bluuebunny/crossref_metadata_2025 huggingface dataset:
Talmi Transformation for Unequal-Mass Particles and Related Formulas
Authors: Kumar Kailash
Published: January 2005

Three-dimensional polynomials which occur as coefficients of the exponential in the wavefunctions of the harmonic oscillator are used in nuclear physics and kinetic theory of gases. A generating function for these polynomials is used to simplify the calculation of several integrals. These include the integrals involving products of two and three polynomials and the coefficients of the Talmi transformation. Explicit formula in terms of recoupling coefficients of angular momentum theory are obtained.
Analyticity Properties of the Scattering Amplitude
Authors: Minguzzi A.
Published: January 2005

Analyticity properties in three variables, energy, momentum transfer, and ``squared mass'' are deduced from single-variable dispersion relations.
Gelfand States and the Irreducible Representations of the Symmetric Group
Authors: Moshinsky M.
Published: January 2005

The set of Gelfand states corresponding to a given partition [h1 … hn] form a basis for an irreducible representation of the unitary group Un. The special Gelfand states are defined as those for which [h1 … hn] is a partition of n and the weight is restricted to (11 … 1). We show that the special Gelfand states constitute basis for the irreducible representations of the symmetric group Sn and use this property to construct explicitly states in configuration and spin-isospin space with definite permutational symmetry.
Analytic Continuations of Higher-Order Hypergeometric Functions
Authors: Olsson Per O. M.
Published: January 2005

Solutions in powers of 1 −x of the differential equation associated with the hypergeometric function pFp−1 are derived and the function is continued analytically in terms of these solutions. The analytic continuation is derived in a simple way from an expansion which is well suited for the purpose and which is valid for all values of the argument x. The usefulness of the 3F2 function in studying certain hypergeometric functions of two variables is emphasized.
On the Propagation of Gravitational Fields in Matter
Authors: Szekeres Peter
Published: January 2005

A purely covariant treatment is made of those solutions of the Einstein field equations which represent pure gravitational radiation propagating in fluid and electromagnetic media. The analysis involves a discussion of the full Bianchi identities in carefully selected tetrad frames. In this way the interaction between the gravitational field and the medium is transferred to a coupling between a preferred frame for the gravitational field and one for the matter field. The gravitational radiation no longer propagates along shear-free null geodesics, as it does in vacuum, and the shear and ray curvature of the propagation vector are shown to depend directly on the properties of the medium. Some new solutions of the field equations, representing transverse gravitational waves propagating in an electromagnetic field, are exhibited and discussed in some detail. It is shown that no such solutions exist, at least in simple cases, for perfect fluids. Finally, the treatment presented here is compared with the more usual electromagnetic treatment, and it is shown why the theories require basically different approaches.
Unitary Representations of the Lorentz Group on 4-Vector Manifolds
Authors: Zmuidzinas Jonas Stasys
Published: January 2005

A review is presented of irreducible unitary representations of the (3 + 1)-dimensional restricted Lorentz group on manifolds of time-, light-, and spacelike 4-vectors. In each case a complete set of orthonormal (in the sense of the distribution theory) basis functions is available. The completeness relation for the nontrivial spacelike case is proved in detail. Expansion formulas, Lorentz-group analogs of the Fourier integral theorem, are given. In particular, expansions of plane-wave solutions of the Klein-Gordon equation for − ∞ < m2 < ∞ are worked out as an illustrative example. Possible physical applications are briefly discussed.
Nonhomogeneous Differential Equation with a Second-Order Turning Point
Authors: McGuinness D. J.
Published: January 2005

The asymptotic behavior of solutions of a class of parameter-dependent second-order nonhomogeneous linear ordinary differential equations with a second-order turning point is investigated. It is shown that, under certain conditions, particular solutions can be represented asymptotically by expansions involving certain special functions. Properties of these special functions are studied.
An Axiomatic Approach to the Formalism of Quantum Mechanics. I.
Authors: Prugovečki Eduard
Published: January 2005

