bluuebunny/crossref_metadata_2025 huggingface dataset:
Geometry of superspaces with Bose and Fermi coordinates and applications to graded Lie bundles and supergravity
Authors: Mansouri Freydoon
Published: March 2003

The geometry of superspaces with Bose- and Fermi-type coordinates is presented from a coordinate independent point of view. Various geometrical quantities of conventional manifolds are generalized so as to be applicable to superspaces. It is shown that these generalizations can be basically arrived at algebraically by replacing, in the definitions of various geometrical quantities, the Lie derivative of the conventional manifolds with a generalized graded Lie bracket. Explicit expressions for connection coefficients, Riemann curvature tensor, etc., are derived. The general formalism is then applied to graded Lie bundles the relevance of which to supergravity theories is demonstrated.
Exact results for second-neighbor surface magnons in an fcc lattice
Authors: Dobson J.
Published: March 2003

An exact dispersion equation f (Ω) =0 is obtained for (001) surface magnons in an fcc lattice with nearest and second nearest neighbor Heisenberg coupling. On the Brillouin zone boundary a closed expression is given for the frequency Ω, while a simple root search yields Ω for wave vectors inside the zone. These exact frequencies confirm the results obtained by Trullinger from a Gottlieb polynomial expansion; a discussion of the latter method is given.
Macrocausal aspects of the S matrix related to the LSZ asymptotic condition
Authors: Doebner H. D. , Lücke W.
Published: March 2003

By use of the LSZ asymptotic condition in Hepp’s form it is shown that one may substitute functions s (x), which converge sufficiently rapidly to 1 in positive timelike direction, for the step function ϑ (x0) in the usual LSZ reduction formulas. This result, partly related to earlier work by Toll, does not depend on microcausality of the interpolating field. Choosing s (x) such that s (x) =0 outside the forward lightcone, a complete reduction to vacuum expectation values of T products of the interpolating field thus shows that it is sufficient to know the n-point Wightman distributions at pairwise timelike arguments x1,...,xn in order to calculate the S matrix completely. It is argued that this fact indicates some macrocausal property of the S matrix introduced by the LSZ asymptotic condition.
A multiple-scales space–time analysis of a randomly perturbed one-dimensional wave equation
Authors: Kohler Werner E.
Published: March 2003

An initial value problem for one-dimensional wave propagation is considered; the medium is assumed to be randomly perturbed as a function of both space and time. The stochastic perturbation theory of Papanicolaou and Keller [SIAM J. Appl. Math. 21, 287 (1971)] is applied directly in the space–time regime to derive transport equations for the first and second moments of the solution. These equations are solved in special cases.
Scalar meson fields in a conformally flat space
Authors: Ray Dipankar
Published: March 2003

Scalar meson fields are studied for the conformally flat metric e+ψ(dx12+dx22+dx32 −dx42). Complete sets of solutions of the field equations have been obtained for massless mesons, and the field equations have been reduced to a single ordinary differential equation in ψ for massive mesons. In either case ψ is found to be a function of x12+x22+x32−x42 or c1x1+c2x2+c3x3+c4x4 (c1,c2,c3,c4 being constants), and φ the meson field is found to be constant or a function of ψ.
Invariants and wavefunctions for some time-dependent harmonic oscillator-type Hamiltonians
Authors: Leach P. G. L.
Published: March 2003

Recently the author has shown that the Hamiltonian, H= (1/2) ωT A (t) ω+B (t)Tω+C (t), in which A (t) is a positive definite symmetric matrix and ωμ=qi, μ=1,n, i=1,n, ωμ=pi, μ=n+1,2n, i=1,n, may be transformed to the time-independent Hamiltonian, H̄= (1/2) ω̄Tω̄, by a time-dependent linear canonical transformation, ω̄=Sω+r. H̄ is an exact invariant of the motion described by H. A matrix invariant may also be constructed which provides a basis for the generators of the dynamical symmetry group SU(n) which may always be associated with H, usually as a noninvariance group. In this paper we examine, by way of example, an oscillator with source undergoing translation, the two-dimensional anisotropic oscillator, general one- and two-dimensional oscillators with Hamiltonians of homogeneous quadratic form and obtain explicit invariants and Schrödinger wavefunctions with the aid of the linear canonical transformations.
A noninvariance group for the n-dimensional isotropic harmonic oscillator
Authors: Major M. E.
Published: March 2003

A semidirect product of the Weyl group N, with the special unitary group SU(n), is proved to be a possible noninvariance group for the n-dimensional isotropic harmonic oscillator. In order to obtain this result, a method is developed for finding the representation W of SU(n) which intertwines the representations UNv and (A+iB) UNv of N [where A+iBεSU(n)]; it is also shown that W=⊕∞a=0Wa, where Wa is an irreducible representation of SU(n), of dimension equal to the degeneracy of the (a+1)th energy level of the n-dimensional isotropic harmonic oscillator.
Neutron transport in plane geometry with general anisotropic, energy-dependent scattering
Authors: Gibbs Alan G. , Larsen Edward W.
Published: March 2003

