bluuebunny/crossref_metadata_2025 huggingface dataset:
Macroscopic Causality Conditions and Properties of Scattering Amplitudes
Authors: Chandler Colston , Stapp Henry P.
Published: February 2004

Two causality conditions that refer only to mass-shell quantities are formulated and their consequences explored. The first condition, called weak asymptotic causality, expresses the requirement that some interaction between the initial particles must occur before the last interaction from which final particles emerge. This condition is shown to imply that if a two-body scattering function is analytic except for singularities in the energy variable at normal thresholds, then (a) the physical scattering functions in two adjacent parts of the physical region separated by any normal threshold are parts of a single analytic function; (b) the path of continuation joining these two parts bypasses the singularity in the upper half-plane of the energy variable; and (c) the integral over the physical function can be represented as an integral over a contour that is distorted into the upper-half energy plane (hence not, for example, by a principal-value integral). Singularities possessing finite derivatives of all orders with respect to real variations of the energy are not encompassed by this result. The second causality condition, called strong asymptotic causality, expresses the requirement that, apart from contributions whose effects fall off faster than any inverse power of Euclidean distance, momentum-energy is carried over macroscopic distances only by stable physical particles. This condition implies that all n-particle scattering functions (n ≥ 4) are analytic, apart from infinitely differentiable singularities, at physical points not lying on any positive-α Landau surface. Moreover, the scattering functions on the two sides of any such Landau surface are analytically connected by a path that passes around the singularity surface in a well defined manner, which is the same as in perturbation theory. Thus, apart from possible infinitely differentiable singularities, the physical region singularity structure is derived from a mass-shell causality requirement. Several properties of the set L+ of physical region positive-α Landau surfaces are derived.
Solution of the Dimer Problem by the S-Matrix Method
Authors: Fan Chungpeng
Published: February 2004

The S-matrix approach of Hurst is applied to rederive the partition function for the dimer problem. By using every two lattice sites as a unit cell and a set of six creation and annihilation operators at each cell, the expression for the partition is reduced to a form equivalent to the vacuum expectation value of an S matrix with a quadratic interaction Lagrangian.
Wave Propagation in Sinusoidally Stratified Plasma Media
Authors: Casey K. F. , Matthes J. R. , Yeh C.
Published: February 2004

The problem of the propagation of electromagnetic waves in a sinusoidally stratified plasma media is treated analytically. The propagation characteristics of TE and TM waves are determined, respectively, from the characteristic equations of the resultant Mathieu and Hill equations. Detailed dispersion characteristics of TE and TM waves in an infinite stratified plasma medium and in waveguides filled longitudinally with this stratified dispersion material are given. It is found that, although the stop-band and pass-band structures exist for the ω-β diagrams of both TE and TM waves, detailed dispersion properties for TE and TM waves are quite different for most frequency ranges except when [(ω/ωp0)2−1]2≫δ2, where ω is the frequency of the propagating waves, ωp0 is the average plasma frequency of the inhomogeneous plasma medium, and δ is the amplitude of the sinusoidally varying term for the electron-density profile (0 ≤ δ ≤ 1).
Statistical Properties of Polycrystalline Dielectrics
Authors: Molyneux John E.
Published: February 2004

In this paper we consider the determination of the two-point electric field correlation tensor in a random polycrystalline medium subjected to a constant average electric field. The medium is supposed to be statistically homogeneous and isotropic and to be composed of crystals all of the same kind. For media whose principal permittivities do not differ greatly from one another, we employ perturbation techniques to linearize the governing equations and derive explicit expressions for both the correlation function and the cross correlation of the electric field and permittivity tensor. We also determine the effective permittivity in this limit. For media with arbitrary principal permittivities, we derive bounds on the effective permittivity which depend on certain two point correlation functions and which reduce to our perturbation solution in the limit of small differences in principal permittivities.
Stationary ``Noncanonical'' Solutions of the Einstein Vacuum Field Equations
Authors: Hoffman Richard B.
Published: February 2004

The complete set of nonflat normal-hyperbolic solutions of the Einstein vacuum field equations is obtained for the metric tensor defined by the quadratic differential form ds2 = α du2 − 2γ du dv − β dv2 − eφ(dx2 + dz2) subject to the condition that αβ + γ2 is constant. These solutions are characterized by the existence of a null hypersurface-orthogonal Killing vector, which is also a four-fold degenerate Debever vector with vanishing covariant derivative, and therefore are a special case of the class of plane-fronted gravitational waves.
Dynamics near Equilibrium of Systems Described in Thermal Hartree-Fock Approximation
Authors: Felderhof B. U.
Published: February 2004

The dynamics of systems described in Hartree-Fock approximation is studied near a stationary point of the free energy. It is shown that the second-order free-energy functional is a constant for the linearized self-consistent equation of motion. This leads to the stability criterion derived by Mermin. A simple collision model is constructed and is shown to satisfy the H theorem. It exhibits the effect of critical slowing down. The formalism is shown to be applicable to superconductors.
Expansion of the Density Matrix of an N-Fermion System in Terms of the Correlation Densities of Fermion Clusters
Authors: Shibuya Tai-ichi , Sinanoğlu Oktay
Published: February 2004

