bluuebunny/crossref_metadata_2025 huggingface dataset:
Four-Body Problem: A Complete System of Angular Functions
Authors: Galbraith Harold William
Published: February 2004

A complete set of angular functions for the four-body problem is given. Such functions form the basis for irreducible representations of the orthogonal group O9, reduced according to the chain O9⊃O31×O32×O33⊃O3⊃O2. The transformation properties of the functions are given and hence a matrix representation of the permutation group on four objects is explicitly specified. The reduction of this representation yields functions suited to Bose-Einstein or Fermi-Dirac statistics.
Functional Calculus Theory for Incompressible Fluid Turbulence
Authors: Rosen Gerald
Published: February 2004

A functional integral representation for the space-time Hopf characteristic functional is derived from the probability theory for a statistical ensemble of velocity fields that satisfy the Navier-Stokes equation for boundary-free incompressible fluid flow. The functional integral representation involves a pair of real vector field integration variables denoted by u and v, and the evaluation of the integral is performed in two steps. First, the integration over the field variable u is effected exactly in the general case by applying methods of explicit functional integration. Second, the resulting functional integral over the field variable v is reduced to a form amenable to specialized analysis by applying a suitable transformation of the integration field variable v → z. Specializing to mathematically defined ``C-dominant turbulence,'' the final functional integration over the field variable z is effected exactly and yields a characteristic functional of Gaussian form. The two-point velocity correlation tensor for C-dominant turbulence is then obtained from the characteristic functional.
SL(2, C) Representations in Explicitly ``Energy-Dependent'' Basis. I
Authors: Szegö K. , Tóth K.
Published: February 2004

Unitary and nonunitary representations of the SL(2, C) group are investigated in such a basis, in which the subgroup diagonalized is that one which in the four-dimensional representation leaves invariant the 4-vector pμ = (½(1 + v), 0, 0, ½(1 − v)) for an arbitrary real value of Pμ2=v. The split of the representation space into irreducible subspaces changes smoothly when varying the value of v. The formalism is of importance in physical theories which postulate analyticity requirements and Lorentz invariance simultaneously (e.g., Regge and Lorentz pole theory). In this paper we construct explicit basis functions of the representation spaces.
Strong Forces
Authors: Anderson J. T.
Published: February 2004

A new analytic function method is utilized to study self-consistent vector interactions in the non-relativistic case. A mass formula is obtained as a function of the current and charge densities and found to yield particle radii near the Compton lengths for a number of elementary particles. With spin-current interactions included, the mass formula gives the baryon masses within 10% at densities corresponding to the Compton lengths. The results lead to definite conclusions regarding the nature of strong forces.
Percolation Processes. II. The Pair Connectedness
Authors: Essam John W.
Published: February 2004

The probability that two sites of a crystal lattice belong to the same cluster (the pair connectedness) is shown to play an important role in percolation theory. Use of the linked-graph method to obtain low-density series expansions leads to the discussion of topological invariants for rooted graphs. These are related to the k-weights which arose in a previous investigation of the mean number of clusters. The mean size of clusters is related to the pair connectedness via sum rules.
Discrete Lorentz and Singleton Representations of the Universal Covering Group of the 3 + 2 de Sitter Group
Authors: Jaffe Leon
Published: February 2004

We consider the relationship between the discrete reduction of S̄O(3, 2) with respect to S̄O(3, 1) and the singleton reduction of S̄O(3, 2) with respect to S̄O(3)⊗S̄O(2).
Generating Function of the N-fold Photoelectric Counting Distribution for Gaussian Light
Authors: Cantrell C. D.
Published: February 2004

An exact expression is obtained for the generating function of the N-fold (i.e., N-detector) photoelectron counting distribution for cross-spectrally pure Gaussian light, in terms of the onefold generating function. It is assumed that the counting times at the different detectors are all equal, but not necessarily short compared to the coherence time of the light. In cases where the onefold generating function can be calculated, a closed formula for the N-fold generating function can be obtained.
Generalized Hidden Variables Theorem
Authors: Deliyannis Platon C.
Published: February 2004

Two versions of the hidden variables theorem are presented with minimum hypotheses. The second is intended to be an answer to a question raised by Jauch and Mackey regarding the existence of approximately dispersion-free states.
Generalized Rajnak-Wybourne Identity
Authors: Oreg J.
Published: February 2004

The representation of the electrostatic interaction by unit operators makes it possible to derive a general equation which provides many identities. The Rajnak-Wybourne identity is obtained as a special case. Some interesting examples are considered. The application of the identities to the construction of the electrostatic energy matrices by computer is discussed.
Abstract Formulation of the Quantum Mechanical Oscillator Phase Problem
Authors: Ifantis Evangelos K.
Published: February 2004

The phase operators ``cosine'' and ``sine'' are characterized as a special and peculiar class of tridiagonal operators, defined on an abstract separable Hilbert space. The two disjoint sets of these operators, which lie on the unit sphere of the algebra of bounded operators, are convex and closed in the uniform topology. The whole treatment gives a new and systematic aspect to the quantum mechanical oscillator phase problem.
Approach to the Eulerian-Lagrangian Problem for Sound Propagation in Continuous Stochastic Media
Authors: Neubert Jerome A.
Published: February 2004