An axiomatic formulation of a quantum mechanical formalism is given. The formulation is not in terms of objects associated with the Hilbert space, but in terms of a different kind of objects for which the name ``complex probability measures'' has been chosen. It is shown that the conventional Hilbert-space formalism obeys the given axioms. A few consequences of the axioms are investigated, some of which are found useful in the second part of this work.
S-Matrix Formalism, Charge Renormalization, and Definition of the Hamiltonian in a Simple Field-Theoretical Model
Authors: Ynduráin F. J.
Published: January 2005

A field-theoretical model (the relativistic version of the Lee model) is exhibited for which one can rigorously prove that the essential features of the S-matrix formalism (in particular analyticity) hold, even for point coupling, and that all charge renormalizations are finite. It is also shown that, although the interaction-picture description fails, the total Hamiltonian may still be defined as a symmetric operator and it governs the dynamics of the interaction. Finally, we point out that the usual pathologies which appear in the current (static) version of the model are not an intrinsic feature of the theory, but rather the result of too crude oversimplifications.
Note on Product Integrals
Authors: Backus G. E. , Gilbert F.
Published: January 2005

Attention is called to Volterra's product integral solution of ordinary linear differential equations with variable coefficients.
Generalized Discrete-Continuum Radial Integrals with Coulomb Functions
Authors: Bebb H. Barry
Published: January 2005

Simple closed-form computational formulas involving only elementary functions are obtained for the hydrogenic, discrete-continuum matrix elements . The results allow for different effective charge parameters Z and Z′ for the discrete and continuum functions. The central radial integral computed is sufficiently general to allow the evaluation of matrix elements of rm exp(− r/ε) between the Coulomb continuum functions and any discrete function formed from rk exp(− r/A). Results are also given for the free-particle limit as Z′ → 0.
On the Development of the Covariant Formulation of the Conservation Laws of General Relativity
Authors: Davis W. R. , Moss M. K.
Published: January 2005

A method of obtaining Komar's covariant formulation of the conservation laws of general relativity directly from the variation of the scalar curvature density is presented. The procedure of obtaining this expression is free of the addition of arbitrary elements and only tensorial terms and operations are employed in the development.
The Most General Clebsch-Gordan Coefficients of the Universal Covering Group of the Inhomogeneous Lorentz Group
Authors: Kummer Martin
Published: January 2005

The most general Clebsch-Gordan coefficients to reduce the physically most important n-fold product representations of the groups P̃+↑ and P̃ (Universal covering groups of the restricted and full inhomogemeous Lorentz groups) are derived. They are used to answer the question: What can be said about the S-matrix if only Lorentz invariance is postulated?
Space Groups and Selection Rules
Authors: Bradley C. J.
Published: January 2005

A rigorous method is presented for obtaining the Clebsch-Gordan coefficients for the Kronecker products of induced representations of finite groups. The result obtained is applied to the theory of space groups, and the final formula for the coefficients has the advantage, as with other subgroup techniques, of being expressed in terms of the characters of small representations, thereby providing an additional proof independent of Lax, yet supporting his point of view the subgroup and full-group procedures are equivalent, and at the same time the result clarifies subgroup treatments so far given. An example using P23 is given.
Some Collapsing Cylinders and their Exterior Vacuum Metrics in General Relativity
Authors: Cocke W. J.
Published: January 2005

A cylindrical form of the Friedman metric is used to obtain nonstatic infinite cylinders of incoherent fluid. The vacuum metrics exterior to the cylinders are determined from the hypothesis that the metric tensor and its first partial derivatives be continuous. This hypothesis is applied by requiring the continuity of the first and second fundamental forms of the boundaries of the cylinders. The exterior metrics are nonstatic and may be expressed in the Einstein-Rosen form, and equations governing their behavior are derived. It is found that the exterior metric carries a flux of gravitational ``C energy,'' the direction of which in the Einstein-Rosen frame is the same as that of the surface of the cylinders.
Wick Polynomials at a Fixed Time
Authors: Jaffe Arthur
Published: January 2005

In general, a Wick polynomial must be smeared with a test function depending on both time and space in order to yield an operator in Hilbert space. However, in space time of two dimensions, it is sufficient to smear in the space direction alone. This statement is proved by an application of Weinberg's asymptotic theorem. Operators formed in this manner are candidates for approximate interaction Hamiltonians.
Unitary Irreducible Representations of SL (3, R)
Authors: Rosen Gerald
Published: January 2005