The N-fermion density operator D = |Ψ〈〉Ψ| is decomposed into the densities of clusters of correlating fermions. The m-body cluster densities γ̂(m) are ``orthogonal'' to the one-body ``Fock-Dirac''-type densities ρ1, i.e., Γr1(ρ1γ̂1,2,(m)…,m)=0. The reduced-correlation-density matrices obtained differ from the conventional reduced-density-matrices and are particularly convenient for the treatment of fermion-fermion correlations.
General Interaction Picture from Action Principle for Mechanics
Authors: Garrido L. M.
Published: February 2004

In this paper we consider a general action principle for mechanics written by means of the elements of a Lie algebra. We study the physical reasons why we have to choose precisely a Lie algebra to write the action principle. By means of such an action principle we work out the equations of motion and a technique to evaluate perturbations in a general mechanics that is equivalent to a general interaction picture. Classical or quantum mechanics come out as particular cases when we make realizations of the Lie algebra by derivations into the algebra of products of functions or operators, respectively. Later on we develop in particular the applications of the action principle to classical and quantum mechanics, seeing that in this last case it agrees with Schwinger's action principle. The main contribution of this paper is to introduce a perturbation theory and an interaction picture of classical mechanics on the same footing as in quantum mechanics.
Codiagonal Perturbations
Authors: Green H. S. , Triffet T.
Published: February 2004

Matrix methods are developed for calculating the eigenvalues and eigenvectors of a large class of quantum-mechanical operators which may be regarded as perturbed forms of special-function operators. Specific representations are obtained for the latter, including all of the important cases treated by Infeld and Hull. To these are added representations for terms sufficient to generate forms corresponding to the Mathieu equation, the Lamé equation, and others. A rapidly convergent computational scheme applicable to asymmetric matrices, which retains its stability even when the perturbing terms become large, is described; and its use is illustrated by application to the operator p(1 − q2)p − α2q2, corresponding to the Legendre-like form (d/dx)(1 − x2)(d/dx) + α2x2. Though group-theoretic considerations are stressed, appropriate correlations with differential and integral equations are presented throughout.
Lattice Dynamics of Simple Cubic Lattices with Long-Range Interactions
Authors: Davies John A. , Yedinak Peter D.
Published: February 2004

An analytic study is made of the dispersion relations and frequency spectra of simple cubic lattices in which there exist long-range potentials of the form 1/rp. The rigid-ion approximation is used. An expansion of the dispersion relations about the maximum propagation vector in the first Brillouin zone is obtained for 1 ≤ p ≤ 3 and the contribution of the region about this point to the vibrational frequency spectrum of the lattice is studied.
Evaluation of ``Kondo'' Integrals
Authors: Glasser M. L.
Published: February 2004

Exact and approximate expressions are given for the integrals vnm= ∫ −DDxn(x2+Δ2)−m(eβx+1)−1dx.
Degenerate Representation Functions for SO(v), SU(v), and SU(ν)⊗SU(ν) and Their Analytical Reductions
Authors: Delbourgo R. , Koller K. , Williams Ruth M.
Published: February 2004

We have studied the problem of obtaining the rotation matrix elements dN(θ) = 〈N|e−iθJ2|N〉, where |N〉 refer to a particular degenerate class of basis vectors of a symmetry group G which embraces the rotations SU(2)J as a subgroup. For G = SO(v), SU(v), and SU(ν)⊗SU(ν), we prove that these particular representation functions are proportional to the Gegenbauer polynomials CN12(ν−2)(cosθ),CN12(ν−1)(cosθ), and CN12ν(cosθ), respectively. The reduction of such functions into one another according to the formula CN′λ′=ΣNaNCNλ has been solved in generality for complex values of N and corresponds to the reduction of Regge poles of G into Regge poles of one of its subgroups. The reduction formula for functions of the second type EN′λ′=ΣNbNENλ has also been derived; here one simply meets an infinite series.
S-Matrix and Classical Description of Interactions
Authors: Iagolnitzer Daniel
Published: February 2004

It is shown quite generally, through a correspondence between S-matrix and classical descriptions of particle states and of their measurements, that an S-matrix theory actually leads, under appropriate conditions, to the classical space-time description of interactions, involving the usual classical concepts and formulas.
Transverse Dielectric Tensor for a Free-Electron Gas in a Uniform Magnetic Field
Authors: Arunasalam V.
Published: February 2004

An elementary method of calculating that part of the tensor dielectric coefficient which determines the propagation of transverse electromagnetic radiation through a free-electron gas in a uniform external magnetic field is presented. The method presented here is based on a particle-orbit analysis and is somewhat analogous to a generalized version of the Kramers-Heisenberg quantum theory of gaseous dispersion. It is shown that the elements of the transverse dielectric tensor can be obtained from a knowledge of the quantum-mechanical transition probabilities for emission and absorption of photons (that is, from a knowledge of the Einstein A and B coefficients). The formal expression for the dielectric tensor thus obtained is shown to be valid for both the degenerate and the nondegenerate system of electrons. The dielectric tensor thus obtained is shown to reduce in the classical limit to the familiar results of the conventional classical hot plasma kinetic theory. The first quantum correction to the classical hot plasma dielectric tensor is explicitly given and it is shown that, under suitable conditions, this quantum correction will play a significant role in the analysis of the experimental studies of the electrodynamic behavior of ``classical electron-hole plasmas'' in a uniform external magnetic field.
Periodic Small-Amplitude Solutions to Volterra's Problem of Two Conflicting Populations and Their Application to the Plasma Continuity Equations
Authors: Roth J. Reece
Published: February 2004