We consider the neutron transport equation in plane geometry with a general energy-dependent anisotropic scattering kernel. We construct the solution of the subcritical half-space albedo problem as a contour integral around the positive half of the spectrum of a reduced transport operator K. The integrand involves the boundary data and two operators which provide the Wiener–Hopf factorization of a third operator contained in (λI−K)−1. Bounds are obtained for the location of the spectrum of K in the complex plane. We also obtain representations of the solutions of the Milne problem and of the full-space and half-space problems with sources. Various simplifications of the general theory, which occur for particular scattering models, are discussed as an illustration of the results.
Uniformly valid solutions to Volterra intergal equations
Authors: Ling Rina
Published: March 2003

Volterra equations on the infinite interval with the kernel multiplied by a small parameter are studied. An approximate solution is obtained and proved to be uniformly valid for all time as the parameter tends to zero. The equation is a generalization of the model for the transport of charged particles in a random magnetic field.
Some remarks on the Wronskian technique and the inverse scattering transform
Authors: Case K. M. , Chiu S. C.
Published: March 2003

A connection between the Wronskian technique of Calogero and Degasperis and the Lax theorem is made by finding the time evolution of the eigenfunctions of the linear operator for the inverse scattering transform of the isospectral flow equations. The significance of the temporal half of the Bäcklund transformations is discussed via specific examples. An explicit proof of the permutability theorem of the Bäcklund transformation for the case r=−q is given. New Wronskian identities with respect to bound-state constants, which hold for all potentials allowable in the inverse scattering transform, are found.
Induced projective representations
Authors: Dirl R.
Published: March 2003

The left- (right-) regular projective representation of a finite group G and the corresponding ’’projective’’ representation of the left-group algebra are defined for a given standard factor system, and special features of these constructions are discussed. Starting from a given projective unitary irreducible representation of a normal (but not necessarily Abelian) subgroup N of G, we obtain by induction the matrix elements of the projective unitary irreducible representations of G, where the corresponding group algebra is used as aid. These considerations are of interest for the construction of projective unitary irreducible representations of little cogroups of nonsymmorphic space groups. For the present method allows us to construct, for a q lying on the ’’surface’’ of the Brillouin zone, these projective representations out from unitary irreducible representations belonging to q’s of ’’lower’’ symmetry. This method is used to determine for all little cogroups of the nonsymmorphic space group Pn3n complete sets of projective unitary irreducible representations.
Generators of infinite direct products of unitary groups
Authors: Kraus K. , Polley L. , Reents G.
Published: March 2003

Under suitable conditions, an infinite direct product ⊗nUn(t) of continuous unitary one-parameter groups Un(t) is again a continuous unitary one-parameter group. This question is discussed here in terms of the generators An of Un(t). It is shown that the generator A of ⊗nUn(t) has a total set of product vectors in its domain of definition. As examples, the particle number, energy–momentum, and angular momentum operators in non-Fock direct product representations of free fields are investigated. The spectra of these operators are determined.
Free particle systems and their dynamics in de Sitter space
Authors: Fabec Raymond C.
Published: March 2003

A first step in determining all the global projective unitary representations describing free particle systems in imaginary Lobachevsky space is made. Essentially we determine explicitly the global form of any representation describing a free particle of spin j on the group generated by rotations and translations of space–time at time t and time translations. We also discuss whether or not positional observables should be preserved under physical equivalence and determine the effects this has on the representation theory of free particle systems.
A tachyon dust universe
Authors: Srivastava Sushil K.
Published: March 2003

In the present paper some investigations have been made on the model suggested by Ray for a tachyon dust universe and the results obtained have been compared with the results in the flat Friedmann universe filled with ordinary dust (here called bradyon dust) moving slower than light, by various scientists, on the ground that the role played by time for ordinary matter is played by spatial coordinates for tachyons. The effect of the cosmological constant (Λ) on the expanding tachyon universe also has been discussed here. The tetrad technique has been used as a mathematical tool for handling the problems of gravitational field equations and perturbation of momentum flux.
On notions of Markov property
Authors: Ekhaguere G. O. S.
Published: March 2003

We exhibit the logical connection between two mathematically and physically interesting notions of Markov property due to Nelson [J. Funct. Anal. 12, 97 (1973)] and to Wong [Ann. Math. Stat. 40, 1625 (1969)], respectively, in the case of Gaussian generalized stochastic fields.
Global structure of the ’’Kantowski–Sachs’’ cosmological models
Authors: Collins C. B.
Published: March 2003

A discussion is given of the ’’Kantowski–Sachs’’ cosmological models; these are defined locally as admitting a four-parameter continuous isometry group which acts on spacelike hypersurfaces, and which possesses a three-parameter subgroup whose orbits are 2-surfaces of constant curvature (i.e., the models possess spherical symmetry, combined with a translational symmetry, and can thus be regarded as nonempty analogs of part of the extended Schwarzschild manifold). It is shown that all general relativistic models in which the matter content is a perfect fluid satisfying reasonable energy conditions are geodesically incomplete, both to the past and to the future, and that at each resulting singularity the fluid energy density is infinite. In the case where the fluid obeys a barotropic equation of state (which includes all known exact perfect fluid solutions) the field equations are shown to decouple to form a plane autonomous subsystem. This subsystem is examined using qualitative (Poincaré–Bendixson) theory, and phase–plane diagrams are drawn depicting the behavior of the fluid’s energy density and shear anisotropy in the course of the models’ evolution. Further diagrams depict the conformal structure of these universes, and a table summarizes the asymptotic properties of all physically relevant variables.
Magnetic monopoles in SU(4) gauge theories
Authors: Brihaye Y. , Nuyts J.
Published: March 2003