The formal solution of the Eulerian-Lagrangian problem for sound propagation in continuous stochastic media is reframed so that the emphasis on the need for complete knowledge of the statistical nature of the Lagrangian functional of interest is shifted to the need for knowledge of the asymptotic behavior of certain stochastic Lagrangian integrals which result from the application of a central limit theorem for stochastic functionals. The resultant practical relation for calculating the Eulerian ensemble expectation corresponding to the Lagrangian functional in question is shown to depend in a natural manner upon the Lagrangian path spreading and, in the case of a statistically isotropic medium, to reduce to the proper nonstochastic limit.
One-Parameter Subgroups of Unitary Groups with Indefinite Metric and in Particular of the Conformal Group
Authors: Belinfante J. G. F. , Winternitz P.
Published: February 2004

Motivated by a problem concerning two-variable expansions of covariant scattering amplitudes, and by recent theories involving indefinite metrics and the conformal group, we study subgroups of unitary groups with indefinite metric. The one-parameter subgroup case reduces to finding canonical matrices for pseudo-Hermitian operators with respect to orthonormal bases. By decomposing the space on which such operators act as far as possible as an orthogonal direct sum of invariant subspaces, one obtains invariant subspaces having indecomposable primary components. The general results, summarized in tables of canonical forms valid for any finite dimension, are supplemented by more detailed tables for low dimensions, including the case of the conformal group of space-time.
Analyticity of Green's Functions of Dilute Quantum Gases
Authors: Ruelle David
Published: February 2004

Previous results on reduced density matrices of quantum gases are used to obtain theorems on the existence and analyticity of Green's functions.
An Approximate Solution of the Vacuum Static Case of Spherical Symmetry in Brans-Dicke Theory
Authors: Mahanta M. N. , Reddy D. R. K.
Published: February 2004

Starting from the usual variational principle, the gravitational field equations for the vacuum static case of spherical symmetry are obtained in Brans-Dicke [Phys. Rev. 124, 925 (1961)] scalar-tensor theory following a technique due to Weyl [H. Weyl, Space-Time-Matter (Dover, New York, 1922)]. The field equations being highly nonlinear, an approximate solution to the second order is presented. It is observed that the results of gravitational redshift, deflection of light, and the rotation of the perihelion of Mercury are in agreement with the earlier results obtained by Brans, Dicke, and Heckmann. But the method, being simpler, can be used in solving other problems in the theory.
Asymptotic Equivalence of Equilibrium Ensembles of Classical Statistical Mechanics
Authors: Galgani Luigi , Manzoni Luciano , Scotti Antonio
Published: February 2004

We start from the solution of the problem of the thermodynamic limit for microcanonical entropy as given by Ruelle and extend his method to solve the analogous problem of consistency, within the same ensemble, for the Legendre transforms of entropy. We solve then in a unified way the problem of the asymptotic equivalence of ensembles.
Stability of Time-Dependent Particlelike Solutions in Nonlinear Field Theories. II
Authors: Anderson David L. T.
Published: February 2004

It is shown that particlelike solutions of the form ψ = φ(r)e−iωt to the nonlinear field ∇2ψ−c−2∂2ψ/∂t2=κ2ψ−μ2ψψ*ψ+λψψ*ψψ*ψcan exist for a certain range of the field parameters. The stability of the lowest-order solution of the above form is examined by first-order perturbation theory and also by direct integration of the perturbed field. Both methods indicate the existence of stable particlelike states, some of which have the further asset of a positive-definite energy density.
O(2, 1) and the Harmonic Oscillator Radial Function
Authors: Armstrong Lloyd
Published: February 2004

The radial functions of the three-dimensional isotropic harmonic oscillator are shown to form bases for unitary representations of the noncompact group O(2, 1). The functions rs are shown to transform simply under the action of the generators of this group. As a result, matrix elements of rs can easily be evaluated. Selection rules on these matrix elements are obtained by studying Kronecker products of representations of O(2, 1).
Lattice Green's Functions for the Cubic Lattices in Terms of the Complete Elliptic Integral
Authors: Morita Tohru , Horiguchi Tsuyoshi
Published: February 2004

The real and imaginary parts of the lattice Green's functions for the simple cubic (actually the tetragonal), body-centered cubic, and face-centered cubic lattices, at the variable from −∞ to +∞, are expressed as a sum of simple integrals of the complete elliptic integral of the first kind. The results of the numerical calculations obtained with the aid of the formulas are shown by graphs.
Calculation of the Lattice Green's Function for the bcc, fcc, and Rectangular Lattices
Authors: Morita Tohru , Horiguchi Tsuyoshi
Published: February 2004

Formulas are provided which are convenient for the evaluation of the lattice Green's functions for the bcc, fcc, and rectangular lattices, at an arbitrary complex variable. The formulas involve the complete elliptic integral of the first kind with complex modulus; the integral has been found to be evaluated efficiently by the method of the arithmetic-geometric mean, generalized for the case with complex modulus. The expansions of the lattice Green's functions around the singular points are given for the bcc and fcc lattices. These lattice Green's functions diverge at a variable. The singular points responsible for the divergences are found to form one-dimensional lines.
Scaling Behavior of Gravitational Energy
Authors: Robinson David C. , Winicour Jeffrey
Published: February 2004

