bluuebunny/crossref_metadata_2025 huggingface dataset:
Generalized static electromagnetic fields in Brans–Dicke theory
Authors: Singh T. , Rai L. N.
Published: March 2003

A general class of static, axially symmetric solutions of the Brans–Dicke–Maxwell equations is obtained under the assumption −r2⋅grr=gtt⋅gφφ⋅gzz These solutions have been subjected to conformal transformation and they are found to be new solutions of the static, axially symmetric Einstein–Maxwell–scalar fields. We have also developed a more general set of solutions under the unit transformations given by Morganstern.
Representation groups for semiunitary projective representations of finite groups
Authors: Cariñena José F. , Santander Mariano
Published: March 2003

Given a finite group G and a subgroup K of index 1 or 2, a method is developed for finding all the finite groups ? (up to equivalence) such that any semiunitary projective representation of G can be lifted to a semiunitary representation of ?. The method is used in simple but interesting groups in physics.
Quantum dynamics of Hamiltonians perturbed by pulses
Authors: Christensen Mark J. , Piepenbrink John
Published: March 2003

There has been a recent controversy between Gzyl [J. Math Phys. 18, 1327 (1977)] and Blume [J. Math. Phys. 19, 2004 (1978)] concerning the correct way to integrate the equation i∂ψ/∂t=H0ψ+δ (t) Vψ where δ is the Dirac delta function. In this paper we: (1) Suggest some physical reasons for rejecting Gzyl’s procedure and (2) Extend the limiting procedure suggested the Blume to unbounded Hamiltonians.
Cyclic pursuit in a plane
Authors: Behroozi F. , Gagnon R.
Published: March 2003

The motion of an arbitrary set of points (or bugs) in a plane chasing one another in cyclic pursuit is studied. It is shown that for regular center-symmetric configurations, analytic solutions are easily obtained by going to an appropriate rotating frame of reference. A few cases of nonsymmetric configurations are discussed. In particular, it is shown that for three bugs in a triangular configuration, the center of the rotating coordinate system relative to which the bugs have no tangential velocity is the point of collapse and coincides with one of the two Brocard points of the triangle. For the case when all the bugs have the same speed, a theorem is proved that whenever a premature (i.e., nonmutual) capture occurs, the collision must be head on. This theorem is then applied to the case of three and four-bug configurations to show that these systems collapse to a point, i.e., the capture is mutual. Some aspects of these results are generalized to the case of the n-bug systems.
Stability and boundedness results of stochastic differential equations relative to a generalized norm
Authors: Moore Marion E.
Published: March 2003

We consider results previously obtained in the context of a generalized norm. In particular, we develop a general comparison principle which permits us to give sufficient conditions for conditional stability and boundedness in the mean relative to a generalized norm. Finally, we provide a decomposition technique together with additional comments which demonstrate the applicability of our results.
Some applications of time-dependent canonical transformations to nonlinear nonconservative classical systems
Authors: Maharatna A. , Dutt Ranabir , Chattarji D.
Published: March 2003

The recently proposed time-dependent canonical transformation method of Leach for the quadratic Hamiltonian has been extended to deal with nonlinear nonconservative classical systems. It is observed that the linear time dependent canonical transformations are not adequate to remove the time dependence of any arbitrary time-dependent nonlinear Hamiltonian. Alternatively, we propose that such a Hamiltonian may be transformed to a quadratic form by means of successive nonlinear canonical transformations. It is also shown that the canonical method is useful to obtain solutions for differential equations governing certain dissipative classical systems.
Invariant *-product quantization of the one-dimensional Kepler problem
Authors: Fronsdal Christian
Published: March 2003

It is shown that, with proper interpretation, phase space trajectories for the one-dimensional Kepler problem retain their significance after quantization. The classical and quantum theories are both entirely conventional; only the Wigner correspondence (Weyl quantization rule) is not. The usual quantum theory may be obtained by so(2,1) -invariant *-product quantization (generalized Moyal mechanics). [The analog in three dimensions is so(4,2) invariant *-quantization; it is believed that this should encounter no new difficulties of principle.] New results concerning invariant *-products on polynomials, in the case of so(2,1), are presented. The Kepler problem is the first known example of a nonanalytic *-representation. Piecewise analytic *-representations are defined and are shown to provide a general framework for invariant quantization on singular orbits of semisimple groups. When piecewise analytic *-representations are allowed, then the specification of an invariant *-product on polynomials is no longer sufficient to determine a unique quantum theory.
Explicit normalization of bound-state wave functions and the calculation of decay widths
Authors: Kaushal R. S. , Müller-Kirsten H. J. W.
Published: March 2003

We present a general method for normalizing nontrivial bound-state wave functions. In particular, we consider explicit and formally complete asymptotic expansions of the solutions of the wave equation for an arbitrary quark confining power potential. The regular solution is identified and shown to be continuable to an eigensolution around a local minimum of the associated potential. The solutions are then normalized and used to derive explicit series expressions for certain decay rates.
Quantum theory of infinite component fields
Authors: Barut A. O. , Schneider C. K. E. , Wilson Raj
Published: March 2003