It is shown that to each finite-dimensional single-valued irreducible representation of SL(3, R) there corresponds an infinite-dimensional representation which is unitary on any member of a certain one-parameter family of Hilbert spaces. We set up an eigenfunction problem for the members of a three-parameter family of Hilbert subspaces on which such a unitary representation is irreducible. The relatively simple but especially important three-dimensional case is worked out completely. Unitary irreducible representations for the unimodular real linear groups SL(N, R) with N > 3 and their subgroups can be obtained by generalizing the formalism described here.
Small-Angle X-Ray Scattering from Rods and Platelets
Authors: Schmidt Paul W.
Published: January 2005

For highly elongated rods or flat platelets, there is a range of scattering angles in which the intensity of small-angle x-ray scattering cannot be conveniently approximated either by techniques normally used at small scattering angles or by the asymptotic expansion which is applicable in the outer part of the scattering curve. Expressions for the scattered intensity from rods and platelets have therefore been developed which can be used both at these intermediate scattering angles and also in the outer portion of the small-angle x-ray scattering curve.
On the Motion of Electrons Scattered from an Infinite Slab
Authors: Taylor C. D.
Published: January 2005

A nonlinear integral equation of the Volterra type is derived to describe the motion of the electrons egressing from an infinite slab—one formed by parallel planes of infinite area. This motion depends on (1) the flux density of electrons egressing from the slab, and (2) the distribution of the forward components of the electrons' velocities upon egressing from the slab, i.e., the velocity components along the normal to the slab. It is proved that the nonlinear integral equation can be solved by a method of successive approximations and that the solution is unique. The integral equation is solved for two special cases.

The most important application of this work is in the study of electrons scattered by the high-density gamma flux from a nuclear explosion. Therefore, the treatment presented is made directly applicable to that study.
Exact Solutions for a Semi-Infinite Square Lattice Gas
Authors: Karayianis N. , Morrison C. A. , Wortman D. E.
Published: January 2005

The problem of a two-dimensional lattice gas with nearest neighbor infinite repulsion is considered by obtaining exact solutions for a sequence of semi-infinite spaces. The exact solutions are obtained for M × ∞ spaces with 2 ≤ M ≤ 14 in even steps, and although there are no phase transitions in these spaces, a criterion for the point of ``closest approach'' to a phase transition is established. The values of the thermodynamic variables evaluated at this point for each M are extrapolated to obtain the properties of the two-dimensionally infinite space. The data indicate that a phase transition occurs with possibly infinite compressibility at an activity z = 3.799, a density ρ/ρmax = 0.7356, and a pressure given by P/kBT = 0.7914. The density is obtained by a rigorous differentiation of the secular determinant that determines the value of the pressure for a given z, thus securing the accuracy of the calculations and enabling the extrapolated values of the thermodynamic variables to be estimated with good precision.
Extraction of Singularities from the S Matrix
Authors: Landshoff P. V. , Olive D. I.
Published: January 2005

Two methods are described for extracting triangle singularities from matrix elements. The first is comparatively simple but involves the use of off-mass-shell amplitudes; the second is rather involved. A proof of the Cutkosky discontinuity formula is given independent of perturbation theory, and it is shown that the Riemann-sheet properties of the singularity in the physical region agree with perturbation theory. The connection between this and a causality requirement is discussed. The relevance of the work to practical computations is explained.
Asymptotic Properties of the Potentials in the Inverse-Scattering Problem at Fixed Energy
Authors: Sabatier Pierre C.
Published: January 2005