The transformation property of gravitational energy under scale transformations is presented in the context of a general asymptotically flat space-time. The relevance of scale transformations to the sign of gravitational energy is discussed. Arguments for the positive-definiteness of gravitational energy are presented and criticized.
Resonant Oscillations: A Regular Perturbation Approach
Authors: Mortell Michael P.
Published: February 2004

The resonant oscillations of a gas in a closed-end tube are treated. The time-periodic motion is given by a regular perturbation method in which the expansion parameter is the Mach number of the resulting flow. The solution at the first order exhibits a shock traveling in the tube, but, to this order, the waves do not interact. The interaction of the waves is calculated at the second order. The perturbation procedure proceeds systematically by an application of the Fredholm alternative at each stage.
Spatially Homogeneous Rotating World Models
Authors: Ozsváth István
Published: February 2004

We derive the Lagrangian function for four different rotating universes simultaneously. These models correspond in a certain sense to Gödel's ``symmetric case.''
Note on the Electrodynamics of Accelerated Systems
Authors: Post E. J. , Bahulikar D. D.
Published: February 2004

Some preliminary results concerning the experimental testability of the free-space constitutive relations are discussed in connection with some recent theoretical developments.
A Nonhomogeneous Boundary-Value Problem for the Linear Transport Equation for a Slab Geometry
Authors: Hintz Gerald R.
Published: February 2004

A nonhomogeneous boundary-value problem for the infinite slab of finite thickness is considered. In this problem, the slab receives radiation from a time-dependent source on one of its surfaces. The intensity of this radiation increases from zero at time zero until a later time t′0, after which the intensity is a function of direction only. This problem is solved in the strong sense. The asymptotic behavior of the solution is determined and related to results for steady-state problems in neutron transport theory and radiative transfer.
Phase Transitions in Binary Lattice Gases
Authors: Lebowitz J. L. , Gallavotti G.
Published: February 2004

We prove the existence of phase transitions in several kinds of two-component lattice gases: Some of these are isomorphic to spin systems and/or to fluids composed of asymmetrical molecules which can have different orientations. Among the models studied is one with infinite repulsion between particles of different species (hard cores), extending over arbitrarily many neighboring lattice sites. Some of these systems have been investigated previously in the mean field approximation and numerically.
Note on the New Symmetry of the Racah Coefficients
Authors: Yakimiw E.
Published: February 2004

It is shown that the ``new symmetry'' of Racah coefficients, recently derived in a paper by Minton [J. Math. Phys. 11, 3061 (1970)], does not exist.
Remark on Minton's Symmetry for Racah Functions
Authors: Joshi Vinaya
Published: February 2004

It is shown that the symmetry relation for Racah coefficients recently given by Minton holds only for an analytical continuation of the Racah coefficients to unphysical angular momenta, and even then is valid only under unrealistically stringent conditions.
Static Gravitational Fields. I. Eight Theorems
Authors: Das A.
Published: February 2004

In a fresh look on static gravitational fields in general relativity, eight new theorems have resulted. Also in the process of deriving theorems a new solution has emerged. In the first of these theorems an invariant necessary integral condition for the existence of a solution has been derived. Physically this condition corresponds to the equilibrium of matter. In the second theorem a scalar condition has been found which implies the flatness of the static gravitational universe. In the third theorem, it has been proved that there cannot occur any group of motion along ``the lines of forces.'' In Theorems 5 and 6, the questions of whether the spatial part of a static gravitational universe can be Einstein, projectively flat, or Stäckel are investigated. In the seventh theorem, the static gravitational field equations have been reduced to the geometrized equations in a spatial universe. In the last theorem, all conformastat gravitational universes have been found. One of these is the universe due to ``an infinite plate,'' and this is a new solution.
Prolate-Spheroidal Expansions of the Spin-Orbit, Spin-Spin, and Orbit-Orbit Operators
Authors: Matcha R. L. , Pritchard R. H. , Kern C. W.
Published: February 2004

Prolate-spheroidal expansions of the spin-orbit, spin-spin, and orbit-orbit operators are derived. These expansions are analogs of the Neumann expansion for 1/r12 and can be used to study the corresponding exchange interactions in diatomic molecules.
Poincaré-Irreducible Tensor Operators for Positive-Mass One-Particle States. I
Authors: Steiger Arno D.
Published: February 2004

The main objective of this article is the relativistic generalization of the ordinary SO(3)-irreducible spin tensor operators for particles with positive mass. Two classes of relativistic one-particle tensor operators are constructed. The tensor operators of the first class transform according to those representations of the Poincaré group that are induced by the one-valued unitary irreducible representations of the pseudo-unitary group SU(1, 1) which belong to the continuous principal and the discrete principal series. These tensors are operator-valued functions of a spacelike 4-momentum transfer. The tensor operators of the second class correspond to vanishing 4-momentum transfer. They transform according to those representations of the Poincaré group that are induced by the unitary irreducible representations of the pseudo-orthogonal group SO(3, 1) or its universal covering group SL(2C) which belong to the principal series. Both classes of Poincaré-irreducible tensor operators are constructed in a spin helicity basis for timelike 4-momentum by means of projection operators which are continuous linear superpositions of unitary operator realizations for the groups SU(1, 1) and SL(2C). The Clebsch-Gordan coefficients associated with the reduction into the two classes of Poincaré-irreducible tensor operators of a dyadic product of spin-helicity basis vectors are calculated.
Transmission of Electromagnetic Waves through a Conducting Plasma Slab
Authors: Wilcox Ralph M.
Published: February 2004