The quantum theory of the infinite component SO(4,2) fields is formulated as a model for relativistic composite objects. We discuss three classes (timelike, lightlike, and spacelike) of physical solutions to a general class of infinite component wave equations. These solutions provide a definite physical interpretation to infinite component wave equations and are obtained by reducing SO(4,2) with respect to its orthogonal, pseudo-orthogonal, and Euclidean subgroups. The analytic continuations among these solutions are established. In the nonrelativistic limit the timelike physical states exactly reduce to the Schrödinger solution for the hydrogen atom—the simplest composite object. The wave equations for the three classes are studied in two different realizations. In one case the equations describe a three-dimensional internal Kepler motion with a discrete and a continuous energy spectrum and in the other case the equations describe a four-dimensional internal oscillatory motion with attractive as well as repulsive potentials. It is found that the Kustaanheimo–Steifel transformation of classical mechanics exactly relates these two internal motions also in the quantum case. Thus a completely relativistic theory of composite systems is established for which the internal dynamics is the generalization of the nonrelativistic two-body dynamics.
Stationary charged C-metric
Authors: Farhoosh Hamid , Zimmerman Robert L.
Published: March 2003

The physical properties of the stationary charged C-metric are fully investigated. Tetrad components of curvature and Maxwell tensors are studied in a Bondi–Sachs coordinate system to show that this solution represents a uniformly accelerating and rotating charged particle with magnetic monopole and NUT parameter. The physical quantities—news function, mass loss, mass, charge, and multipole moments—are calculated. The different mass loss definitions are compared and it is shown that the definition given by Bondi is the more appropriate one. It is also shown that the magnetic monopole in the presence of rotation affects the electric charge.
Dissipative operators for infinite classical systems and equilibrium
Authors: Pulè J. V. , Verbeure A.
Published: March 2003

Dissipative differential operators for infinite classical systems are characterized and used to obtain correlation inequalities for equilibrium states.
Transmission and reflection coefficients in the slowing down region
Authors: El Wakil S. A. , Haggag M. H. , Saad E. A.
Published: March 2003

The Green’s function approach which was formulated by Case is used to obtain the reflection and transmission coefficients for slab geometry in the slowing down region using the Greuling–Goertzel approximation for the scattering kernel. We obtain a set of linear equations for the coefficients using the principles of invariance.
Low-temperature thermodynamics of a weakly interacting Bose gas confined to restricted geometries
Authors: Zasada C. S. , Pathria R. K.
Published: March 2003

The low-temperature internal energy and specific heat of a hard sphere Bose gas confined to a general cuboidal enclosure are calculated under periodic boundary conditions. The special cases of a film and a channel geometry are considered in some detail. It is shown that, in the appropriate limits, one recovers the recent results of Pajkowski and Pathria, and of Zasada and Pathria, for a system of phonons confined to different geometries. Systematic applications of the Poisson summation formula enable us to obtain strongly convergent expansions, in both λ/L≪1 and λ/L≫1 regimes, and to see how the magnitude of the finite size corrections in the asymptotic limit (L/λ≫1) is directly linked with the dimensionality of the system. Special attention is paid to examining the combined influence of the dispersion in the phonon spectrum of the system and the finiteness of the enclosure.
The non-Markovian relaxation process as a ‘‘contraction’’ of a multidimensional one of Markovian type
Authors: Ferrario Mauro , Grigolini Paolo
Published: March 2003

A new approach for obtaining the Fokker–Planck equation to be associated with the generalized Langevin equation is discussed. By using the Mori expansion of the ’’memory kernel,’’ it is shown that any information of interest may be provided by a suitable multidimensional Fokker–Planck equation of Markovian type. A suitable ’’contraction’’ process, furthermore, enables us to find the same two-point conditional probability as the one recently obtained by Fox. This approach may be useful to overcome the Markov approximation which is present in the stochastic Liouville equation theory.
Linear response theory revisited. II. The master equation approach
Authors: van Vliet K. M.
Published: March 2003

We consider a system perturbed by an external field and subject to dissipative processes. From the von Neumann equation for such a system in the weak coupling limit we derive an inhomogeneous master equation, i.e., a master equation with dissipative terms and streaming terms, using Zwanzig’s projection operator technique in Liouville space. From this equation the response function, as well as expressions for the generalized conductivity and susceptibility, is obtained. It is shown that for large times only the diagonal part of the density operator is required. The various expressions are found to be in complete harmony with previous results (Part I) obtained via the van Hove limit of the Kubo–Green linear response formulas. In order to account for the properties at quantum frequencies, the evolution of the nondiagonal part in the weak coupling limit is also established. The complete time dependent behavior of the dynamic variables in the van Hove limit is expressed by B (t) =exp[−(Λd−iℒ0) t] B, where Λd is the master operator and L0 the Liouville operator in the interaction picture. The cause of irreversibility is discussed. Finally, the inhomogeneous master equation is employed to obtain as first moment equation a Boltzmann equation with streaming terms, applicable to quantum systems.
All spontaneously broken symmetries for noncovariant currents
Authors: Garber W. D.
Published: March 2003