The problem of finding a nonrelativistic central potential from a knowledge of all the phase shifts at one energy had been previously shown by Newton to reduce to the inversion of a given infinite matrix M. In the framework of Newton's theory, the solution is not unique but depends on one parameter. In the present work, the inverse matrix is explicitly given, together with the vectors annihilated by M. These enable one to construct all the solutions of the problem. The asymptotic behavior of the equivalent potentials is exhibited, and it is shown that one (and only one) of them decreases asymtotically faster than r−2+ε, provided that the phase shifts decrease asymptotically faster than l−(3+ε′) (for arbitrarily small ε, ε′). All the other equivalent potentials have an oscillating tail damped by a factor r−3/2. The ``transparent potentials,'' which give all phase shifts equal to zero at one energy, are also studied. In subsequent publications, analytic continuation of the potentials in the r plane and of the Jost function in the angular momentum complex plane is studied.
Percolation Processes. I. Low-Density Expansion for the Mean Number of Clusters in a Random Mixture
Authors: Essam J. W. , Sykes M. F.
Published: January 2005

A cluster expansion, valid at low densities, is derived for the mean number of clusters in a random mixture of sites or bonds on a graph. It is shown that only clusters without a cut-point (stars) are required, and a number of general theorems for determining the weights are proved.
The r-Particle Distribution Function in Classical Physics
Authors: Blood F. A.
Published: January 2005

An expression for the r-particle distribution function (r ≥ 3) for classical gases in terms of the pair potential is converted to an expression in terms of the pair correlation function by graph-theoretical means. The new formula involves a sum over all basic graphs with G-bonds, having r root points, where G(r) + 1 is the pair correlation function.
On Quantization in Space with Torsion
Authors: Finkelstein R.
Published: January 2005

Some elementary quantization questions are discussed under the hypothesis that physical space is a homogeneous space of constant torsion. In such a space, a freely propagating point particle appears to have extension in the sense that it obeys the Schrödinger equation of a symmetric top. Modifications of commutators and scattering amplitudes are given. The geometrical methods are based on the correspondence with the associated group-space.
Relativistic Hydromagnetic Waves and Group Velocity
Authors: Giere Albert C.
Published: January 2005

The velocities of relativistic hydromagnetic waves in a compressible, perfect fluid of infinite conductivity are calculated in the framework of general relativity. In the absence of viscuous and Joule heat losses, the flow is isentropic, and, therefore, the wave surfaces are propagated without change of shape. The velocities are first obtained in terms of the four-vector magnetic field and then in terms of the three-dimensional field. Several limiting cases are considered, and, in particular, it is shown under what conditions the expressions reduce to the nonrelativistic forms. Finally, the group velocities are calculated. The existence of a group velocity for such waves is based on the fact that the velocities exhibit a directional dependence. The group velocity in this case is of significance because it is the velocity of energy propagation, just as in the case when dispersion exists.
Algebraic Aspects of Trilinear Commutation Relations
Authors: Scharfstein H.
Published: January 2005

An attempt is made to derive from the formalism of Schwinger's action principle, in a more convincing manner than previously described, a set of trilinear equal-time commutation relations which contains the commutation relations first discussed by H. S. Green as special cases. Matrix representations of field operators satisfying the trilinear commutation relations are considered. Two representations are explicitly discussed: a four-dimensional and an eight-dimensional representation. The representations considered and the bilinear equal-time commutation relations between the associated ``component fields'' obeying ordinary statistics are specified by irreducible representations of an algebra which is suggested by the trilinear commutation relations. The component fields associated with the same representation and of the same spin differ from each other in their bilinear equal-time commutation relations with other fields. This difference is reflected in the interactions into which the various fields can enter.
On the Existence of Field Theory. I. The Analytic Approach
Authors: Taylor J. G.
Published: January 2005

The problem of existence of solutions to local field equations is studied. We set up the field equations so that the solutions correspond to fixed points of a mapping of the space of Green's functions into themselves. We attempt to use analytic methods to determine these fixed points, in particular, the contraction mapping principle. To do this we perform a rotation to Euclidean space from Lorentz space; in Euclidean space we prove the existence of solutions to a large class of approximating equations to the field equations, obtained by requiring the Green's functions to be zero if they have more than a certain number of external particles. By this method we prove that there is only the trivial zero solution to certain types of bootstrap equations. The contraction mapping theorem does not appear powerful enough to discuss the complete field equations.
Lorentz Equivalence, Unitary Symmetry, and Spin Unitary Symmetry
Authors: Teitler S.
Published: January 2005