Some new approaches to the problem of transmission of electromagnetic waves through a finite conducting plasma slab, as formulated by Baraff, are presented. The two-point boundary value problem for the integro-differential equation of nonlocal wave interaction is reduced to a Cauchy system. It is pointed out that under circumstances where computational difficulties may be expected to occur with this Cauchy system a transformation to rotating coordinates will be beneficial. Consequently, a Cauchy system is derived for rotationally transformed equations also. Some alternative approaches are discussed, and an approximate perturbation formula is derived.
Geometrization of a Massless Complex Scalar Field
Authors: Ludwig Garry
Published: February 2004

This paper presents the necessary and sufficient conditions that a Riemannian geometry have as its source a massless complex scalar field.
Classification of the Harrison Metrics
Authors: d'Inverno R. A. , Russell-Clark R. A.
Published: February 2004

Harrison's 40 space-time metrics have been checked to see if they represent vacuum solutions. Four of them are found to be nonvacuum. The Petrov classification is found for all the metrics, and those of type D are placed in their (invariantly defined) Kinnersley classes.
Contributions of Spin-J Baryon Poles to πN → πN and πN → γN Amplitudes
Authors: Arif-Uz-Zaman
Published: February 2004

Contributions of baryon poles of spin J to the πN → πN and πN → γN amplitudes have been calculated using the Wigner-Bargmann formalism. An ambiguity arising from off-the-mass-shell continuation of the propagator has been discussed and a continuation which gives pure spin-J behavior of the propagator for timelike propagator momentum has been given. Moreover, it has been shown that the parts of the amplitudes (with timelike propagator momentum) containing the highest power of the cosine of the scattering angle are free of this ambiguity.
Electromagnetic Sources in a Moving Conducting Medium
Authors: Johannsen Günther
Published: February 2004

The problem of an arbitrary source distribution in a uniformly moving, homogeneous, isotropic, nondispersive, conducting medium is solved. The technique used is to solve the problem in the rest system of the medium and then write the result in an appropriate four-dimensional, covariant form which is valid in any inertial system.
Equivalence of Different Representations of the Generalized Bose Operator
Authors: Katriel J. , Adam G.
Published: February 2004

The infinite series representation of the generalized Bose operator given by Brandt and Greenberg is shown to be equal to an operator introduced by Demkov.
Functions Whose Poisson Brackets Are Constants
Authors: Roels Jacques , Weinstein Alan
Published: February 2004

A local normal form under canonical transformation is found for n independent functions of 2n variables, with the condition that the Poisson bracket of each pair of the functions be constant. The normal form, closely related to work of Lie, is used to prove a conjecture of Avez on 1-forms in involution and to obtain a criterion for n independent functions of 2n variables to be extendable to a canonical coordinate system. The last result has been obtained in different ways by Lie and Kruskal.
Remarks on the Existence of Solutions of the Two-Particle Lippmann-Schwinger Equation
Authors: Rajagopal A. K. , Shastry C. S.
Published: February 2004

We prove the following: The kernel Kl of the partial wave Lippmann-Schwinger (LS) equation for the lth partial wave with complex energy having positive- or negative-definite imaginary part belongs to the Hilbert-Schmidt (L2) class if the potential V is spherically symmetric and such that lim lim r→0 rδV(r)=0,−∞<δ<32,V(r)r→∞=O(r−η),η>12,(B) for V(r)=g/rα,1<α<32, the kernel K of the full Lippmann-Schwinger equation satisfies Tr {(K†)mKm}<∞,if α>(2m+1)/2m,m=2,3,⋯. For ½ < α ≤ 1, Tr {(K†)mKm} is not absolutely convergent for any finite m, even though, for each partial wave, Kl belongs to L2 class. An appendix deals with obtaining expressions for the T matrix in terms of eigensolutions of the mth iterated kernel when it belongs to L2 class.
Fredholm Methods in the Three-Body Problem. I
Authors: Newton Roger G.
Published: February 2004

It is shown that, for three particles interacting via potentials that are bounded and decrease at least as fast as r−72, the Green's function of the Schrödinger equation at physical energies can be calculated by the classical Fredholm methods for L2 kernels.
On the Two-Dimensional Ising Model with Random Impurities
Authors: Barouch Eytan
Published: February 2004

The McCoy-Wu treatment of the two-dimensional Ising model with random impurities is generalized to allow both vertical and horizontal interactions to vary randomly from row to row (while still keeping them constant in any row). If the random impurities are narrowly distributed, the order-one term in the specific heat at Tc is infinitely differentiable but nonanalytic.
Vector-Scalar Sector Solutions to the Spinor-Spinor Bethe-Salpeter Equation
Authors: Nakanishi Noboru
Published: February 2004