The coupled set of first-order nonlinear differential equations describing a generalized form of Volterra's problem of two conflicting populations ẋ=C0+C1x+C2y+C3xy+C4x2+C5y2,ẏ=A0+A1x+A2y+A3xy+A4x2+A5y2are solved by an approximate method which gives y(t) for the particular case in which the variables x and y vary periodically, the coefficients Ci and Ai are real, and the peak-to-peak amplitude of x is small compared with the mean value of x. The peak-to-peak amplitude of y, however, is not necessarily small compared with the mean value of y. When these conditions are satisfied, the functional form of y(t) is approximated by Jacobian elliptic functions. The solutions obtained in this analysis are relevant to special cases of the classical problem of predator and prey, and also to certain low-frequency oscillations in partially ionized plasmas that arise from periodic solutions to the neutral and charged-particle continuity equations.
Solution of the Faddeev Equation for Local Potentials by Approximate Product-Integration
Authors: Kim Y. E.
Published: February 2004

A practical method of solving the Faddeev equation for short-range local potentials is proposed. The method consists of (a) transforming the Faddeev equation into a form in which the inhomogeneous term satisfies a Hölder condition and then (b) solving the resultant two-variable integral equations by approximate product-integration.
Reciprocity Principle and the Lorentz Transformations
Authors: Berzi Vittorio , Gorini Vittorio
Published: February 2004

By using the principle of relativity, together with the customary assumptions concerning the nature of the space-time manifold in special relativity, namely, space-time homogeneity and isotropy of space, a simple but rigorous proof is given of the reciprocity relation for the relative motion of two inertial frames of reference, which is usually assumed as a postulate in the standard derivations of the Lorentz transformations without the principle of invariance of light velocity. A critical discussion is set forth of the question of eliminating the transformations with invariant imaginary velocity, which one unavoidably obtains together with the Lorentz transformations and the Galilean ones in adopting a procedure of this kind.
One-Dimensional Phase Transition
Authors: Strecker Joseph L.
Published: February 2004

The Berlin-Witten-Gersch model of a classical gas gives a phase transition in one dimension for a potential V=−gγe−γR, R>δ,=∞,      R<δ,in the limit γ → 0. The correlation function is nonvanishing in the transition region; it vanishes outside. Investigation of the P-L isotherms (where L is the one-dimensional volume) shows a discontinuity in the first derivative at the transition points.
Quantization of the Generalized Hamiltonian
Authors: Hayes C. F.
Published: February 2004

Quantization of systems described by Lagrangians with higher-order derivatives is performed. It is shown that the usual Lagrangian with first-order derivatives may be consistently replaced by one with second-order derivatives, the resulting wavefunction being one of a mixed representation.
On the Renormalization of the Susceptibility of a Fermi Liquid
Authors: Amit Daniel J.
Published: February 2004

It is shown that the susceptibility of a normal Fermi liquid can be renormalized without using Ward identities for the derivatives of the mass operator with respect to the magnetic field. The procedure is completely analogous to the renormalization of the compressibility. The result which expresses the susceptibility in terms of Landau parameters is correct only to lowest order in temperature. The behavior of higher-order terms in temperature is discussed.
Potentials for Three-Body Systems
Authors: Whitten R. C.
Published: February 2004

Simple expressions for the Coulomb, Gaussian, and harmonic-oscillator potentials acting between pairs of particles in a three-body system are developed. Each expression consists of an expansion in the S-wave generalized angular-momentum eigenfunctions for three particles.
Linear Physical Chains with Sturm-Liouville Characteristic Polynomials
Authors: Cook F. L. , Jayne J. W.
Published: February 2004

This paper deals with the existence and construction of linear physical chains whose characteristic (secular) polynomials are essentially one of four classical types: Hermite, generalized Laguerre, generalized Bessel, or Jacobi. Each of the results is useful for determining the natural frequencies (normal frequencies or eigenvalues) of the systems involved. A chain of coupled harmonic oscillators or the corresponding electrical analog can be regarded as a prototype of the systems under consideration. Chains of both arbitrary finite order and infinite order are considered. Let N be a prespecified positive integer. Consider a finite sequence {Sn}n=1N of linear dissipationless spring-mass chains in which Sn consists of masses m0, m1, …, mn−1 and springs with spring constants k0, k1, …, kn, and in which Sn+1 is obtained from Sn by attaching mass mn and spring with spring constant kn+1. Sn is connected to a wall by the spring having spring constant kn, but the chain may be free at the other end. In this case S1 is to consist only of mass m0 and spring with spring constant k1. Three major results relating to such a sequence are obtained. First, given a positive integer N, a procedure is developed whereby an existing Nth-order spring-mass system can readily be tested to determine whether the characteristic polynomials φ1, φ2, …, φN associated with chains S1, S2, …, SN are all classical polynomials of a single type; and if so, which type. The testing procedure can also be extended to the infinite-order case. Secondly, by means of large classes of examples, it is demonstrated that physical systems of any preassigned order N can actually be constructed so that for 1 ≤ n ≤ N the characteristic polynomials of Sn are all a specified one of the four classical types. Finally, it is shown that of the four possible kinds, only Jacobi- and Laguerre-type infinite-order systems can be generated; and the latter type can occur only if relatively stringent conditions on the physical parameters are satisfied.
Representation Theory of SP(4) and SO(5)
Authors: Holman Wayne J.
Published: February 2004