The enumeration and classification of the minimal ideals (spinor spaces) of the vector Clifford algebra generated from the vector basis of Lorentz space-time obtained previously is used in a discussion of equivalence mappings among these minimal ideals. Lorentz equivalence is defined as an equivalence mapping which possesses Lorentz symmetry. The concept of regular decomposition is introduced by which any element of the complete algegra is expressed in terms of a complete set of minimal ideals or spinor spaces. A regular current density which is invariant under unitary symmetry U4 among the spinor spaces of the regular decomposition is defined. The spin unitary symmetry, within a spinor space under which the spinor current density is invariant, is discussed.
One-Dimensional Ising Model with General Spin
Authors: Suzuki Masuo , Tsujiyama Bunjiro , Katsura Shigetoshi
Published: January 2005

The one-dimensional Ising model with general spin S has been formulated as an eigenvalue problem of order 2S + 1. Two methods to reduce the order to [S + 1] have been developed for calculating the energy and the susceptibility at zero external field. Exact solutions for S = 32 and S = 1 have been obtained. Numerical calculations of S = 32, 1, and ½ have been compared.
van der Waals Wiggles, Maxwell Rule, and Temperature-Dependent Excitations
Authors: Emch Gérard G.
Published: January 2005

Starting from a temperature-independent Hamiltonian, we discuss for some models the coexistence of the van der Waals wiggles and the Maxwell-van der Waals isotherms. The main tool of this paper is provided by the temperature-dependent excitations techniques developed in an earlier paper. Some ferromagnetic models and lattice-gas models are treated along similar lines. The van der Waals wiggles and the Maxwell-van der Waals isotherms appear below the critical temperature as two solutions of a system of self-consistent equations. The choice between the two solutions is then dictated by energy considerations.
Certain Bootstraps and Related Equations
Authors: Broido Michael M.
Published: January 2005

Methods of deriving existence and nonexistence theorems for certain classes of nonlinear integral and other equations are discussed. The methods are illustrated by examples from high-energy physics of equations of the bootstrap type.
Calculation of Exchange Second Virial Coefficient of a Hard-Sphere Gas by Path Integrals
Authors: Lieb Elliott H.
Published: January 2005

By direct examination of the path (Wiener)-integral representation of the diffusion Green's function in the presence of an opaque sphere, we are able to obtain upper and lower bounds for that Green's function. These bounds are asymptotically correct for short-time, even in the shadow region. Essentially, we have succeeded in showing that diffusion probabilities for short-time intervals are concentrated mainly on the optical path. By integrating the Green's function, we obtain upper- and lower-bound estimates for the exchange part of the second virial coefficient of a hard-sphere gas. We can show that, for high temperature, it is asymptotically very small compared to the corresponding quantity for an ideal gas, viz., Bexch/Bexch0=exp {−12π3(a/Λ)2+O[(a/Λ)2/3]},where Λ is the thermal wavelength and a is the hard-sphere radius. While it was known before that Bex ch/B0ex ch is exponentially small for high temperatures, this is the first time that a precise asymptotic formula is both proposed and proved to be correct.
Recoupling Coefficients for the Group SU(3)
Authors: Resnikoff M.
Published: January 2005

The Hilbert space method, employed in the previous article to obtain the coupling coefficients of SU(3), is used here to obtain the recoupling, or 6(λμ), coefficients of SU(3). The coefficients are formulated in terms of a generating function involving an integral, and an explicit expression is integrated out for the general nondegenerate case. The symmetries of the 6(λμ) coefficients are discussed.
Surface-Energy Tensors
Authors: Rosenkilde Carl E.
Published: January 2005

In this paper the surface-energy tensors are defined and general expressions for their first variations are obtained. These quantities are appropriate for an investigation of the equilibrium and the stability of a charged liquid drop (held together by a constant surface tension) using the method of the tensor virial, which was developed by Chandrasekhar and Lebovitz for the theory of self-gravitating masses. The definitions are shown to be consistent with the conservation laws.
Surface-Energy Tensors for Ellipsoids
Authors: Rosenkilde Carl E.
Published: January 2005