A new method is proposed to discuss the exact J = 0 vector-scalar sector solutions to the equal-mass spinor-spinor Bethe-Salpeter equation for the massless-meson exchange ladder model at the vanishing total 4-momentum. Under the assumption that all solutions belonging to a discrete spectrum have a discrete spectral representation in the relative 4-momentum squared, it is proved that no discrete solutions other than the solution (in the vector-coupling case) found by Bastai, Bertocchi, Furlan, and Tonin exist in any case of the scalar, pseudoscalar, and vector couplings. As for the case of the axialvector coupling, it is shown that possible eigenvalues have to belong to one of three exponentially increasing sequences; but the existence of any solution other than Keam's one is quite unlikely. It is mathematically interesting that in the above analysis one encounters some Diophantine equations of the second degree.
Observables and the Field in Quantum Mechanics
Authors: Gudder S. , Piron C.
Published: February 2004

Corresponding to any irreducible proposition system L in general quantum mechanics there is a division ring D with an anti-automorphism * and a vector space (V, D) over D with a definite sesquilinear form φ such that L is isomorphic to the set of φ closed subspaces of (V, D). The main task remaining in connecting the general quantum mechanics to the conventional quantum theory in a complex Hilbert space is to give physical arguments which force D to be the complex field. In this paper it is shown that if L admits a certain type of observable (together with other structure which seems to be physically justified), then D contains the real field as a subfield. Steps are then indicated that can be taken to move from the reals to the complexes or quaternions.
Modification Rules and Products of Irreducible Representations of the Unitary, Orthogonal, and Symplectic Groups
Authors: King R. C.
Published: February 2004

Modification rules, expressible in terms of the removal of continuous boundary hooks, are derived which relate nonstandard irreducible representations (IR's) of the unitary, orthogonal, and symplectic groups in n dimensions to standard IR's. Tensorial methods are used to derive procedures for reducing the outer products of IR's of U(n), O(n), and Sp(n), and for reducing general IR's of U(n) specified by composite Young tableaux with respect to the subgroups O(n) and Sp(n). In these derivations the conjugacy relationship between the orthogonal and the symplectic groups is fully exploited. The results taken in conjunction with the modification rules are valid for all n.
Matrix Elements for the Most Degenerate Continuous Principal Series of Representations of SO(p, 1)
Authors: Boyer Charles P.
Published: February 2004

The matrix elements for finite group transformations of the most degenerate continuous principal series of unitary irreducible representations of SO(p, 1) are calculated. They are shown to agree with special cases already known.
Complex 2-Form Representation of the Einstein Equations: The Petrov Type III Solutions
Authors: Brans Carl H.
Published: February 2004

The geometric structure equations of a manifold satisfying the vacuum Einstein equations are expressed in terms of a complexification of the space of 2-forms adapted to the Petrov classification. The Petrov type III problem is invariantly reduced to the solution of one partial differential equation. Examples of solutions containing one arbitrary function are given, corresponding to spaces with groups of motions of dimensions 0, 1, and 2.
Lattice Green's Functions for the Rectangular and the Square Lattices at Arbitrary Points
Authors: Katsura Shigetoshi , Inawashiro Sakari
Published: February 2004

The lattice Green's functions of the rectangular and the square lattices Irect(a;m,n;α,β)≡1π2[double integral operator]0πcosmxcosny dx dya−iε−αcosx−βcosy,Isq(a;m,n)≡Irect(a;m,n;1,1)are considered. The integral Irect(a, m, n; α, β) for a > α + β is evaluated and expressed in terms of the generalized hypergeometric function F4. Expressions of Isq(a; m, n) for a > 2, a < 2, and a ∼ 2, and Irect(a; m, m; α, β) in terms of pFp−1 are presented by the method of the analytic continuation using the Mellin-Barnes type integral. They are useful for the understanding of the nature of the singularity and for numerical calculation. The behaviors of Isq(a; m, n) are shown in figures.
Perturbation Theory of a Nonideal Bose Gas. I
Authors: RamaRao I. , Mohling Franz
Published: February 2004

With the pair Hamiltonian model as the starting point, perturbation theory calculations are performed for the average energy and the momentum distribution through second order in the two-body interaction potential. A phenomenological theory of helium II is proposed. The chief underlying feature of this phenomenological theory, which is shown to have a firm basis in the microscopic theory, is the presence of a double quasiparticle spectrum. Phenomenological expressions for the average energy and other quantities of interest are also proposed. Simple prescriptions are obtained for calculating the quasiparticle energies and the chemical potential from the average energy. Via these prescriptions, the quasiparticle energies and the chemical potential are calculated through second order in the interaction potential at T ≠ 0 °K, and the results are compared with earlier work in the literature.
Coupling of de Sitter Space-Time and Internal Symmetry
Authors: Tait W. , Cornwell J. F.
Published: February 2004

Via Levi's radial splitting theorem for Lie algebras, all possible unifications of the de Sitter algebras with a real, simple, internal symmetry algebra are found.
Collective and Single-Particle Coordinates in Nuclear Physics
Authors: Zickendraht W.
Published: February 2004