All spherically symmetric magnetic poles are explictly constructed in SU(4). We show the relevance of the concept of the little group which transforms spherically symmetric solutions among themselves. Unlike the SU(2) and SU(3) situation this little group is not always Abelian in SU(4). On the other hand, it is shown that while the total strength of the pole is always quantized its projection along the Higgs field is sometimes arbitrary. This is also in contrast with the SU(2) and SU(3) cases.
Stationary gravitational fields of a charged perfect fluid
Authors: Kloster S. , Das A.
Published: March 2003

Einstein’s field equations which include electromagnetism are investigated when the metric admits a timelike Killing motion and the source is a charged perfect fluid under isometric motion. It is shown that the pressure must necessarily be a function of the electrostatic and gravitational potentials. A class of solutions is found under the following simplifying assumptions: (i) The pressure is a constant, (ii) the Lorentz force vanishes, and (iii) the magnetic and twist potentials are functionally related. In this class the ratio of σ/(ρ+3p) is a constant and this resembles an equilibrium condition. Finally a four-parameter group (maximal) is supplied which can generate new solutions of this class.
Lee model with 3V particles
Authors: Raju Cvavb. Chandra
Published: March 2003

The 3V-particle Lee model is proposed. The NΘ scattering amplitude, the VΘ scattering amplitude and the nΘΘ production amplitude are evaluated. The integral equation in the VΘ sector is solved. The usual deductive method cannot be applied here to solve the integral equation of the VΘ sector. A nondeductive method is applied to solve the integral equation. The solution obtained correctly reduces to the solution of the VΘ integral equation of the ordinary Lee model, whenever any two bare interaction constants in the Hamiltonian are switched off. The two resonances that appear in the NΘ sector, again appear in the VΘ sector at the same energies.
Discrete path approach to linear recursion relations
Authors: Antippa Adel F.
Published: March 2003

It is shown that the solutions of linear homogeneous recursion relations, with arbitrarily specified boundary conditions, are related, by a mapping, to the totality of discrete paths joining the two ends of an interval and made up of a predetermined set of directed segments. We study the dependence of these solutions on the way the boundary conditions are specified. When the boundary conditions are given as initial conditions, the present approach reduces to the formalism already developed for that specific case, and which is based on the partitions of an interval into classes.
Translation kernels for velocity dependent interactions
Authors: Coz M. , Rochus P.
Published: March 2003

We reconsider first the representation of solutions defined by a condition at the origin and recognize the difficulty of extending the representation outside simple cases. By eliminating the study of solutions defined at the origin in further studies the translation kernels for velocity dependent interactions are constructed only for solutions defined by their behavior at infinity. Two methods are proposed: They are shown to be equivalent in physical cases and to extend to these physical situations.
On the properties of collision probability integrals in annular geometry. I. Analysis
Authors: Milgram Michael S.
Published: March 2003

Two integrals fundamental to the analysis of the integral transport equation in infinitely long, annular geometry are defined and represented as sums of Meijer’s G-function. Transformations useful for thick or thin annuli are derived, limiting forms for voided annuli are recorded, and asymptotic series are investigated. Special results include the identification of probability integrals for infinite cylinders and generalized, associated Bickley-Nayler functions as G-functions with appropriate parameters and variables. The incomplete, generalized, associated Bickley-Nayler functions are defined for annuli of finite length, and represented as sums of G-functions for long and short annuli. Asymptotic forms are given for both integrals, one of which reduces to Sievert’s integral. Some illustrative examples important for numerical analysis, evaluation of multiple integrals, summation of series, and the study of the transport equation are reported.
Coherent scalar field in pair-correlated random distributions of aligned scatterers
Authors: Twersky Victor
Published: March 2003

Dispersion equations for coherent propagation of scalar waves in random distributions of pair-correlated obstacles (aligned or averaged over alignment), are obtained by averaging the functional equations relating the multiple and single scattered amplitudes of the obstacles. The resulting bulk indices of refraction and bulk parameters, for aligned nonradially symmetric scatterers, specify anisotropic media; the anisotropy arises either from the scatterers’ properties (physical parameters or shape, or both) or from their distribution, or from both. The illustrations include both isotropic and anisotropic cases (in one to three dimensions), and the explicit results generalize earlier ones.
Operator density current and relativistic localization problem
Authors: Jancewicz Bernard
Published: March 2003

The well-known difficulties with the relativistic localization in quantum theory of one particle are revisited. Among them the noncausal propagation is shown to be connected with the positivity of the time translations generator. A proposal for solving this problem is presented, namely searching for an operator probability density current being the 4-vector quantity. The operator of multiplication by the argument of the Dirac wavefunction is an example of a causal position operator.
An application of the nonstandard Trotter product formula
Authors: Sloan Alan
Published: March 2003