The basis states for all the irreducible unitary representations of Sp(4) are constructed by means of a calculus of boson operators. The Gel'fand states are explicitly expanded in terms of their constituent Weyl patterns. In terms of these states the matrix elements of finite rotations in five dimensions are obtained.
Concerning the Zeros of Some Functions Related to Bessel Functions
Authors: Boyer Timothy H.
Published: February 2004

The real zeros of the Riccati-Bessel functions (12πx)12Jv(x), (12πx)12Yv(x), of their derivatives d[(12πx)12Jv(x)]/dx, d[(12πx)12Yv(x)]/dx,and of their cross products 12πx[Jv(x)Yv(Kx) − Yv(x)Jv(Kx)],ddx[(πx2)12Jv(x)]ddx[(πx2)12Yv(Kx)] − ddx[(πx2)12Yv(x)]ddx[(πx2)12Jv(Kx)]are investigated. Expansions analogous to those provided by McMahon and Olver for the zeros of the Bessel functions are obtained for the zeros of the derivatives of the Riccati-Bessel functions. The analysis of Kalähne for the zeros of the cross product of Bessel functions is considerably expanded and analogous results are obtained for the zeros of the cross product of the derivatives of the Riccati-Bessel functions. Included are derivations of the expansions for large zeros at fixed v, of asymptotic expansions for large v at fixed number of the zero, and also asymptotic expansions for the zeros as K→1 and K→∞. Figures illustrating the behavior of the zeros are provided for v = l + ½, where l is an integer. These zeros correspond to the TE and TM electromagnetic normal modes inside a conducting spherical shell and in the region between two concentric conducting shells.
Diffraction of Plane Acoustic Waves and Pulses as a Singular Perturbation Problem
Authors: Harper Edward Y.
Published: February 2004

The diffraction of plane waves and pulses by cylindrical cavities is studied as a singular perturbation problem for long waves and broad pulses. The solution, which is obtained to a given order of approximation by the method of matched asymptotic expansions, is applicable to arbitrary cavity shapes and, in the case of pulse diffraction, incident profiles of arbitrary form.
Kernel Integral Formulas for the Canonical Commutation Relations of Quantum Fields. II. Irreducible Representations
Authors: Hegerfeldt Gerhard C.
Published: February 2004

Continuing our investigation of the kernel or group integral for the canonical commutation relations introduced by Klauder and McKenna, we prove that a representation fulfilling any sort of kernel integral formula is irreducible. This has been conjectured by Klauder and McKenna. After collecting some auxiliary results, a complete classification of all representations is given for which a kernel integral formula in the form of a limit superior holds. It is shown that these are just the partial tensor-product representations and that the limit superior can be replaced by an ordinary limit over a fixed subsequence, thus allowing the transition from norms to scalar products. Then the basis-independent kernel integral in the form of a sup lim¯ is investigated. Here the supremum is taken over all bases of the test-function space. Under a not-very-strong irreducibility assumption, we show that this can be reduced to the vacuum functional and that there exists a fixed sequence of subspaces of the test-function space such that the sup lim¯ can be replaced by an ordinary limit which again allows a transition to scalar products. The results are strikingly similar to the case of cyclic field. This tempts us to conjecture that a representation fulfilling a kernel integral formula is both irreducible and cyclic with respect to the field just as in the case of finitely many degrees of freedom.
Relativistic Analogs of Scalar-Tensor Cosmologies
Authors: McIntosh C. B. G.
Published: February 2004

Relativistic analogs of Brans-Dicke and Hoyle-Narlikar scalar-tensor cosmologies are given in terms of two- or three-fluid models. Each fluid has an equation of state of the form pressure = const × density. The models discussed have the matter and scalar fluids interacting and are expressed by different forms of Ei, where this is the total new rate of transfer of energy per unit volume to the ith fluid from all other fluids.
Semisimple Subgroups of Semisimple Groups
Authors: Stone Anthony P.
Published: February 2004

The projection theorem for weights of a representation of a semisimple group G on restriction to a semisimple subgroup is derived, and the existence of a subgroup corresponding to a given projection is discussed. Dynkin's definition of the index of a simple subgroup is extended to the case of G being only semisimple, and the geometrical meaning of the index is given. A method is developed for finding branching rules for both regular and nonregular subgroups. Explicit general formulas for the branching multiplicities are obtained for all cases when G is of rank 2 and for B3(R7) → G2. Applications to the construction of weight diagrams and the ``state-labeling'' problems for B2 and G2 are mentioned.
An Axiomatic Formulation of the Theory of Coinciding Simple Poles and Multiple Poles
Authors: Nakanishi Noboru
Published: February 2004