The Schrödinger equation of A nucleons is transformed to new coordinates. Six of them have collective nature and 3A − 9 are single-particle coordinates. The connection is given to the conventional collective model in which five collective coordinates are used. The additional sixth collective coordinate of this paper gives a simple description of monopole vibrations. The new coordinates can also be used in the theory of nuclear reactions: By introducing a symmetrized distance vector for reaction partners, the antisymmetrization procedure is simplified considerably.
Bose Gas in One Dimension. I. The Closure Property of the Scattering Wavefunctions
Authors: Gaudin M.
Published: February 2004

We verify the closure relation of a continuum basis of Lieb's wavefunctions, describing the scattering states of identical bosons interacting via a δ-function potential in one dimension.
Bose Gas in One Dimension. II. Orthogonality of the Scattering States
Authors: Gaudin M.
Published: February 2004

A direct calculation gives the normalization integral for a basis of scattering wavefunctions of interacting bosons in one dimension.
Euler Factorization of SO(p, q) and SU(p, q) Groups
Authors: Maduemezia Awele
Published: February 2004

A parametrization scheme for orthogonal and unitary groups is developed. This scheme is broadly similar to one developed earlier by Wigner, but differs from it in some essential details. It is shown that an arbitrary element g of the group SO(p, q), [SU(p, q)], 3 ≤ p < ∞, 0 ≤ q < ∞, p + q = N, can be written as a product of three factors, g = aBc, such that the extreme factors a and c belong to SO(p, q − 1) [SU(p, q − 1)] and the middle factor is an element of SO(p, q), [SU(p, q)] depending on at most two parameters and representing a ``rotation'' (real, complex, unitary or pseudo-unitary, as the case may be) in the (1 − N) plane. This parametrization includes the Euler parametrization R = R12(φ1) R13(θ)R12(φ2) of the group SO(3) as a special case, and is therefore a generalization of the Euler angle concept to more general orthogonal and unitary groups. The present factorization scheme differs from Wigner's, which is of the form g=[SO(p)⊗SO(q)]K[SO(p)⊗SO(q)] [and similarly for SU(p, q)], in that the extremal factors of this latter scheme are not the next natural subgroup of the original group. Consequently, the middle term K may depend on more than two parameters. Furthermore, the method of proof presented here is entirely different from Wigner's, and may serve as a useful alternative, if further generalization to real Lie groups that preserve some other types of bilinear forms is envisaged. By stepwise factorization, the element g may ultimately be expressed as a product of real, complex, unitary or pseudo-unitary ``rotations'' in the plane.
Abnormal Lattice Thermal Conductivity of a One-Dimensional, Harmonic, Isotopically Disordered Crystal
Authors: Rubin Robert J. , Greer William L.
Published: February 2004

Energy transport is investigated in a model system for which exact analytic results can be obtained. The system is an infinite, one-dimensional harmonic crystal which is perfect everywhere except in a finite segment which contains N isotopic defects. Initially, the momenta and displacements of all atoms to the left of the defect region are canonically distributed at a temperature T, and the right half of the crystal is at a lower temperature. This initial nonequilibrium state evolves according to the equations of motion, and ultimately a steady state is established in the vicinity of the region containing the defects. The thermal conductivity is calculated from exact expressions for the steady state energy flux and thermal gradient. For a crystal in which the N isotopic defects are distributed at random but in which the overall defect concentration is fixed, we demonstrate that the thermal conductivity approaches infinity as least as fast as N1/2. A Monte Carlo evaluation of the thermal conductivity for a given defect-to-host mass ratio and concentration is carried out for a series of random configurations of N defects for N in the range, 25 ≤ N ≤ 600. The thermal conductivity is proportional to N1/2 within the statistical uncertainty except for slight deviations at the smallest values of N.
Mathematics of the Measurement Problem in Quantum Mechanics
Authors: Tutsch J. H.
Published: February 2004

The mathematical structure of the simplest nontrivial hidden variable theory is derived. The core of the resulting theory is an essentially unique nonlinear differential equation which gives a causal description of the continuous collapse of the wavefunction during a measurement. It is shown that the simplest collapse equation is the same as the equation given ad hoc by Bohm and Bub.
Properties of Some Connected Kernels in Multiparticle Systems
Authors: Combes J. M.
Published: February 2004

Connectivity of products of many-particle operators is investigated. Connected products of compact and Hilbert—Schmidt operators are in the same class as their factors. However, even in the simplest case of rank-one many-particle factors, the connected products are not necessarily in the trace class, but simple sufficiency conditions are established.
Kinks and the Dirac Equation
Authors: Skyrme T. H. R.
Published: February 2004

In a model quantum theory of interacting mesons, the motion of certain conserved particlelike structures is discussed. It is shown how collective coordinates may be introduced to describe them, leading, in lowest approximation, to a Dirac equation.
Comment on a Paper of Chiang
Authors: Gould H. W.
Published: February 2004

This is a rebuttal to a paper by Chiang [J. Math. Phys. 10, 2098 (1969)].
Useful Procedure for Computing the Lattice Green's Function-Square, Tetragonal, and bcc Lattices
Authors: Morita Tohru
Published: February 2004