The nonstandard Trotter product formula is used to extend the Feynman integral interpretation of solutions to the Schrödinger equation in the presence of a highly singular potential.
On the Kerr–Tomimatsu–Sato family of spinning mass solutions
Authors: Yamazaki Masatoshi
Published: March 2003

Some analytic properties of the Kerr–Tomimatsu–Sato family of solutions with arbitrary integer deformation parameter δ for gravitational fields of spinning masses are studied. It is shown that all ring singularities are of first order and all ergosurfaces are simple zeros of metric functions A.
On an exceptional case concerning plasma oscillations
Authors: Siewert C. E.
Published: March 2003

The method of elementary solutions is used to analyze the situation in plasma oscillations when there exists a real discrete eigenvalue.
On the separation of Einsteinian substructures
Authors: Plebański Jerzy F.
Published: March 2003

Within the spinorial version of the Cartan structure formulas with the built-in (complex) Einstein vacuum equations some closed semi-Einsteinian substructures are isolated and discussed. Then the idea of semigraviton is introduced, and its relationship to Penrose’s nonlinear graviton is described.
Some solutions of stationary, axially-symmetric gravitational field equations
Authors: Gürses Metin
Published: March 2003

Stationary, axially-symmetric solutions of the gravitational field equations for vacuum, perfect fluid, and massless scalar field are considered. For the vacuum case, a similiar formulation to the one introduced by Ernst is presented by use of quarternions. Null dust solutions are found, and it is shown that they match with the van Stockum exterior solutions. An extension of the theorem by Eriş and Gürses is given which enables one to construct solutions to the gravitational field equations coupled with a charged dust and a massless scalar field from the solutions of the field equations coupled only with a charged dust.
Universal singular functions in local field theory
Authors: Wu Alfred C. T.
Published: March 2003

The singularity structure of the universal singular functions in local field theory is simply seen by the stationary-phase method applied to the Lorentz group manifold.
Convergence acceleration technique for lattice sums arising in electronic-structure studies of crystalline solids
Authors: Harris Frank E.
Published: March 2003

Slowly convergent lattice summations arise when ab initio quantum-mechanical studies of electronic structure in crystalline solids are carried out by Fourier representation methods. Summations of this type are identified and discussed, and it is shown how a technique related to, but not identical with, that of Ewald can be used to accelerate their convergence. The presentation is illustrated with numerical examples.
Casimir invariants and vector operators in simple and classical Lie algebras
Authors: Okubo Susumu
Published: March 2003

A method of computing eigenvalues of certain types of Casimir invariants has been developed for simple and classical Lie algebras. Especially these eigenvalues for algebras An, Bn, Cn, Dn, and G2 have been computed in closed terms. We also enumerate numbers and functional forms of all linearly independent vector operators in terms of generators in any irreducible representation of these algebras. Some polynomial identities among infinitesimal generators of these algebras are derived by means of the same technique.
A new class of superalgebras and local gauge groups in superspace
Authors: Mansouri Freydoon
Published: March 2003

It is shown that there is a new class of superalgebras associated with a given Lie algebra or a superalgebra. The structure constants of the new algebras either vanish or else are directly related to those of the original algebra. The new algebraic structures provide a possible link between the local gauge groups constructed over superspace and those over ordinary space–time.
The diffraction of sound pulses by a circular cylinder
Authors: Chen Pocheng , Pao Yih−Hsing
Published: March 2003

The diffraction of pulses in acoustic medium (scalar waves) by a circular cylinder is analyzed by applying the Cagniard method. Solutions for the incident, reflected, diffracted, and creeping pulses in the illuminated and shadow zones are all obtained by a unified approach. Numerical results are shown for the forward, backward, and side scattering of an incident pulse with a step or square time function.
Regularization of the Roy equations with a smooth cutoff
Authors: Atkinson D. , Pool T. P. , Slim H. A.
Published: March 2003

The Roy equations for ππ scattering are combined with unitarity to give a nonlinear system of equations for the determination of the low-energy amplitudes. A Hölder continuous interpolation between the input high-energy absorptive parts and the output low-energy absorptive parts is implemented; and the resultant singular equations are regularized by means of an effective inelastic N/D method. If the scattering lengths, the CDD parameters, and the high-energy absorptive parts satisfy certain constraints, then there exists a locally unique solution of the system.
Massless quantum sine–Gordon equation in two space–time dimensions: Correlation inequalities and infinite volume limit
Authors: Park Yong Moon
Published: March 2003

We prove new correlation inequalities for the massive and massless quantum sine–Gordon equations. These results are then used to construct infinite volume limit theory for the massless (S–G)2 model that satisfies the Osterwalder–Schrader axioms. As consequences, infinite volume limit theories for the classical, neutral, statistical mechanical systems with two-body Coulomb potentials and for the massive Thirring model exist.
Time dependent canonical transformations and the symmetry-equals-invariant theorem
Authors: Cary John R.
Published: March 2003

Expressions for the remainder function of a time dependent infinitesimally generated canonical transformation have recently been found by Dewar, who considered the action of the transformation operators on Liouville’s equation. Here an alternate proof of the remainder function expression is given, based on the transformations of particle trajectories. Then, using this expression, a proof of the symmetry-equals-invariant theorem is given.
Neutron slowing down and transport in a medium of constant cross section. I. Spatial moments
Authors: Cacuci Dan G. , Goldstein Herbert
Published: March 2003