For a current not covariant under translations, the associated symmetry can be spontaneously broken even in the case of a mass gap. The most general form of such a symmetry in a Wightman field theory is determined; it is shown that the symmetry generator can be evaluated on scattering states, commutes (as a form) with the S matrix, and has vanishing matrix elements between states whose particle number differs by more than one.
Classification of gauge fields
Authors: Cho Y. M.
Published: March 2003

A recently proposed classification of non-Abelian gauge fields is reexamined and refined to accommodate the internal symmetry structure of an arbitrary group. The concept of the canonical forms and the canonical frames is introduced and utilized to represent all the physically inequivalent realizations for each type of the field strengths. The local stability of the classification is shown to be minimal.
A first order system of differential equations for covariant σ models
Authors: Reina C. , Martellini M. , Sodano P.
Published: March 2003

A first order system of differential equations is obtained for a covariant σ model defined on a Riemannian (or pseudo-Riemannian) manifold of arbitrary dimension n. In the case of compact groups, i.e., SO(n), the first order system coincides with the one yielded by topological arguments. Our considerations hold true also for SO(p,q), p+q=n+1, invariance groups. The scale invariance of the problem is discussed.
Internal Lorentz basis for two-particle states
Authors: Daumens M. , Perroud M.
Published: March 2003

A basis for the space of states of two relativistic particles with arbitrary spins is constructed, suitable for obtaining two variable relativistic expansions of two-body scattering amplitudes. This basis is obtained starting from a representation of an ’’internal Lorentz group’’ which acts on the space of the two particle states in the pseudo-barycentric frame (p1/m1+p2/m2=0). The ’’internal Lorentz group’’ is defined as the maximal subgroup of the direct product of two Lorentz groups, which leaves invariant the null space of p1/m1+p2/m2.
Albedo problem of radiative transfer in inhomogeneous isotropically scattering atmospheres: Application of the maximum variational principle
Authors: Kanal Madhoo
Published: March 2003

An infinite medium Green’s function, constructed from a maximum variational principle, is used to solve the albedo problem of radiative transfer in an optically inhomogeneous medium. We assume that the medium is isotropically scattering; however, the albedo for single scattering is kept as an arbitrary continuous function of the optical depth. For a finite medium (such as the slab problem in neutron transport theory) we recommend that use of some experimental measurements be made to circumvent the mathematical difficulty of solving coupled singular integral equations. For a semi-infinite medium we obtain analytic solution for the albedo problem in the framework of the trial Green’s function obtained from the maximum variational principle. For the basis functions we make heavy use of Case’s eigenfunctions with a slight generalization to account for the inhomogeneous character of the medium. We also make heavy use of our previous work (c.f. Kanal and Moses, a reference in this paper) which should be consulted in conjunction with the present work.
Classical oscillators excited parametrically and their applications in plasma physics
Authors: Lucena S. T. , Minelli T. A. , Pusterla M.
Published: March 2003

Oscillators coupled directly and through time dependent external periodic forces, are considered here as a scheme that describes the motions of two plasmas in interaction with each other and with external fields. The analytical aspects of the equations are investigated both in their differential and integral forms. The formalism of Green’s functions is widely emphasized with a particular attention towards the resolvent. ’’Structural’’ Green’s functions in relation with the periodic time dependence of the external forces are introduced as a valid calculational tool in order to compute relevant physical features of the system. In particular, correlations between the mathematical singularities of the resolvent ’’structural’’ Green’s function, the dispersion relations, and the parametric instabilities are established. Exact solutions, with the use of the Green’s function approach and the direct one on the amplitudes, are obtained for particular models that exhibit a quite simplified but physically meaningful time dependence for the periodic external forces.
Zeros of the grand partition function: One-dimensional Widon–Rowlinson lattice gas
Authors: Runnels L. K. , Runnels John
Published: March 2003

The distribution of zeros of the partition function is studied for a one-dimensional symmetric two-component lattice gas. It is shown explicitly that the (complex) activities of the two components need not in general be of equal magnitude for the partition function to vanish, although such is the case if the geometric mean activity is sufficiently high. The effect of boundary conditions on the distribution of zeros is also studied.
Metastable states in the infinite Ising model
Authors: Vanheuverzwijn Paul
Published: March 2003

Using a characterization of metastability recently introduced by Sewell, taking the ’’lifetime’’ of a state to be determined by the evolution of the polarization density only, we show that the infinite Ising model can support metastable states, describing polarization in opposition to a weak external field, even in the presence of globally acting thermal perturbations.
Singular perturbations approach to the limit cycle and global patterns in a nonlinear diffusion-reaction problem with autocatalysis and saturation law
Authors: Bonilla L. L. , Velarde M. G.
Published: March 2003

A two-time scales method (singular perturbations) is used to construct the limit cycle and the global nonuniform steady patterns that appear in a diffusion-reaction process with autocatalysis and the Langmuir–Hinshelwood (Michaelis–Menten, Holling) saturation law. The stability of these nonlinear structures is also established in this paper.
The complete exact solution to the translation-invariant N-body harmonic oscillator problem
Authors: Hall Richard L. , Schwesinger B.
Published: March 2003