A recurrence relation, which gives the values of the lattice Green's function along the diagonal direction from a couple of the elliptic integrals of the first and second kind, is derived for the square lattice by an elementary partial integration. The values of the square lattice Green's function at an arbitrary site are then calculated in a successive way with the aid of the difference equation defining the function. Discussions are given of the application of this result to the calculation of the lattice Green's function of the tetragonal and body-centered cubic lattices.
Canonical Perturbation Theory for Nonlinear Quantum Oscillators and Fields
Authors: Carhart R. A.
Published: February 2004

The method of successive canonical transformation is developed to study both the classical and quantum versions of a system of n weakly interacting nonlinear oscillators. The method reproduces the essential features of the solutions to these nonlinear differential equations. A general quartic polynomial in the oscillator coordinates is taken as the interaction Hamiltonian. After the canonical transformations to the desired order, the classical system is quantized, resulting in immediate identification of the raising and lowering operators for the perturbed eigenstates in the nonresonant case. In the resonant case (commensurable frequencies) the transformed operators lead to finite-dimensional subspaces within which eigenstates lie, and are obtained by matrix methods. In each case the Heisenberg equations for the operators are solved as fully as presently possible. A particular case of two quantum oscillators is studied in detail, both for the resonant and nonresonant cases. Finally, the method is generalized to the continuum and applied to the Lee model. The usual results for the lowest sector are obtained to second order: the physical V particle and the mass shift of the V. Instability of this particle is related to the occurrence of nonlinear resonance in the lowest-order ``interaction.''
Tensor and Spinor Spherical Harmonics and the Spin-s Harmonics sYlm(θ, φ)
Authors: Campbell William B.
Published: February 2004

A set of Cartesian tensor spherical harmonics is constructed from the spin weighted harmonics of Newman and Penrose, sYlm(θ, φ). It is shown that these tensor harmonics are eigenfunctions of total angular momentum, z component of total angular momentum, total spin and radial component of spin. In particular, − s may be thought of as a helicity for outgoing radiation. Tensor operators are introduced which lower and raise this helicity. They are shown to correspond to the operators ð and ð̄ introduced by Newman and Penrose. Because the sYlm(θ, φ) can be defined for half-integer values of l, m, and s, a set of spinor spherical harmonics is also constructed which has properties paralleling those of the tensor harmonics.
Canonical Transformations and Matrix Elements
Authors: Quesne C. , Moshinsky M.
Published: February 2004

We use the ideas on linear canonical transformations developed previously to calculate the matrix elements of the multipole operators between single-particle states in a three-dimensional oscillator potential. We characterize first the oscillator states in the chain of groups Sp(6)⊃Sp(2)×O(3), Sp(2)⊃OS(2), and O(3)⊃OL(2), and then expand the multipole operators in terms of irreducible tensors with respect to the Sp(2)×O(3) group. Their matrix elements are obtained by applying the Wigner-Eckart theorem with respect to both the Sp(2) and O(3) groups. In this way an explicit expression for the radial integral of rk, k > 0, is obtained.
Remarks on Lightlike Continuous Spin and Spacelike Representations of the Poincaré Group
Authors: Chakrabarti A.
Published: February 2004

Certain classes of unitary representations of the lightlike continuous spin and the spacelike cases are constructed. The generators in these representations involve operators forming the ``intrinsic'' algebras (i.e., commuting with the orbital parts) E3 and O(3, 1) for P2 = 0 and P2 < 0, respectively. The parallel construction for P2 > 0 involving an intrinsic O4 algebra is indicated. Equivalence relations with certain other forms are given through a unitary transformation. The physical significance of the ``translation'' generators of E3 is brought out in terms of the projections of W orthogonal to P. Corresponding results for the O(3, 1) and O(4) algebras are given. For the continuous-spin case, these operators are shown to provide a basis with extremely simple transformation properties, related to a certain symmetric toplike behavior even under Lorentz transformations. With a view to future use, the matrix elements of W on the energy-rotation basis are calculated in a unified manner for all the three cases, P2⋛0. A deformation formula leading from zero-mass continuous-spin representations to spacelike ones is studied. Certain types of nonunitary representations are briefly introduced at the end.
Lorentz Basis of the Poincaré Group. II
Authors: Chakrabarti A.
Published: February 2004

The transformation coefficients connecting the momentum and Lorentz bases of the unitary representations of the Poincaré group are derived for timelike, lightlike, and spacelike momenta P2⪌0 and for arbitrary spin (i.e., for general values of W2) in each case.
Polynomial Expansion Method for Problems Involving a Relativistic Maxwellian Distribution
Authors: Nishimura Keiichi
Published: February 2004

With the aim of extending the Sonine polynomial expansion method to the region of relativistic Maxwellian distribution functions, a new set of polynomials has been introduced in terms of their orthogonality equation. Their coefficients have been derived and tabulated as functions of the temperature for several lowest orders.
Point Charge in the Vicinity of a Schwarzschild Black Hole
Authors: Cohen Jeffrey M. , Wald Robert M.
Published: February 2004

The electrostatic field of a point charge at rest in Schwarzschild space is derived. The solution is used to study the problem of a point charge slowly lowered into a nonrotating black hole. We find that the electric field of the charge remains well behaved as the charge is lowered and that all the multipole moments except the monopole fade away. We conclude that a Reissner-Nordstrom black hole is produced.
Generalization of the Cook Formalism for Fock Space
Authors: Schroeck F. E.
Published: February 2004