Some aspects of the problem of neutron slowing down and transport have been investigated in an infinite medium consisting of a single nuclide scattering elastically and isotropically without absorption and with energy-independent cross sections. The method of singular eigenfunctions has been applied to the Boltzmann equation governing the Laplace transform (with respect to the lethargy variable) of the neutron flux. Formulas have been obtained for the lethargy dependent spatial moments of the scalar flux applicable in the limit of large lethargy. In deriving these formulas, use has been made of the well-known connection between the spatial moments of the Laplace-transformed scalar flux and the moments of the flux in the ’’eigenvalue space.’’ The calculations have been greatly aided by the construction of a closed general expression for these ’’eigenvalue space’’ moments. Extensive use has also been made of the methods of combinatorial analysis and of computer evaluation, via FORMAC, of complicated sequences of manipulations. It has been possible to obtain for materials of any atomic weight explicit corrections to the age theory formulas for the spatial moments M2n(u), of the scalar flux, valid through terms of order of u−5. Higher order correction terms could be obtained at the expense of additional computer time. The evaluation of the coefficients of the powers of n, as explicit functions of the nuclear mass, represent the end product of this investigation.
Finite and infinite measurement sequences in quantum mechanics and randomness: The Everett interpretation
Authors: Benioff Paul A.
Published: March 2003

The quantum mechanical description of both a finite and infinite number of measurement repetitions, as interactions between copies of an object system and a record system, are considered here. States describing the asymptotic situation of an infinite number of repetitions are seen to have some interesting properties. The main construction of the paper is the association of states to sequential tests for randomness. To each such test T and each positive integer m one can associate states ΘnTm and Θ∞Tm corresponding respectively to those length-n and finite outcome sequences which pass test T at the significance level 2−m. Following the methods of Martin Löf, a universal sequential test V, which includes an infinity of sequential statistical tests for randomness, is given and the corresponding states ΘnVm and Θ∞Vm are discussed. Finally, a possible use of these states in the Everett interpretation of quantum mechanics is discussed.
Causal solutions of nonlinear wave and spinor equations obtained by Gel’fand–Shilov regularization
Authors: Baumgarten D. , Braunss G. , Wagner O.
Published: March 2003

By extending the Gel’fand–Shilov regularization method to products of locally integrable functions it can be shown that the nonlinear Klein–Gordon equations ∂2u/∂t2−∂2u/∂x21− ⋅⋅⋅ −∂2/∂x2n +ku2p+1=0, where k=const≳0, n⩾3, p=integer⩾1, have causal solutions which have no δ singularities. It is further shown that this also can be expected for the nonlinear Dirac equation γλ∂ψ/∂xλ+l2ψ (⩾ψ) =0.
Conservative neutron transport theory
Authors: Bowden R. L. , Cameron W. L. , Zweifel P. F.
Published: March 2003

A functional analytic development of the Case full-range and half-range expansions for the neutron transport equation for a conservative medium is presented. A technique suggested by Larsen is used to overcome the difficulties presented by the noninvertibility of the transport operator K−1 on its range. The method applied has considerable advantages over other approaches and is applicable to a class of abstract integro–differential equations.
Prolongation structures and nonlinear evolution equations in two spatial dimensions. II. A generalized nonlinear Schrödinger equation
Authors: Morris H. C.
Published: March 2003

The prolongation structure approach of Wahlquist and Estabrook is used to determine an inverse scattering formulation for a generalization of the nonlinear Schrödinger equation to two spatial dimensions.
Axisymmetric stationary Brans–Dicke vacuum fields
Authors: Nayak B. K. , Tiwari R. N.
Published: March 2003

It is shown that the axisymmetric stationary Brans–Dicke vacuum solutions can be obtained from the solutions of the axisymmetric stationary Einstein vacuum fields and also the axisymmetric static Brans–Dicke vacuum fields.
Exact diagonalization of relativistic Hamiltonians including a constant magnetic field
Authors: Weaver D. L.
Published: March 2003

It is shown how to exactly diagonalize the Dirac and Sakata–Taketani Hamiltonians, including the effect of a constant, external magnetic field, using a unitary transformation. In the latter case, the magnetic moment coupling must be of the Yang–Mills type in order to perform the transformation.
On the definition of scattering subspaces in nonrelativistic quantum mechanics
Authors: Dollard John D.
Published: March 2003

A physically motivated definition of scattering subspaces is given for problems in nonrelativistic quantum mechanics. The definition is more stringent than earlier similar definitions. It is applicable to potential scattering and to n-body problems.
A new family of solutions of the Einstein field equations
Authors: Ernst Frederick J.
Published: March 2003

An ordinary differential equation is presented, from solutions of which may be constructed solutions of the Einstein field equations. The study of these solutions may shed light upon the still obscure systematics of the Tomimatsu–Sato spinning mass fields.
The Killing form for graded Lie algebras
Authors: Backhouse Nigel B.
Published: March 2003

