Schrödinger equation fxx +a (f,g)+ift=0, gxx+a (g,f) −igt=0 one invariance group of the equations is always associated. The well-known series of constants of motion of the KdV equation and the cubic Schrödinger equation will be recovered from the invariance groups of the equations. The doublet solution of the KdV equation will be characterized as the invariant solution of one of the groups. In a more general context, it will be shown that the well-known equation of quantum mechanics (d/dt) 〈U〉=〈[iH,U] +∂U/∂t〉 can be generalized to a class of nonlinear time evolution equations and that if U is a generator of an invariance group of the equation then (d/dt) 〈U〉=0. The class includes equations such as the KdV, the cubic Schrödinger, and the Hirota equations.
An exact solution for diffraction of a line-source field by a half-plane
Authors: Boersma J. , Lee S. W.
Published: March 2003

This paper deals with the exact solution of a special electromagnetic diffraction problem namely, diffraction of a line-source field by a half-plane. The line source is located on the surface of the half-plane, and radiates an E-polarized wave described by uin=H(1)n (kr1)  sinnφ1, where n=1,2,3,⋅⋅⋅, and (r1,φ1) are polar coordinates with the origin at the source point. A new, closed-form, exact solution for the total field on the shadow boundary is presented. This exact solution consists of n terms of order k−p, where p=1,2,...,n. Its first two terms, which are of orders k−1/2 and k−3/2 relative to the incident field, agree with the asymptotic solution derived in a companion paper by the uniform asymptotic theory of edge diffraction.
Some aspects of the N-representability problem in finite dimensions. I. Operator endomorphisms which induce necessary conditions
Authors: Kummer H. , Absar I. , Coleman A. J.
Published: March 2003

The connection between operator endomorphisms and conditions for N-representability is established. The sets 𝒩N and 𝒮N are defined as the sets of operator endomorphisms which induce necessary conditions and sufficient conditions respectively. A detailed characterization of 𝒩N is presented.
Short derivation of a formula due to Lubkin
Authors: Epstein Saul T.
Published: March 2003

We present a short derivation of Lubkin’s formula for the ensemble of maximum entropy subject to mean value constraints involving noncommuting operators.
Correction of ’’Extension of the statistical mechanics of equilibrium to noncummutative constraints’’ to cover singular constraints
Authors: Lubkin Elihu
Published: March 2003

In a previous paper, a Gibbs ensemble formula was given for that ensemble P which maximizes the entropy S=−TrP lnP subject to constraints TrPAi=Qi, where the Ai need not commute. An oversight, namely, cases where the constraints though consistent force P to be singular, is here properly incorporated into the argument. The result is that one must first regard the constraints as limiting discussion as much as possible to a sub-Hilbert space of constraint C, then the maximum entropy solution is indeed given by a Gibbs formula as before, but referring to matrices over C.
Some aspects of the N-representability problem in finite dimensions. II. Operator endomorphisms which induce sufficient conditions
Authors: Kummer H. , Absar I.
Published: March 2003

Given the set 𝒮N of all operator endomorphisms T with the property that whenever D is any 2-density operator, then T (D) is N-representable is considered. We specify a pair {Q2,PN} of extreme points of 𝒮N which are related to each other via the particle-hole duality (Theorem 1.2). The rest of the paper is devoted to a complete characterization of the set ŜN of all operator endomorphisms T with the property that whenever D is any 2-density operator then T (D) is quasi-N-representable, i.e., satisfies the necessary conditions Id, QN, BN, and CN.
A new type of soliton with particle properties
Authors: Enz U.
Published: March 2003

This paper describes stable field configurations of two scalar fields ϑ (x,y,z,t) and φ (x,y,z,t). The field configurations follow from a simple least action principle based on an energy density which is a function of ϑ, φ, and their first derivatives. The description is Lorentz-invariant. The structures are of a stringlike type and are characterized by several integers. It is shown, that the simplest closed strings, described by the integers N=1, M=1, P±1, are stable. The structures P=1 and P=−1 are related by mirror symmetry. Three constants enter in the basic action principle: a length l, a constant E with the dimension of energy time length, and a dimensionless parameter γ. All properties of these field configurations have discrete values, which is a direct consequence of the nonlinearity of the basic expression for the energy density. An attempt is made to identify these structures with elementary particles, the electron and the positron in the simplest case P=1 and P=−1. To this aim, the total energy of the field structures is equated to the rest energy of the particles. The constants E, l, and γ are related to the fundamental physical constants h, m, e. The model proposed represents a classical field structure with quantized properties.
Ordering of the exponential of a quadratic in boson operators. I. Single mode case
Authors: Mehta C. L.
Published: March 2003

The Weyl ordered form of the operator exp[αâ2+βâ2++γ (â+â+ââ+)] is derived in a very simple way. Using this result, we also obtain the normal and antinormal ordered forms as well as the diagonal coherent states representation of this operator.
Wigner–Eckart theorem for tensor operators of graded Lie algebras
Authors: Mezincescu L.
Published: March 2003

An invariant functional, analog to the group integral associated with a Lie group, is defined for the graded Lie algebras. A sufficient condition for the vanishing of the group volume is given. Orthogonality relations of the matrix elements of the representations are obtained, and the Wigner–Eckart theorem is proved for a class of graded Lie algebras.
Wightman distributions on conformal space
Authors: Mayer D. H.
Published: March 2003