The Cook formalism for Fock space is extended by finding additional properties of the creation and annihilation operators and by giving a rigorous definition of the second-quantized form for n-body operators (for any n). Properties of these second-quantized operators are given, including an expansion in terms of the creation and annihilation operators.
The Boson Calculus for the Orthogonal and Symplectic Groups
Authors: Lohe M. A. , Hurst C. A.
Published: February 2004

The boson calculus as used for U(n) cannot be applied directly to O(n) and Sp(n). Modifications are made to boson operators, in order to obtain new operators which enable explicit states of irreducible representations of O(n) and Sp(n) to be constructed. Calculations for O(3) and O(4) show how these operators permit a greater simplicity, and reveal more fully the group structure than has previously been the case.
Asymptotic Form of the Three-Particle Scattering Wavefunction for Free Incident Particles
Authors: Nuttall J.
Published: February 2004

It is shown that second-order multiple scattering terms lead, in some directions, to an anomalous term in the asymptotic form of the wavefunction for three free incident particles, which falls off as the inverse second power of distance. The boundary of the region in which this occurs is given, together with the form of the wavefunction near this boundary.
Nearly Symmetric Kinematic and Hydromagnetic Dynamos
Authors: Soward A. M.
Published: February 2004

Certain aspects of the hydromagnetic and kinematic dynamo theory related to the Earth's magnetic field are considered. The work of Tough and Roberts [J. G. Tough and P. H. Roberts, Physics of the Earth and Planetary Interiors (North-Holland, Amsterdam, 1968), Vol. 1, p. 288] on the hydromagnetic dynamo is extended in two respects. First, the most general form of the prescribed body force which is consistent with the model is considered. Secondly, the mean quantity 〈Sφ〉 [see Eqs. (18)] is determined up to order R−1/2, where R is the magnetic Reynolds number. It is shown that the remarkable effective variables first introduced by Braginskii {S. I. Braginskii, Zh. Eksp. Teor. Fiz. 47, 1084 (1964) [Sov. Phys. JETP 20, 726 (1965)]} are relevant in the hydromagnetic dynamo in the second approximation. It is also shown by considering a related problem concerning the heat conduction equation that effective variables are unlikely to have any relevance in the kinematic dynamo theory in the third approximation.
Multiple Density Correlations in a Many-Particle System
Authors: Wu F. Y.
Published: February 2004

A closed expression similar to the Ursell-Mayer expansion is obtained for the static multiple density correlation function In=〈ρk1⋯ρkn〉 of a many-particle system. It is shown that In breaks into products of lower ones, if there exist partial momentum conservations among the k's. Using the convolution approximation for the n-particle correlation function, we evaluate In in a closed form. The result is shown to be accurate in the small k region.
Trapped Surfaces and the Development of Singularities
Authors: Pajerski David Walter , Newman Ezra T.
Published: February 2004

The study of singularities in general relativity was given a strong impetus by a topological approach due to Penrose and others, and powerful theorems concerning their existence have been developed. In particular a theorem by Penrose states that under certain conditions the existence of a trapped surface in a space-time guarantees that singularities will develop. Using the spin coefficient formalism we generalize from the Schwarzschild solution and prove the existence of a wide class of solutions possessing such trapped surfaces by displaying the solutions to terms linear in a certain null coordinate. Then, using an asymptotic procedure, the method is generalized to include a class of solutions possessing ``asymptotically trapped surfaces.''
Unified Treatment of Diatomic Electron Interaction Integrals over Slater-type Atomic Orbitals
Authors: Silver David M.
Published: February 2004

General expressions are developed for the evaluation of both Coulomb and hybrid electron repulsion integrals over basis sets of arbitrary Slater-type atomic orbitals. In each case, a single numerical integration over a product of a one-center and a two-center charge distribution function is required for the recovery of the integrals. The one-center charge distribution functions are shared by both integral types. The two-center charge distributions are different for the two cases, but the constants and special functions required are the same. The results lead to an efficient computer-oriented procedure for the resolution of these integrals. The charge distribution functions can be used to obtain two-center overlap, nuclear attraction, kinetic energy, and, somewhat less efficiently, exchange integrals as well.
Linear Random Operator Equations in Mathematical Physics. II
Authors: Adomian G.
Published: February 2004

This paper is a continuation of Paper I [J. Math. Phys. 11, 1069 (1970)]. A general expression is determined for the stochastic Green's function (SGF) for two-point correlation functions, and various useful relationships are determined between the stochastic Green's functions for various statistical measures and between the stochastic Green's functions, random Green's functions, and ordinary Green's functions. In the author's dissertation and earlier papers, SGF was given as an ensemble average of the product of random Green's functions. This random Green's function is now specified in terms of an ordinary Green's function for a deterministic operator and a resolvent kernel which can be calculated for the random part of the stochastic operator. Hence that SGF is determinable which yields the desired statistical measure of the solution process directly. Second, the two-point correlation function of the solution process is found for the perturbation case. It is also demonstrated that, in the event that perturbation theory is adequate to deal with the randomness involved, the correct two-point correlation of the solution process is easily specialized from the general expression, i.e., the results of perturbation theory are obtained from the SGF of Adomian when perturbation theory is applicable.