A Killing form with nice symmetry and invariance properties is constructed for an arbitrary graded Lie algebra. When this form is nondegenerate, Casimir operators can be constructed, and the graded Lie algebra possesses properties analogous to those possessed by semisimple ordinary Lie algebras.
Closure in anisotropic cosmological models
Authors: Galloway Gregory J.
Published: March 2003

The closure result of Friedmann cosmology is briefly reviewed. A new closure result is presented for nonrotating, dust filled, but otherwise anisotropic, inhomogeneous cosmological models. The isotropy assumptions are replaced by much milder physical assumptions while the crucial Friedmann condition, 8πκρ−3h2≳0, is replaced by the only slightly stronger 4πκρ−3h2≳0.
Higher spin states in the stochastic mechanics of the Bopp–Haag spin model
Authors: Dankel Thad
Published: March 2003

The author has previously shown that the dynamically natural random variable representing angular momentum in the stochastic mechanics of the Bopp–Haag spin model has the expectation values predicted by quantum mechanics for spin=1/2. The result is generalized to all higher values of the spin.
Spin-frame independent variables in general relativity
Authors: Wódkiewicz K.
Published: March 2003

The purpose of this paper is to present the spin-frame independent variables in general relativity. The work is based on the fact that the tetrad Newman–Penrose form of Einstein’s equations can be put into the Yang–Mills form with the group SL(2,C) as the gauge group. The set of Mandelstam path-dependent dynamical variables for such a theory forms spin-frame independent variables in general relativity. The empty-space field equations for spin-frame independent variables have formally the same form as Maxwell’s equations. In addition, the full set of field equations for spin-frame independent variables have formally the same form as the equations of nonlinear electrodynamics.
Global operator product expansions for free fields of arbitrary mass m⩾0
Authors: Völkel A. H.
Published: March 2003

A set (more than countably many) of global operator expansions—’’on and off the vacuum’’—are proved to hold for free fields of any mass m⩾0. Conformal invariance (m=0) singles out exactly one of them in the case of the ’’vacuum expansion.’’ There does not exist any termwise conformal covariant expansion ’’off the vacuum.’’
Convergence of lattice approximations and infinite volume limit in the (λφ4−σφ2−μφ)3 field theory
Authors: Park Yong Moon
Published: March 2003

By unified method we prove the convergence of the lattice approximation of the (λφ4−σφ2−ψφ)3 field model with periodic, Dirichlet and Neumann boundary conditions in a finite box. This then allows us to take the inifinite volume limit of the Dirichlet states by the Nelson’s monotonicity argument. The model under consideration satisfies all the Wightman axioms except possibly the uniqueness of vacuum for μ=0 and the mass gap.
Equilibrium properties of fluids in the semiclassical limit
Authors: Sinha S. K. , Singh Y.
Published: March 2003

The problem of calculating the equilibrium properties of dense fluids in the semiclassical limit when the quantum effects are small is studied. Expressions are given for the pressure, free energy, and the radial distribution function in terms of the properties and correlation functions of the classical system and s-body ’’modified’’ Mayer functions fs1,2,...,s. It is shown that the correct radial distribution function of a fluid in the semiclassical limit is generated from the classical radial distribution function if we replace in turn each f0 bond (f012=e−βφ(1,2)−1) by an effective feff bond, wherefeff=f0+(1+f0) fII +(1+f0)(1+fII) ℒ and where L is subset of the line-irreducible graphs each of which contain one fIII bond. The effective pair bond correct to the second order in thermal wavelength λ (={2πh/2β/m}1/2) for a fluid of hard spheres is calculated for λ/d=0.1, and 0.2 at reduced densities ρ=0.3 and 0.6. The most striking effect of the quantum mechanics on the structure of a hard-sphere fluid is found at and near the point of contact of the hard spheres.
The lattice of verifiable propositions of the spin-1 system
Authors: Hultgren Bror O. , Shimony Abner
Published: March 2003

A lattice of verifiable propositions LV for a spin-1 system is constructed by admitting only propositions which correspond to appropriate Stern–Gerlach filters. LV is a complete, orthocomplemented, weakly modular lattice, and it satisfies the first part of the atomicity axiom of Jauch and Piron, but not the second part (the covering law) nor related axioms of Zierler and MacLaren. Doubt is therefore thrown upon the program of recovering the Hilbert space formulation of quantum mechanics from empirically justified axioms. The class of admissible states on LV is exhaustively characterized, and it is shown that there exist some nonquantal states but none that are dispersion free.
Ordering of the exponential of a quadratic in boson operators. II. Multimode case
Authors: Agrawal G. P. , Mehta C. L.
Published: March 2003

We derive the Weyl, the normal, and the antinormal ordered forms of the exponential of a multimode quadratic expression in boson operators. The trace of this exponential operator is also evaluated.
Unitary analytic representations of SL(3,R)
Authors: Güler Y.
Published: March 2003

Unitary, analytic representations of SL(3,R) are studied by operator formalism. It is found that SL(3,R) has two different principal series of representations. Analytic representations are labeled by an integer n and a real number a. The Hilbert space of analytic functions f (z,x) is constructed, and an invariant scalar product is formed.
Evolution of isometries in the Bondi formalism
Authors: Berezdivin R. , Herrera L.
Published: March 2003