It is shown that Schrödinger’s nonrelativistic equation for a translation-invariant system of N particles with arbitrary masses interacting by harmonic pair potentials with arbitrary coupling constants is exactly soluble. An explicit matrix KV is given whose eigenvalues and eigenvectors determine all the exact energies and corresponding eigenfunctions of the N-particle problem. The result is extended to include systems composed of an arbitrary number of groups of identical particles.
Does there exist a scattering theory for time automorphism groups of C*-algebras corresponding to two-body interactions?
Authors: Narnhofer H.
Published: March 2003

It is shown that at least on the level of perturbation theory there does not exist a scattering automorphism between free time evolution and time evolution corresponding to two-body interaction for the C*-algebra of fermions on a lattice system.
Positive and negative frequency decompositions in curved spacetime
Authors: Panangaden Prakash
Published: March 2003

In this note we derive a formula for the positive and negative frequency parts of a solution in terms of the Feynman propagator. Our arguments are valid in the presence of particle creation. We also derive a formula for an operator 𝒥, that gives the particle creation rate. The formalism uses complex structures to capture the notion of positive and negative frequencies and thus avoids using analyticity arguments. The results obtained clarify the relation between approaches to quantum field theory based on the complex structure and approaches in which the propagator is the basic object. We will consider only scalar fields for simplicity.
Crossing properties of scattering operators
Authors: Klink William H.
Published: March 2003

For scattering operators that have the cluster decomposition property, it is shown that crossing relations for the scattering operator are consequences of the assumed crossing relations of the kernels of the connected parts of the scattering operator.
Ladder operators of group matrix elements
Authors: Schneider C. K. E. , Wilson Raj
Published: March 2003

All ladder operators and some recurrence relations of the matrix elements of certain group elements of SO(3), SO(2,1), E(2), SO(4), SO(3,1), and E(3) have been explicitly determined and the underlying factorizations of the second- and the fourth-order linear ordinary differential equations in terms of first- and second-order ladder operators have been transparently demonstrated as an extension to the Schrödinger–Infeld–Miller factorization. These ladder operators are very useful in physical applications where the corresponding matrix elements represent certain physical transitions.
On the definition and properties of generalized 6-j symbols
Authors: Raynal Jacques
Published: March 2003

Whipple’s work on the symmetries of well-poised 7F6(1) and Saalschürtzian 4F3(1) series with unit argument is applied to study the properties of 6-j symbols generalized to any arguments. For SU2, we obtain eleven different looking 4F3(1) series which can be used. Whipple’s parameter x s provide a good description of symmetries. We obtain quite simple recurrence relations, valid for any arguments, in terms of these parameters.
A particular N-soliton solution and scalar wave equations
Authors: Couch W. E. , Torrence R. J.
Published: March 2003

A special class of N-soliton solutions of the Korteweg–deVries equation is examined. It is shown that the nonscattering wave equation based on the corresponding special reflectionless potentials can be obtained by a coordinate transformation of the ordinary wave equation and that these reflectionless potentials and others occur in the scalar wave equation on black hole geometries of general relativity.
Restoration of a functional from its functional derivatives
Authors: Garczyński W. , Hańćkowiak J.
Published: March 2003

Inverse operation to a functional differentiation is considered.
Visual geometry and the algebraic properties of spinors
Authors: Hellsten H.
Published: March 2003

Key words of the present paper are visualization and concrete geometry. We develop ordinary two-component spinor algebra from a concrete geometrical model of spinor space. The null flag picture may be said to constitute such a model as far as topological and differential properties of spinors go. In our model it is also possible to visualize the algebraic properties of spinors by straightforward geometrical constructions. Notably, an interpretation of spinor addition is given in terms of a geometrical procedure, analogous to the addition of real 3-vectors via the parallelogram rule. By this procedure the relation between the projection of spinors on the 2-sphere and the projection of their sum can directly be read off. The connection between null flags and our presentation of spinors is touched upon. It is planned to discuss the connection to Minkowski space more closely in a forthcoming paper.
World-line invariance in predictive mechanics
Authors: Salas Angel
Published: March 2003

The Currie–Hill conditions for the relativistic world-line invariance of a Newtonian-like dynamical system of interacting particles are generalized to cover the case of invariance under any given finite-dimensional continuous group of transformations of space–time. Necessary and locally sufficient conditions are obtained both in the general case and in the important particular case when the group of transformations includes time translations as a subgroup.
Time ordered operator cumulants: Statistical independence and noncommutativity
Authors: Fox Ronald Forrest
Published: March 2003

A cumulant identity for noncommuting operator random processes is discussed. Its validity is negated by exhibiting a counterexample in which statistical independence and noncommutativity are clearly separated.
Conformal electrodynamics in Einstein spacetime
Authors: Heidenreich W.
Published: March 2003

Conformally invariant Maxwell equations in the closed Einstein spacetime are derived, using the diffeomorphism between Einstein spacetime and the universal covering of conformal space. Spatial integration of the charge density yields the total charge 0.
Canonical Schwartz spaces and generalized operators
Authors: Peck S. N.
Published: March 2003