In the Bethe-Salpeter formalism, the scattering Green's function is known to have multiple poles synthesized out of coinciding simple poles. The present paper proposes an axiomatic approach to the problem of finding the residues of the multiple poles in terms of those of M coinciding simple poles. The latter residues are regarded as finite-dimensional, mutually orthogonal projection operators on a reflexive Banach space and its dual. Then various properties of the residues of the multiple poles are derived without recourse to the original Bethe-Salpeter equation, and especially it is shown mathematically that they can be decomposed into a direct sum of operators which commute with the Bethe-Salpeter operator. The residues of multiple poles are explicitly determined in two particular cases, M = N + 1 and M = 2, where N denotes the highest order of the singularities (in a parameter) of the residues of the coinciding simple poles.
Labeling States and Constructing Matrix Representations of G2
Authors: Patera J.
Published: February 2004

A method is developed for labeling G2-internal states and for finding the matrices representing G2-generators. The simple Lie algebra G2 is embedded into A6, whose representation spaces are labeled by Gel'fand patterns. For a given irreducible finite-dimensional representation Ψ(G2) of G2, an optimal representation Φ(A6)⊃Ψ(G2) is chosen, and a lemma is formulated which enables us to select the subspace R(Ψ) from the representation space R(Φ).
Symmetries of the Racah Coefficients
Authors: Minton B. M.
Published: February 2004

A new symmetry of the Racah coefficients is derived using a property of a generalized hypergeometric function of unit argument. The symmetry is similar in appearance, though not derivation, to that given by Regge.
Diagrammatic Perturbation Expansion for Ensembles of Random Matrices
Authors: McDonald J. F. , Favro L. D.
Published: February 2004

A method for obtaining a perturbation expansion of various eigenvalue distributions corresponding to a certain class of perturbed ensembles of random matrices is given. The terms in the expansion can be written down immediately as diagrams analogous to those used in other kinds of perturbation theory. Further, part of the expansion can be summed explicitly, and the result of the summation read off the diagrams. In addition, a new perturbing ensemble is introduced. It has the advantage that the number of matrix elements which are perturbed simultaneously and the size of the perturbation can be varied independently. The expansion given is an expansion in the number of perturbed matrix elements rather than the usual expansion in the size of the elements. Finally, the conditions for convergence of the expansion are discussed.
Method of Constructing General Solutions of Certain Nonlinear Differential Equations Describing Plasma Oscillations
Authors: Barrett E. B.
Published: February 2004

A general solution is derived for a system of nonlinear partial differential equations describing longitudinal plasma oscillations. The method of construction of the solution involves the imposition of arbitrary functional relationships among the integrals of an associated system of ordinary differential equations.
Two-Dimensional Hydrogen Bonded Crystals without the Ice Rule
Authors: Sutherland Bill
Published: February 2004

Models of 2-dimensional hydrogen bonded crystals obeying the ice rule, which previously have been solved exactly, are generalized by removing the ice rule. Many of the peculiar and unique properties of the solutions for the constrained models are now explained by showing that these models, above critical temperature, are equivalent to new unconstrained models at critical temperature. In addition to locating the critical temperature for the general but unsolved models, we locate the singularities of the ground state energy of a related ring of interacting spins.
Equations of the de Broglie Wave Field and Their Relationship to Riemann's Curvature Tensor
Authors: Kulhánek J.
Published: February 2004

The equations of the de Broglie wave field (field equations) [J. Kulhanek, Nuovo Cimento Supp. 4, 172 (1966)] under special conditions require a very particular geometry together with a specific interpretation of the curvature scalar. The purpose of the present paper is to show that the same condition turns the conservation law (which is a consequence of the field equations) into an identity and that the Rainich [Nature 115, 498 (1925)] decomposition of Riemann's curvature tensor gives only one component.
N-Representability Problem: Particle-Hole Equivalence
Authors: Ruskai Mary Beth
Published: February 2004

It is shown that every p matrix has a dual matrix which describes the p-hole properties of the system. A general procedure is given for using particle-hole equivalence to obtain new N-representability conditions. In particular, necessary and sufficient conditions are given for both pure and ensemble N-representability of p matrices whose 1-rank is N + p.
Existence of Charged States of the Yang-Mills Field
Authors: Loos Hendricus G.
Published: February 2004

For a tentative choice of configuration space Ω, it is proved that the Yang-Mills field, self-interacting but not coupled to other fields, has states with a nonvanishing isospin component if gauge-invariant quantization is used. This is shown by proving existence of a solution for the elliptic boundary-value problem ▿β▿βζi(x) = 0 on all of 3-dimensional Euclidean space, subject to the asymptotic condition ζi = ci + O(r−1), ∂β∂βζi = O(r−4) as r → ∞, where ci are constants; ▿β is the covariant derivative belonging to the spatial Yang-Mills potentials bβi(x). The existence proof is a modification of Schauder's proof to an unbounded domain. Ω consists of all numerical real multiplet functions bβi(x) which are of order O(r−2) as r → ∞, have ∂βbβi = O(r−4), and satisfy certain smoothness conditions. Also, for this configuration space, the problem of existence of equivalent transverse potentials is reduced to a simpler uniqueness problem. In the classical theory, the existence of solutions ζi implies that the constraint equation can be satisfied for any choice of the ``covariant-transverse'' part of B0βi within a very large class, by a unique ``covariant-longitudinal'' part of B0βi, if the potentials bαi(x) have the full SU(2) as holonomy group.
Singularity Structure of Causal Distributions and Restricted Equal-Time Limits
Authors: Otterson P. J. , Sucher J.
Published: February 2004