It is shown that if an additional symmetry, assumed part of the BMS group, is imposed in the Bondi formalism at one retarded time, and if gravitational radiation is absent, then the symmetry will evolve to fill the region of space–time where the Bondi metric is nonsingular. Furthermore, that region will admit a static Weyl metric. There is no necessary evolution if there is radiation present. The evolution of vector field which are nearly isometric is then examined: These evolve as small perturbations off a Weyl metric. A simple and nonlinear but approximate energy formula is written in terms of a quadrupole moment.
Time-dependent dynamical symmetry mappings and associated constants of motion for classical particle systems. II
Authors: Katzin Gerald H. , Levine Jack , Sane Robert N.
Published: March 2003

This paper is a continuation of a previous paper with a similar title [J. Math. Phys. 17, 1345 (1976)]. In this paper we develop further properties of time-dependent symmetries of dynamical systems expressible in the form (a) Ei(χ̈,χ̇,x,t) ≡ Ei(χ̈1,...,χ̈n; χ̇1,...,χ̇n; x1,...,xn;t) = 0. Such dynamical symmetries are based upon infinitesimal transformations of the form (b) χ̄i=xi +δxi, δxi≡ξi(x,t) δa, (c) t̄=t +δt, δt≡ξ0(x,t) δa, which satisfy the condition (d) δEi=0 whenever Ej=0. It is shown that if (ξiA, ξ0A), A=1,...,ρ, is a complete set of solutions of the symmetry equations as determined by (d), then these solutions generate a ρ-parameter complete group of symmetry mappings, and the group structure implies linear dependency relations between first and second derived time-dependent constants of motion as obtained by a related integral theorem. The complete groups of time-dependent symmetry mappings are obtained for all conservative systems (n≳1) with spherically symmetric potentials. These groups are classified into six types according to the associated form of the potential. A similar analysis leads to three types of Noether symmetries. In the case where (a) takes the form (e) Ei(χ̈,χ̇,x) =0, it is shown that if (ξi, ξ0) defines a symmetry mapping then in general (∂Kξi/∂tK, ∂Kξo/∂tK), K=1,2,..., will also define symmetry mappings; similar properties are shown for Noether symmetries. These results when applied to a large class of time-dependent constant of motion defined in terms of (ξi, ξ0) lead to further contants of motion.
Meta universe
Authors: Srivastava Sushil K. , Pathak Mahendra P.
Published: March 2003

Foster and Ray have pointed out that since tachyons are particles having energy and momentum, they should hence contribute to the gravitational field through the energy–momentum tensor. Following them, a spacelike metric for the tachyon dust model has been proposed, and the problem of condensation of tachyons, after a slight perturbation of the model, has been examined. The tetrad technique has been frequently used for the purpose.
The singular coupling and weak coupling limits
Authors: Palmer P. F.
Published: March 2003

We show that the analysis of the motion of a system coupled to an infinite reservoir in the singular coupling limit and the weak coupling limit can be performed in the same mathematical framework. This enables us to clarify the way in which the motion of the system in the singular coupling limit depends on the temperature of the reservoir.
Soliton solutions and the higher order Korteweg–de Vries equations
Authors: Morris H. C.
Published: March 2003

A prolongation structure is determined for a single equation from which the Korteweg–de Vries and all of its higher order forms can be derived. As result, inverse scattering problems for all of the equations are determined simultaneously.
Collineations and motions in self-gravitating magnetofluids
Authors: Asgekar G. G. , Date T. H.
Published: March 2003

For the self-gravitating magnetofluid admitting a Ricci collineation with respect to the flow vector, it is proved that (i) the stream lines are expansion-free if and only if the heat-flux vector is divergence-free; (ii) the stream lines are geodesic if and only if the heat-flux vector remains invariant along the system of stream lines. The affine collineation with respect to the geodesic and expansion-free flow of the magnetofluid is a motion. Conformal motions with respect to the flow vector, the magnetic field vector, and the heat flux vector are investigated.
Note on the representation spaces of O(2,1)
Authors: Basu Debabrata
Published: March 2003

We use Gel’fand’s theory of invariant bilinear functionals to study a class of realizations of the representation spaces of O(2,1). We construct suitable Hermitian, invariant bilinear forms for the principal and supplementary series of representations. For the principal series the construction yields essentially the Bargmann realization of the Hilbert space while for the supplementary series we obtain other realizations in addition to the Bargmann space with nonlocal metric.
Eigenvalue problem for Lagrangian systems. VIII. Eigenvalue bounds with application to fluid and plasma flows
Authors: Barston E. M.
Published: March 2003

Circle theorems are obtained which furnish bounds for the complex eigenvalues arising from the linear stability analysis of states of steady motion of conservative dynamical systems. These results generalize the well-known circle theorems of Howard, Eckart, and others for fluid flows to arbitrary gyroscopic Lagrangian systems. Explicit bounds are obtained for the plane parallel flows of an inviscid fluid and a multicomponent plasma. YAG
Discrete spectrum for a system of electrically charged particles
Authors: Demiralp Metin , Şuhubi Erdoğan
Published: March 2003