For a C∞ multiplier ω, on Rn we define the concepts of differentiability and codifferentiability in the Von Neumann algebra generated by the regular ω representation of Rn. Analogs of the classical Schwartz space and its dual are formulated and the case where ω is fully antisymmetric is studied. Connections with the canonical Fourier transform of an earlier paper are investigated.
Group-theoretical foundations of classical and quantum mechanics. II. Elementary systems
Authors: Martínez Alonso L.
Published: March 2003

Classical and quantum elementary systems are investigated from the point of view of invariance under a connected Lie group. The classification and characterization of elementary systems are considered in a unified way. The representation theory of symmetric and enveloping algebras is used as a tool in order to characterize the observables physically and also to analyze the analogies between classical and quantum mechanics. The results obtained are applied to the Galilei, Poincaré, and Weyl Lie groups.
Exotic spinors in superconductivity
Authors: Petry Herbert Rainer
Published: March 2003

The existence of inequivalent types of spinors in spaces which are not simply connected is mathematically investigated. The mathematical results provide a purely geometrical explanation of the charge dependence of quantized flux and Josephson current in superconductivity.
Conformal flatness and the Schwarzschild interior solution
Authors: Raychaudhuri A. K. , Maiti S. R.
Published: March 2003

The paper gives a rigorous proof of the theorem that the only static conformally flat metric for a perfect fluid distribution is the Schwarzschild interior metric.
Automorphisms of the Bianchi model Lie groups
Authors: Harvey Alex
Published: March 2003

A derivation of the group of automorphisms of the Lie group of isometries characteristic of each of the nine Bianchi types of cosmologies is presented.
Perturbative solution of the Percus–Yevick integral equation for a general class of intermolecular potential
Authors: Chen M.
Published: March 2003

A qualitative investigation of the Percus–Yevick integral equation by perturbation method is discussed for a general class of intermolecular potential. Under some general assumptions it is proved that the Percus–Yevick integral equation has a unique solution when the particle density ρ is in the region 0<ρ<0.33, and a divergent solution when ρ is greater convergent if the supremum norms of the nth order solutions are less than or equal to n!
Classification of gauge fields
Authors: Anandan J.
Published: March 2003

It is shown that the Lorentz invariants of an arbitrary gauge field are double valued functions of a Lorentz invariant matrix Lij when rank L=3 and single valued functions of Lij when rank L≠3. The question of how many Lorentz inequivalent realizations of the Lorentz invariants there are is answered. This leads naturally to a classification of an arbitrary gauge field at a space–time point, given previously by Anandan and Tod based on the rank of L. The answer to the analogous question for the gauge invariants of the SU(2) gauge field leads to a new classification of this field. Five more classifications of this field, including one which is symmetric with respect to space–time and isospin groups, are also presented.
Exceptional gauge groups and quantum theory
Authors: Horwitz L. P. , Biedenharn L. C.
Published: March 2003

It is shown that a Hilbert space over the real Clifford algebra C7 provides a mathematical framework, consistent with the structure of the usual quantum mechanical formalism, for models for the unification of weak, electromagnetic and strong interactions utilizing the exceptional Lie groups. In particular, in case no further structure is assumed beyond that of C7, the group of automorphisms leaving invariant a minimal subspace acts, in the ideal generated by that subspace, as G2, and the subgroup of this group leaving one generating element (e7) fixed acts, in this ideal, as the color gauge group SU(3). A generalized phase algebra A⊇C7 is defined by the requirement that quantum mechanical states can be consistently constructed for a theory in which the smallest linear manifolds are closed over the subalgebra C(1,e7) (isomorphic to the complex field) of C7. Eight solutions are found for the generalized phase algebra, corresponding (up to an overall sign), in effect, to the use of ±e7 as imaginary unit in each of four superselection sectors. Operators linear over these alternative forms of imanary unit provide distinct types of ’’lepton–quark’’ and ’’quark–quark’’ transitions. The subgroup in A which leaves expectation values of operators linear over A invariant is its unitary subgroup U(4), and is a realization (explicitly constructed) of the U(4) invariance of the complex scalar product. An embedding of the algebraic Hilbert space into the complex space defined over C(1,e7) is shown to lead to a decomposition into ’’lepton and ’’quark’’ superselection subspaces. The color SU(3) subgroup of G2 coincides with the SU(3) subgroup of the generalized phase U(4) which leaves the ’’lepton’’ space invariant. The problem of constructing tensor products is studied, and some remarks are made on observability and the role of nonassociativity.
Scattering theory and polynomials orthogonal on the unit circle
Authors: Geronimo J. S. , Case K. M.
Published: March 2003

The techniques of scattering theory are used to investigate polynomials orthogonal on the unit circle. The discrete analog of the Jost function, which has been shown to play an important role in the theory of polynomials orthogonal on a segment of the real line, is defined for this system and its properties are investigated. The relation between the Jost function and the weight function is discussed. The techniques of inverse scattering theory are developed and used to obtain new asymptotic formulas satisfied by the polynomials. A set of sum rules satisfied by the coefficients in the recurrence relaxation is exhibited. Finally, Szegö’s theorem on Toeplitz determinants is proved using the recurrence formulas and the Jost function. The techniques of inverse scattering theory are used to find the correction terms.
Particle–boson interactions and the weak coupling limit
Authors: Davies E. B.
Published: March 2003