We show that every tempered distribution Tnε𝒮′ (Mn4) which is the boundary value of a function fn(z) holomorphic in the field theoretic tube domain 𝒯4n can be uniquely continued to a distribution T̃n on the universal covering space M̃n4 of the conformally compactified Minkowski space M4nc. It can be shown that T̃n is the boundary value of a function f̃n holomorphic in a certain domain F̃n4 of the complex manifold ℂM̃n4= (ℂ×Σ3)n, where Σ3 denotes the affine complex three-dimensional unit sphere.
Approximating functions with a given singularity
Authors: Hillion Pierre
Published: March 2003

In this paper, assuming that one knows one of the singularities s1 of the function f (z) and its power series expansion on a domain 𝒟 of the complex plane, we introduce some sequences of Gammel–Baker generalized Padé approximants with the same type of singularity s1. Two examples are given: One concerns the convergence acceleration of approximations for functions with a logarithmic singularity; in the other one, a physical application to optical polarizability is discussed.
A gauge invariant formulation of quantum electrodynamics using local currents
Authors: Menikoff R. , Sharp D. H.
Published: March 2003

In this paper we formulate nonrelativistic quantum electrodynamics in a local and manifestly gauge invariant manner. This is accomplished by using the electromagnetic field strengths, rather than potentials, to describe the electromagnetic field and local currents, rather than canonical fields, to describe the matter. The exponentiated currents and field strengths form a group, whose representations can be studied using the Gel’fand–Vilenkin formalism. The currents and electromagnetic field strengths can be represented on a physical Hilbert space having positive norm. (The necessity for an indefinite metric does not arise here.) Furthermore, the classical equations of motion hold as operator equations on this Hilbert space. In this formulation, the requirement of gauge invariance is essentially replaced by imposing the Maxwell initial value equtions, which in turn lead to constraints on systems of Gel’fand–Vilenkin multipliers.
Statistical theory of effective electrical, thermal, and magnetic properties of random heterogeneous materials. VII. Comparison of different approaches
Authors: Hori Motoo
Published: March 2003

A general analysis is given for the theoretical evaluation of the effective permittivity of random heterogeneous materials that are statistical homogeneous. The perturbative and variational formulations presented in Papers I–VI in this series of work are reconstructed from a slightly different point of view and compared with recent approaches developed by other authors. Perturbation expansions for the effective permittivity are derived through electric field, electric displacement, Lorentz field, and T matrix. The validity of various approximate solutions involving the effective-medium approximation and the cumulant expansion method is discussed with the aid of a diagrammatic representation of the perturbation series. It is confirmed that, at the present stage, the cumulant theory is the best approximation for a three-dimensional system, while the effective-medium theory is the best for a two-dimensional system. The meaning and applicability of variational approaches are also reviewed.
On invariance groups and Lagrangian theories
Authors: Houard J. C.
Published: March 2003

The problem of determining the Lagrangian theories whose equations of motion are invariant under a given transformation group is formulated and studied.
A prolongation structure for the AKNS system and its generalization
Authors: Morris H. C.
Published: March 2003

A prolongation structure is determined for the AKNS system of equations. Using an interpretation in terms of Cartan–Ehresmann connections, a generalization is then constructed which leads to an inverse scattering problem for the multicomponent nonlinear Schrodinger equation iqαt= (1/2) qαxx +qα(Σnβ=1‖qβ‖2) (α=1,...,n).
Monopole theory without string
Authors: Cheng Kuo-Shung
Published: March 2003

We propose a Schrödinger equation for the nonrelativistic charge-monopole system without using strings and demonstrate that it is a correct equation for this system.
The Zeno’s paradox in quantum theory
Authors: Misra B. , Sudarshan E. C. G.
Published: March 2003

We seek a quantum-theoretic expression for the probability that an unstable particle prepared initially in a well defined state ρ will be found to decay sometime during a given interval. It is argued that probabilities like this which pertain to continuous monitoring possess operational meaning. A simple natural approach to this problem leads to the conclusion that an unstable particle which is continuously observed to see whether it decays will never be found to decay!. Since recording the track of an unstable particle (which can be distinguished from its decay products) approximately realizes such continuous observations, the above conclusion seems to pose a paradox which we call Zeno’s paradox in quantum theory. The relation of this result to that of some previous works and its implications and possible resolutions are briefly discussed. The mathematical transcription of the above-mentioned conclusion is a structure theorem concerning semigroups. Although special cases of this theorem are known, the general formulation and the proof given here are believed to be new. We also note that the known ’’no-go’’ theorem concerning the semigroup law for the reduced evolution of any physical system (including decaying systems) is subsumed under our theorem as a direct corollary.
Second-quantized representation for a model system with composite particles
Authors: Gilbert J. Dennis
Published: March 2003

A second-quantized representation for nonrelativistic systems with composite particles is given in which composite particles of two-fermion constituents are described as elementary bosons. The Tani transformation of Girardeau is used to introduce elementary composite fields. An equivalent linear equation of motion method—introducing a ’’d matrix’’—is used in place of the usual nonlinear equation of motion method. This and a diagram formalism are developed to calculate a Hamiltonian and subsidiary condition for this model system and to derive some properties of the Tani transformation.
The theory of one-dimensional Schrödinger operators with a periodic potential
Authors: Meiman N. N.
Published: March 2003

We carry out the spectral analysis of the n-band Hill equation by examining the external problem for a class of entire functions with least derivation from zero. The spectrum is characterized in terms of hyperellyctic integrals and the geometry of admissible points (band edges).