We study aspects of the space-time singularity structure of several classes of causal distributions, including the cases usually encountered in perturbation theory. Various definitions of restricted equaltime limit are considered which allow for the presence of highly singular Schwinger terms. It is shown that, with one definition, every causal distribution has a restricted equal-time limit. A form of sum rule valid even in the presence of singular Schwinger terms is given.
Representations of Local I-Spin Charge Densities. I. Spaces Where Each I Occurs Only Once
Authors: Mendes Rui V. , Ne'eman Yuval
Published: February 2004

An approach to the problem of representation of the algebra of currents that puts essential emphasis on the study of infinite-parameter Lie algebras is proposed. As an example, a class of irreducible Hermitian representations of the commutation relations [Vi(φ1), Vj(φ2)] = iεijkVk(φ1φ2), where the φ's are elements of a commutative algebra with identity, is derived. The dependence of the representations on the algebra {φ} is completely characterized by two functional equations that are explicitly solved, for {φ} an algebra of polynomials. States of well-defined momentum and rotational properties are constructed using translational and rotational invariance and forming direct integral spaces. The representations so constructed are seen to belong to two distinct subclasses, distinguished by the vanishing or nonvanishing of a length parameter |η|. The subclass with |η| = 0 is unbounded in isospin and has the trivial momentum-transfer structure characteristic of field-theoretical point particles. On the other hand, the spaces characterized by |η| ≠ 0 are bounded in isospin and suited to describe particles with structure. A brief discussion on how to derive invariant form factors from the results here presented is included.
Inverse Problem for a Cylindrical Plasma
Authors: Degasperis Antonio
Published: February 2004

We study the Maxwell equation for the electric potential inside a neutral nonuniform cylindrical plasma in an external oscillating electric field, from the point of view of the inverse problem. The logarithmic derivatives of the radial Fourier components of the electric potential at the edge of the cylinder are considered as experimental data. We obtain an explicit and exact representation of the electron density in terms of the high frequency behavior of the experimental data. The general analyticity properties in the complex-frequency plane are also discussed.
Perturbation Theory for Large Coupling Constants Applied to the Gauss Potential
Authors: Müller Harald J. W.
Published: February 2004

As an example of a perturbation technique for large coupling constants g2, we investigate the solutions and eigenvalues of the Schrödinger equation for a Gauss potential. In particular, we obtain the regular solution, valid for r2 < 1/|g|, in terms of confluent hypergeometric functions by expanding the potential in the neighborhood of the origin. The Jost solution is obtained in an analogous manner in terms of a certain integral and is valid for r2 > 1/|4g|. Both solutions are eigensolutions belonging to the same eigenenergy E = k2. These eigenvalues are derived in the form of large-g asymptotic expansions which are useful and valid over a wide range of g. A noteworthy aspect of the investigation is the close analogy of the underlying mathematics with that of well-known periodic equations.
Parastochastics
Authors: Frisch U. , Bourret R.
Published: February 2004

The generalized commutation relations AiBj − λBjAi = ΓijI are introduced, where Ai and Bi are adjoint of each other, I is the identity, and Γij is a real covariance. For λ = +1 (−1, or 0, respectively) the parastochastic function Ai + Bi is given an interpretation in terms of Gaussian random functions (a two-valued stationary Markov process, or infinite symmetric random matrices of the type considered by Wigner in connection with energy levels of heavy nuclei, respectively). In the Fock-space realization, Ai and Bi appear as destruction and creation operators for bosons (fermions or boltzmannons, i.e., distinguishable particles, respectively). A few purely algebraic theorems are proved, which are applied to linear stochastic equations (equations with random coefficients). Existence and uniqueness being presupposed, mean Green's functions are shown to satisfy closed master equations. A linear functional differential master equation is obtained for equations with Gaussian coefficients. It is shown that the often-used first cumulant-discard closure assumption, which leads to a very simple master equation, is exact for differential equations with a two-valued stationary Markovian coefficient. A parastochastic reformulation of the theory of Kraichnan is given, and his nonlinear master equations are, for the first time, rigorously derived without any recourse to perturbation theory or to diagrams. Kraichnan's random-coupling model is obtained by replacing scalar stochastic quantities by Wigner matrices or, equivalently, bosons by boltzmannons (i.e., changing λ from +1 to 0). Finally, the nonlinear Kraichnan equation,dy(t)/dt=− ∫ 0ty(t−t′)Γ(t−t′)y(t′)dt′,is reduced to a linear parastochastic equation in the Fock space; existence, uniqueness, boundedness, and asymptotic behavior are obtained.
On Hidden-Variable Theories
Authors: Gudder Stanley P.
Published: February 2004

An abstract definition of a general hidden-variables theory is given, and it is shown that such a theory is always possible in the present framework of quantum mechanics and is, in fact, unique in a certain sense. It is noted that the Bohm-Bub hidden-variables example is contained in this theory and an attempt is made to clarify the position of this theory with respect to hidden-variable impossibility proofs. The general definition is used in the consideration of quantum-mechanical ordering and the measurement process.
Mathematical Description of a System Consisting of Identical Quantum-Mechanical Particles
Authors: Kummer H.
Published: February 2004