We consider the interaction of a finite number of nonrelativistic particles with a positive or zero mass quantum field. We show that in the weak coupling limit the quantum field gives rise to an effective interaction between the particles of a Yukawa or Coulomb type, as well as, in some cases, a mass renormalization. In a simple exactly soluble model we investigate the higher order radiation processes.
Microscopic theory of superfluid Fermi systems. II. Application to low density hard sphere system
Authors: Reichl L. E.
Published: March 2003

This is the second of two papers in which the binary expansion is used to study properties of hard core Fermi systems with broken gauge symmetry. In this paper, we make contact with the phenomenology of superfluid Fermi systems commonly used in field theory. This requires, however, that each scattering event is approximated by its forward scattering value, an approximation which, at best is valid at very low densities. Within this approximation we show that a hard sphere Fermi fluid can exhibit superfluidity.
Classification and construction of finite dimensional irreducible representations of the graded algebras; application to the (Sp(2n); 2n) algebra
Authors: Bednář Miroslav , Šachl Vladimír F.
Published: March 2003

A method, which enables us to construct the finite-dimensional representations of the graded Lie algebras [explicitly the GLA (Sp(2N); 2N)] on the irreducible tensors is suggested. Those tensors are constructed with the aid of the specifically symmetrized products of vectors from the fundamental [i.e., (2N+1) -dimensional] representation space of the graded Lie algebra. The tensors, on which it is possible to represent the graded algebra (Sp(2N); 2N) irreducibly, represent a generalization of tensors which are known from the general representation theory of the symplectic Lie algebra Sp(2N). The knowledge of the irreducible tensors of the algebra Sp(2N) gives us then the possibility of solving the problems of classification as well as construction of the irreducible tensors of the graded algebra (Sp(2N); 2N). For illustration, by using the suggested method of tensors the irreducible representations of the simplest graded algebra, i.e., of the algebra (Sp(2); 2) are constructed.
On the diagonalization of the general quadratic Hamiltonian for coupled harmonic oscillators
Authors: Tikochinsky Yoel
Published: March 2003

It is shown that the general quadratic Hamiltonian for coupled harmonic oscillators can be diagonalized, provided the matrix of the quadratic form is positive definite. This condition is also necessary if the frequencies of the resulting uncoupled oscillators are to be positive. The construction of a diagonalizing matrix follows the usual procedure as in the Hermitian case; the only difference being a change of the metric from I= (1 1) to J= (1 −1).
Conservation laws for the classical Maxwell–Dirac and Klein–Gordon–Dirac equations
Authors: Glassey R. T. , Strauss W. A.
Published: March 2003

Solutions to the classical coupled Maxwell–Dirac and Klein–Gordon–Dirac equations in a space–time of dimension four are considered. These equations are invariant under the 15-dimensional conformal group, in the case of zero mass. The resulting conservation laws are explicitly exhibited in terms of the Cauchy data at a fixed time in a form suitable for analysis by the techniques of partial differential equations.
The Cauchy problem in general relativity. III. On locally imbedding a family of null hypersurfaces
Authors: Smallwood J.
Published: March 2003

This paper is concerned with the problem of locally imbedding a null hypersurface in a Riemannian manifold. More precisely, on a one-parameter family of null hypersurfaces, rigged by an arbitrary null vector field, in a four-dimensional space–time manifold, a particular symmetric affine connection is used to derive the corresponding generalized Gauss–Codazzi equations. In addition, expressions are obtained for the projections of the Ricci tensor, which are relevant to the characteristic initial-value problem of general relativity.
Remarks on the Hamiltonian path integral in polar coordinates
Authors: Langguth Wolfgang , Inomata Akira
Published: March 2003

Problems associated with the derivation of the Hamiltonian path integral in polar coordinates are examined. First the use of the ill-defined asymptotic formula of the modified Bessel function is pointed out. A procedure is proposed to justify its practical use, in which the mass m is complexified and the limit Imm→0 is taken after path integrations. Hereby a restriction is imposed on the class of allowed potentials. The difference between the Hamiltonian path integral so obtained and the phase space path integral formally defined is also discussed.
On the problems of object restoration and image extrapolation in optics
Authors: Bertero M. , De Mol C. , Viano G. A.
Published: March 2003

In this paper we consider the problems of object restoration and image extrapolation, according to the regularization theory of improperly posed problems. In order to take into account the stochastic nature of the noise and to introduce the main concepts of information theory, great attention is devoted to the probabilistic methods of regularization. The kind of the restored continuity is investigated in detail; in particular we prove that, while the image extrapolation presents a Hölder type stability, the object restoration has only a logarithmic continuity.
Lowering and raising operators of IU(n) and IO(n) and their normalization constants
Authors: Wong M. K. F. , Yeh Hsin-Yang
Published: March 2003

Lowering and raising operators for the vector space U(n) ⊇IU(n) and O(n) ⊇IO(n) have been obtained, and their normalization constants evaluated. For U(n) ⊇IU(n), we obtain two forms, one according to Nagel and Moshinsky, and the other according to Bincer. For O(n) ⊇IO(n),we obtain the shift operators according to Bincer.
Multiplicities for space group representations
Authors: Dirl R.
Published: March 2003