For a system of electrically charged particles, the time-independent Schrödinger’s equation is transformed into hyperspherical coordinates. By using the hyperharmonic expansion, the hyperradial equation is obtained, and its discrete spectrum is investigated. To this end, only negative energy values are taken into consideration. The functional equation which yields the discrete spectrum of the hyperradial equation is obtained by means of a matching technique in the Laplace transform domain of hyperradial Schrödinger’s equation.
On the semiclassical expansion in quantum mechanics for arbitrary Hamiltonians
Authors: Mizrahi Maurice M.
Published: March 2003

It is shown that if the quantum-mechanical propagator, satisfying the n-dimensional Schrödinger equation (H−ih/∂/∂tb) 〈qb,tb‖qa,ta〉 =0, with 〈qb,tb‖qa,tb〉 =δ (qb−qa) and arbitrary classical Hamiltonian Hc, admits a semiclassical (WKB) approximation, then the latter is of the form KWKB=const ×h/−n/2 (detM)1/2 exp(iSc/h/), where Sc is the classical action, Mij≡−∂2Sc/∂qai∂qbj, and K−1WKB(H−ih/∂/∂tb) KWKB =O (h/2). The restrictions on the correspondence rule chosen to pass from Hc to the operator H are spelled out in detail, and it is found that one has a considerable amount of leeway in choosing such a rule. Differential equations for higher-order corrections can be generated at will. This generalizes previously known partial results to arbitrary Hamiltonians. The arbitrariness of the Hamiltonian makes the method useful as a general tool in the theory of partial differential equations.
Bernoulli sequences and trajectories in the anisotropic Kepler problem
Authors: Gutzwiller Martin C.
Published: March 2003

The anisotropic Kepler problem is investigated in order to establish the one-to-one relation between its trajectories and the binary Bernoulli sequences. The Hamiltonian has a quadratic kinetic energy with an anisotropic mass tensor and a spherically symmetric Coulomb energy. Only trajectories in two dimensions with a negative energy (bound states) are discussed. The previous study of this system was based on extensive numerical computations, but the present work uses only analytical arguments. After a review of the earlier results, their relevance to the understanding of the relation between classical and quantum mechanics is emphasized. The main new result is to show the existence of at least one trajectory corresponding to each binary Bernoulli sequence. The proof employs a number of unusual mathematical tools, although they are all elementary. In particular, the virial as a function of the momenta (rather than the action as a function of the position coordinates) plays a crucial role. Also, different kinds of limiting trajectories, mostly involving a collision with the center of the Coulomb attraction are treated in some detail.
Further applications of harmonic mappings of Riemannian manifolds to gravitational fields
Authors: Eriş Ahmet
Published: March 2003

We consider static, spherically-symmetric and stationary, axially-symmetric gravitational fields in the framework of harmonic mappings of Riemannian manifolds. In this approach the emphasis is on a correspondence between the solution of the Einstein field equations and the geodesics in an appropriate Riemannian configuration space. Using Hamilton–Jacobi techniques, we obtain the geodesics and construct the resulting space–time geometries. For static space–times with spherical symmetry we obtain the well-known solutions of Schwarzschild, Reissner–Nordström, and Janis–Newman–Winicour, where in the latter two cases the source for the geometry is the static, source-free Maxwell field and the massless scalar field respectively. When we consider the source to be a triad of massless scalar fields with the internal symmetry SU(2) × SU(2), we find that the space–time geometry is once again that of Janis–Newman–Winicour. Finally we formulate the stationary, axisymmetric gravitational field problem in terms of composite mappings and obtain the Weyl, Papapetrou, and the generalized Lewis and van Stockum classes of axisymmetric solutions.
Linearization stability of the Einstein–Maxwell system
Authors: Arms Judith M.
Published: March 2003

We obtain conditions on a compact Cauchy surface sufficient to insure linearization stability of the coupled Einstein–Maxwell equations, and identify these conditions with the absence of globally defined infinitesimal symmetries of the fields. The appropriate domain for these symmetries is a circle bundle over spacetime. The vector potential of the electromagnetic field is identified with the connection on the bundle.
Multiquark models and the embedding of groups
Authors: Gruber B. , Santhanam T. S.
Published: March 2003

Recent experimental results have clearly indicated that the usual quark model must be extended. Several multiquark models are already under consideration. In this paper a classification of all possible symmetry chains (group extensions) is given for the embedding of the group SU(3) in semisimple Lie groups for the case that the basic quark fields transform with respect to SU(3) either as (3+3*), (3+3), (3+3*+1) or (3+3+1).
Periods on manifolds, quantization, and gauge
Authors: Kiehn R. M.
Published: March 2003

It is suggested that the quantization of flux, charge, and angular momentum be interpreted as a set of independent natural concepts which physically exhibit certain topological properties of the fields on a space–time manifold. These quantum, or topological, properties may be described in terms of one-, two-, and three-dimensional periods, respectively. In terms of this viewpoint, topological constraints between the one-, two-, and three-dimensional periods can be put into correspondence with various gauge theories. If a dynamical system is to be nondissipative, in the sense that its one-, two-, and three-dimensional topological periods are reversible invariants of the motion, then it is proved herein that the dynamical field V must be a Hamiltonian vector field, the field currents must be proportional to V, and the Lagrangian difference between the elastic and inertial energy density must be twice the interaction energy density, respectively.