In this paper a rigorous description of a system consisting of identical particles is given for which the particle number is a superselection rule. A state of such a system is described by a sequence of density operators D = (D0, D1, …, Dn, …), where Dn acts in n-particle space and the asymptotic behavior is determined by the requirement ∑ n=0∞kn|Dn|<∞  for all  k=1,2,…,where | | denotes the trace norm. The (bounded) observables in turn are described by sequences of bounded self-adjoint operators: B = (B0, B1, …, Bn, …) such that sup lim nk−n ‖Bn‖<∞  for some  k=1,2,…. The expectation value of the observable B in the state D can be expressed as 〈B〉D=(Γ(B)|D)=(B|L(D)),where (B|D)= ∑ n=0∞Tr(BnDn);Γ denotes the expansion operator, whereas L stands for its adjoint, the contraction operator. The analog to the n-representability problem, i.e., the so-called representability problem, is put forward and its solution is connected with the solutions of the n-representability problem for different n. Finally, a possible mathematical foundation of the BCS theory is given.
Polariton-Phonon Interaction in Molecular Crystals
Authors: Mavroyannis C.
Published: February 2004

A general theory is presented concerning the interaction between the polaritons and the acoustic phonons in molecular crystals. Using a one-phonon approximation to truncate the hierarchy of the Green's functions involved and disregarding mixing of different polariton bands, we derive an expression for the dielectric permeability of the crystal. The absorption coefficient for the coupled polariton-phonon spectrum is found to have an asymmetric Lorentzian lineshape even if the frequency dependence of the energy shift and spectral width is neglected. The damping function causing the asymmetry of the spectral line depends entirely on the coupling between the dressed electron subsystem and the phonon field. Expressions are developed for the energy shift and spectral width of the resonance line, and their temperature dependence is discussed. Far from the resonance peak, the frequency and temperature dependence of the absorption coefficient is established. In the transparent region of frequencies of the crystal, the expression for the absorption coefficient consists of two terms that have delta-function distributions and are peaked at different frequency regions, depending on whether or not the polariton and the phonon fields are coupled. In the limiting case where retardation can be ignored, the bare exciton-phonon interaction is discussed. The average energy of the crystal resulting from the polariton-phonon interaction at finite temperatures has been derived in a closed form.
Construction of Weight Spaces for Irreducible Representations of An, Bn, Cn, Dn
Authors: Gilmore Robert
Published: February 2004

An algebraic technique is presented by means of which the weight space for the irreducible representations (λ) of An, Bn, Cn, Dn can be constructed from the weight spaces associated with the representations (λ′) of the subalgebras An−1, Bn−1, Cn−1, Dn−1. Since each chain ends with A1, all weight spaces of the classical simple Lie algebras associated with (λ) can be constructed, ultimately, from the well-known representations of A1.
Note on Relating Pfaffians and Hafnians with Determinants and Permanents
Authors: De Luca A. , Ricciardi L. M. , Vasudevan R.
Published: February 2004

In connection with renormalization problems in quantum field theory, Pfaffians and Hafnians are considered. A noteworthy expansion of determinants and permanents is given, in terms of Pfaffian-like and Hafnian-like objects, that immediately leads to the known reduction of a determinant to a single Pfaffian. Finally, some auxiliary results are presented.
Remarks on Morse Theory in Canonical Quantization
Authors: Hurt Norman E.
Published: February 2004

The Morse index is studied in the theory of canonical quantization of dynamical systems. Standard results on the Hodge index and vanishing theorems are translated into the language of quantizable dynamical systems.
Gravitational Radiation: Cutting the Tail
Authors: Hallidy William H. , Janis Allen I.
Published: February 2004

Using the Newman-Penrose spin-coefficient approach to gravitational radiation, we consider necessary conditions for stationary-radiative-stationary transitions to occur between states in a Riemannian space-time which satisfies the empty-space Einstein field equations everywhere outside of a spatially bounded timelike cylinder. It is found that for axially symmetric radiation of finite multipole expansion such transitions cannot occur; however, a model has been constructed for nonaxially symmetric radiation for which these transitions can occur to a certain asymptotic order in a relevant parameter while satisfying the Newman-Penrose conservation laws.
Galilean Relativity, Locality, and Quantum Hydrodynamics
Authors: Garrison John C. , Morrison Harry L. , Wong Jack
Published: February 2004

In this work we study the consequences of locality and Galilean covariance for the operators that occur in Landau's quantum hydrodynamics. We specifically consider the following requirements: (1) Galilean covariance of the velocity field, (2) locality of the velocity field, and (3) Landau's assumption that the momentum density is a symmetrized product of the velocity and density operators. It is demonstrated that the density-velocity commutation relation of the Landau theory is essentially a direct consequence of (1) and (2). The addition of (3) is sufficient to determine the velocity-velocity commutation relation, also in agreement with Laudau. We further show that the density-velocity commutation relation, independent of (3) or any specific form for the velocity field, is inconsistent with the nonnegative character of the local density.
Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0 Subject to the Initial Condition P(x,y,0)=Φ(x,y)
Authors: Goldstein M. E.
Published: February 2004