The multiplicity formula for nonsymmorphic space group representations is reinvestigated by using explicitly projective representations for the little cogroups Pq↘≃Gq↘/T. Thereby useful identities and relations concerning the wave vector selection rules are derived for various cases which may occur for the elements of the Brillouin zone. These relations allow for nearly all cases a closed expression for the multiplicity without reference to a special space group.
Clebsch–Gordan coefficients for space groups
Authors: Dirl R.
Published: March 2003

A general method for finding Clebsch–Gordan coefficients is used to calculate them for nonsymmorphic space groups. This method is based on the fact that the columns of the Clebsch–Gordan matrices can be seen as G-adapted vectors and that the multiplicity index can be traced back to special column indices of the Kronecker product. Using this method we obtain simple defining equations for the multiplicity index and for nearly all cases without reference to a special space group by a simple calculation the corresponding Clebsch–Gordan matrices.
Clebsch–Gordan coefficients for P
n3n
Authors: Dirl R.
Published: March 2003

A general method for calculating Clebsch–Gordan coefficients is applied to determine such coefficients for the nonsymmorphic space group Pn3n.
Generalized Lie algebras
Authors: Scheunert M.
Published: March 2003

The generalized Lie algebras, which have recently been introduced under the name of color (super) algebras, are investigated. The generalized Poincaré–Birkhoff–Witt and Ado theorems hold true. We discuss the so-called commutation factors which enter into the defining identities of these algebras. Moreover, we establish a close relationship between the generalized Lie algebras and ordinary Lie (super) algebras.
Null electromagnetic fields in the generalized Einstein–Maxwell field theory
Authors: Horndeski Gregory Walter
Published: March 2003

In this paper solutions to the source-free generalized Einstein–Maxwell field equations with a null electromagnetic field are investigated. It is argued that the principal null congruence of the null electromagnetic field need not be geodesic, shear-free or a repeated principal null congruence of the gravitational field. However, if the principal null congruence of the null electromagnetic field is geodesic and shear-free, then it is shown that it must be hypersurface orthogonal, expansion-free, and a repeated principal null congruence of the gravitational field. The local form of all such solutions of Petrov type III or N is presented.
On the static Einstein–Maxwell field equations
Authors: Das A.
Published: March 2003

The static Einstein–Maxwell field equations are investigated in the presence of both electric and magnetic fields. The sources or bodies are assumed to be of finite size and to not affect the connectivity of the associated space. Furthermore, electromagnetic and metric fields are assumed to have reasonable differentiabilities. It is then proved that the electric and magnetic field vectors are constant multiples of one another. Moreover, the static Einstein–Maxwell equations reduce to the static magnetovac case. If, furthermore, the variational derivation of the Einstein–Maxwell equations is assumed, then both the total electric and magnetic charge of each body must vanish. As a physical consequence it is pointed out that if a suspended magnet be electrically charged then it must experience a purely general relativistic torque.
Space–time homogeneous models with torsion
Authors: Rosenbaum Marcos , Ryan Michael P. , Shepley L. C.
Published: March 2003

A space-time homogeneous model is one in which the metric and the connection are invariant under a four-dimensional transitive Lie group. The Einstein-Cartan theory describes the effect of spin on geometry. The field equations require a stress-energy tensor and a spin tensor for a perfect fluid, and we give the required forms here. The main part of this paper is a presentation of several classes of space-time homogeneous solutions of the Einstein-Cartan equations for perfect fluid cosmological models.
Direct determination of the Langlands decompositions for the parabolic subalgebras of noncompact semisimple real Lie algebras
Authors: Cornwell J. F.
Published: March 2003

A direct method for the determination of the Langlands decompositions for the parabolic subalgebras of any noncompact semisimple real Lie algebra is described in detail. The method is based on the canonical form of the Lie algebra. The physically important Lie algebras so(3,2) and so(4,2) are treated as illustrative examples.
Formulation of the linearized Vlasov-fluid model for a sharp-boundary screw pinch
Authors: Lewis H. Ralph , Turner Leaf
Published: March 2003

A theoretical formulation is derived for analyzing linearized equations appropriate to a straight, cylindrical, sharp-boundary screw pinch within the framework of the Vlasov-fluid model. Surrounding the plasma is a cylindrical conducting wall, and there is a nonconducting vacuum between the plasma and the wall. By introducing a perturbation-dependent transformation of the phase space and linearizing about a zeroth-order state which depends on the perturbation, the linearized equations of Freidberg’s Vlasov-fluid model are put into a form which would be correct for a hypothetical problem in which the plasma boundary is a rigid cylinder. The effects of the impulsive electric field at the actual perturbed boundary are taken into account in the zeroth-order state. The boundary conditions at the perturbed plasma boundary are continuity of the normal component of B and vanishing of the normal component of the net current density.
Semiclassical quantization of nonseparable systems
Authors: Klein Abraham , Li Ching-teh
Published: March 2003

The problem of semiclassical quantization of nonseparable systems with a finite number of degrees of freedom is studied within the framework of Heisenberg matrix mechanics, in extension of previous work on one-dimensional systems. The relationship between the quantum theory and multiply-periodic classical motions is derived anew. A suitably averaged Lagrangian provides a variational basis not only for the Fourier components of the semiclassical equations of motion, but also for the general definition of action variables. A Legendre transformation to the Hamiltonian verifies that these have been properly chosen and therefore provide a basis for the quantization of nonseparable systems. The problem of connection formulas is discussed by a method integral to the present approach. The action variables are shown to be adiabatic invariants of the classical system. An elementary application of the method is given. The methods of this paper are applicable to nondegenerate systems only.
Quartic trace identity for exceptional Lie algebras
Authors: Okubo Susumu
Published: March 2003

Let X be a representation matrix of generic element x of a simple Lie algebra in generic irreducible representation {λ} of the Lie algebra. Then, for all exceptional Lie algebras as well as A1 and A2, we can prove the validity of a quartic trace identity Tr(X4) =K (λ)[Tr(X2)]2, where the constant K (λ) depends only upon the irreducible representation {λ}, and its explicit form is calculated. Some applications of second and fourth order indices have also been discussed.
Spectral and scattering theory for the adiabatic oscillator and related potentials
Authors: Ben-Artzi Matania , Devinatz Allen
Published: March 2003

We consider the Schrödinger operator H=−Δ+V (r) on Rn, where V (r) =a sin(brα)/rβ+VS(r), VS(r) being a short range potential and α≳0, β≳0. Under suitable restrictions on α, β, but always including α=β=1, we show that the absolutely continuous spectrum of H is the essential spectrum of H, which is [0,∞), and the absolutely continuous part of H is unitarily equivalent to −Δ. We use these results to show the existence and completeness of the Mo/ller wave operators. Our results are obtained by establishing the asymptotic behavior of solutions of the equation Hu=zu for complex values of z.
An analytical theory of pulse wave propagation in turbulent media
Authors: Furutsu K.
Published: March 2003

The theory of pulse wave propagation in turbulent media is developed starting from the space–time transport equation with the forward-scattering approximation. The solutions are obtained by a fully analytical method based on the eigenfunction expansion, and the averaged intensity of plane wave pulse is presented by two different expressions for both the Gaussian and Kolmogorov turbulence spectra. These two expressions are given in the series, and the convergence of each series is good when the convergence of the other series is poor; in the case of the Gaussian turbulence spectrum, one of these expressions precisely agrees with the previous one obtained by Sreenivasiah et al. (1976). In connection with the pulse wave width, the pulse moments are evaluated in detail. The resolvent function is fully used to find the eigenvalues and eigenfunctions.
On an inhomogeneous Schrödinger equation and its solutions in scattering theory
Authors: van Haeringen H.
Published: March 2003

We prove that ψs,l, the partial-wave projection of the irregular Coulomb wavefunction ψs, is a solution of an inhomogeneous Schrödinger equation. New expressions for ψs,l and ψs are obtained in terms of the Coulomb Green functions GC,l and GC, respectively. We discuss irregular solutions, the analogs of ψs, for Coulomb-like and short-range potentials. We find that in general these functions do not approach asymptotically the scattering amplitude times an outgoing spherical wave, in contrast to the pure Coulomb function ψs.
The classical limit of quantum nonspin systems
Authors: Gilmore R.
Published: March 2003

The classical limit of operators X belonging to any compact Lie algebra g is computed. If X∈g, the classical limit in the representation ΓΛ, whose highest weight is Λ, is lim ΓΛ(X/N) =Σsig (fi,X,Ω), where the limit is taken as N→∞, the sum runs from i=1 to r=rank g, Λ=Σμifi,fi are the highest weights of the r fundamental representations of g,si=lim μi/N, and g (fi,X,Ω) is the expectation value of X with respect to the coherent states ‖fi, Ω〉 in the representation Γfi. Examples and applications are given.
Higgs mechanism and the inverse Einstein–Infeld–Hoffman problem
Authors: Mallett Ronald L.
Published: March 2003

The Guralnik–Hagen model for a self-coupled spin −1/2 field is minimally coupled to a gauge gravitational field. The corresponding free gravitational Lagrangian is not explicitly introduced. It is shown that, using spontaneous breakdown of Lorentz invariance and the generalized Gordon decomposition, the Higgs mechanism generates a gravitational Lagrangian which leads to the usual linearized Einstein gravitational field equations.
The spectral properties of many-electron atomic Hamiltonians and the method of configuration interaction. II. Compactness proof associated with an infinite system of linear equations for two-electron atoms
Authors: Choudhury M. H.
Published: March 2003

The Schrödinger equation for a two-electron atomic system is reduced to an infinite system of linear equations. The linear operator defined by this system of equations is then shown to be compact in a region of the complex energy plane which excludes the various bound state and multiparticle scattering cuts (i.e., the eseential spectrum of the Hamiltonian of the two-electron atomic system). This permits one to truncate the infinite system of equations with the assurance that the N energy eigenvalues obtained from the N×N truncated system will uniformly approximate the lowest N energy eigenvalues of the original infinite system.