A simple form of the solution to the differential equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0,subject to the initial condition P(x,y,0)=Φ(x,y),is given.
Relation between the O(4) and O(3, 1) Partial-Wave Expansions
Authors: Akyeampong D. A. , Boyce J. F. , Rashid M. A.
Published: February 2004

The t = 0, O(3, 1), expansion of a square-integrable equal-mass-scattering amplitude is considered. By assuming the existence of an unsubtracted dispersion relation, it is explicitly shown to continue to an O(4) expansion for (m1 − m2)2 ≤ s ≤ (m1 + m2)2. The continuation requires the introduction of O(3, 1) signature; nonsense-channel terms arise; however, their complete sum is zero.
On the Ising Model with Long-Range Interaction. II. Critical-Region Analysis
Authors: Thompson Colin J. , Siegert Arnold J. F. , Vezzetti David J.
Published: February 2004

The high-temperature expansion for the free energy in powers of γ (the reciprocal of the range of interaction) developed in a previous paper is studied in the critical region. In terms of the graphology introduced in the previous paper, it is proved that the ring diagrams give the dominant contribution in the critical region, if and only if the integral R(νγ)=(12π)D ∫ 2π… ∫ 0g(ω)dDω1−νγg(ω)diverges no worse than logarithmically at [the Curie-Weiss (CW) point] νCW = J/kTCW = [γg(0)]−1, where D denotes dimensionality and γg(ω) the Fourier transform of the interaction potential. The results are in agreement with various model results, and it is conjectured that the above condition is also a necessary and sufficient condition for the existence of a phase transition.
Space-Temperature Correlations in Quantum-Statistical Mechanics
Authors: Kunkin William , Percus Jerome K.
Published: February 2004

The method of functional differentiation, used in classical statistical mechanics to obtain approximate integral equations for the pair distribution function, is extended to quantum systems obeying Maxwell-Boltzmann statistics. The grand partition function is written as a path integral, and space-temperature distributions are generated from it by successive functional differentiation. Distributions can be expanded in powers of an external potential via a functional Taylor series. When the series is truncated so that no distributions higher than second order enter and the external potential is specialized to one arising from a fixed particle in the system, coupled integral equations result for the two kinds of pair distributions. The first-order Ursell function calculated from these equations yields the Montroll-Ward ring summation for the grand potential. This approximate Ursell function determines also the Fourier transform of the momentum density (useful in calculating the p = 0 occupation number). Although divergences appear in the low-temperature limit, they can be removed by a simple modification of the independent functional. An extension to Fermi-Dirac and Böse-Einstein statistics is indicated at appropriate places in the text.
Recursion and Symmetry Relations for the Clebsch-Gordan Coefficients of the Homogeneous Lorentz Group
Authors: Anderson R. L. , Rączka R. , Rashid M. A. , Winternitz P.
Published: February 2004

Recursion and symmetry relations are obtained for the Clebsch-Gordan coefficients associated with the coupling of two SL(2, C) principal-series representations. An explicit procedure based on the recursion relations which are not restricted to the case of principal-series representations is given for generating a set of coefficients from a single ``initial'' coefficient. A program for the study of a possible connection, through analytic continuation, between the coupling coefficients for finite-dimensional representations and those for the infinite-dimensional case is presented.
On the Solution of the Differential Equation (∂2∂x∂y+ax∂∂x+by∂∂y+cxy+∂∂t)P=0
Authors: Kolsrud M.
Published: February 2004

The following solution is obtained: P(x,y,t)=e−γxy−δP0(e−αx,e−βy,ε),where P0(x, y, t) is the solution when the constants a, b, and c are zero, and where the time functions α, …, ε are given explicitly.
Theory of Neutron-Wave Propagation through an Interface
Authors: Baldonado O. C. , Erdmann R. C.
Published: February 2004

Neutron-wave propagation in a system consisting of two adjacent half-spaces having different properties is investigated using four models: (A) one-speed diffusion theory; (B) one-speed transport theory; (C) energy-dependent diffusion theory; (D) energy-dependent transport theory. An oscillating exponential source of neutrons is located in the left medium. Isotropic scattering is assumed for the transport models B and D, and a one-term degenerate kernel is used for the energy-dependent models C and D. Elementary solutions for each model are obtained and are used to construct the general solution. The resulting solutions are identified in terms of incident, reflected, and transmitted components of the wave. Both discrete and continuum solutions are seen to exist for models B, C, and D. The analyses given are exact except for model C, where the continuum solutions are neglected in the evaluation of the coefficients. The expansion coefficients in model B are evaluated by solving a Riemann-Hilbert problem with discontinuous coefficients. A similar, but generalized Riemann-Hilbert problem was solved to obtain the expansion coefficients in model D.
Infilling for NUT Space
Authors: Jackson J. C.
Published: February 2004

A method of generating interior NUT solutions from spherically symmetric ones is presented. It is similar to the well-known ``derivation'' of the corresponding vacuum metric from the Schwarzschild solution. These sources turn out to consist of material bridges, joining otherwise independent vacuum regions through a ``wormhole.'' It is shown that this matter cannot have an equation of state which is physically reasonable everywhere.