The surface-energy tensors are evaluated for ellipsoidal surfaces in terms of particular types of elliptic integrals which have simple algebraic recursion relations that are useful for numerical evaluation. The final expressions are given in a form appropriate for an investigation of stability using the method of the tensor virial.
Stability of Axisymmetric Figures of Equilibrium of a Rotating Charged Liquid Drop
Authors: Rosenkilde Carl E.
Published: January 2005

The method of the tensor virial is used to investigate the equilibrium and stability of a rotating, uniformly charged (with a total charge Q), incompressible liquid drop (of volume V) held together by a constant surface tension T. The tensor virial theorems provide relations which define the sequences of equilibrium figures and perturbation equations which govern the oscillations. Since spheroids satisfy the virial theorems of orders one, two, and three, the stability of exact axisymmetric equilibrium figures with respect to second- and third-harmonic deformations can be inferred from the nature of the characteristic oscillation frequencies of spheroids. As the rotation increases for a given fission-ability parameter x = Q2/10TV (0 ≤ x < 1), a sequence of oblate spheroids representing initially stable rotating ground states exhibits a neutral point (where an ellipsoidal sequence bifurcates), but remains stable (in the absence of dissipation) until one of the three second-harmonic modes of vibration (the toroidal or γ mode) becomes overstable. Later, for third harmonics, it exhibits a second neutral point (where a sequence of asymmetric figures bifurcates), but again remains stable until the onset of the associated overstability. A third neutral point does not indicate the bifurcation of pear shapes. The error in using oblate spheroids is less than 5% up to the first overstable point. One class of saddle shapes can be represented by prolate spheroids (which must rotate about the symmetry axis) in the neighborhood of x = 1. They are initially unstable with respect to the other two second-harmonic modes of vibration (the pulsation or β mode and the transverse-shear mode).
Unitary Irreducible Representations of SU(2, 2). I
Authors: Yao Tsu
Published: January 2005

This paper, which is the first of three, is concerned with the general properties of the noncompact group SU(2, 2), the Lie algebra of which is isomorphic to the Dirac algebra. In the course of our study of the unitary representations, we first obtained all the finite dimensional irreducible representations. The associated Young diagrams are shown to have simple properties; the degenerate Young diagrams always denote degenerate representations. Through a theorem of Harish-Chandra, which relates the finite representations to the unitary representations in the discrete series, we are able to obtain explicitly all the unitary infinite-dimensional irreducible representations in this series, both degenerate and non-degenerate. The notion of multiplicity for nondegenerate representations is introduced and discussed in connection with a new operator F3, which is required for a complete labeling of states.
Interpolation Formulas in the Angular Momentum Plane
Authors: Sabatier Pierre C.
Published: January 2005

When the potential is an analytic function of a rational power of r, analytical properties of the wave-functions enable one to derive interpolation formulas in the angular-momentum plane. In these formulas, products of the wavefunctions which correspond to two different potentials are expanded in terms of their values at an infinite discrete set of points on the real axis. These expansions hold uniformly in z. Properties of the expansion coefficients are investigated. They allow the author to construct generating functions, and to obtain several interpolation formulas for functions of mathematical physics. Results are applied to the inverse scattering problem at fixed energy. They provide further information on an ``angular-momentum dispersion relation'' obeyed by the Jost function. A semiclassical approximation is given for the interpolation coefficients, and its meaning is investigated. Finally, an elementary derivation of the interpolation formulas is sketched and suggests a curious symbolic writing of the wavefunctions.
General Space-Momentum Commutation Relation
Authors: Rosenbaum David M.
Published: January 2005

This paper derives the general commutator [qm, pn] for all integers m and n, positive or negative. Two new identities for the binomial coefficients are derived using the general commutator. A simple example of the use of the general commutation relation is given in the expansion of (Ap + Bq)n (A, B, constants) in normal form for integer n.
Analytic Properties of Certain Radial Matrix Elements
Authors: Almström H. , Olsson P.
Published: January 2005

The analytic properties of the Laplace transform of products of two confluent hypergeometric functions as function of certain parameters are investigated. The radial matrix element of multipole type that contain Coulomb-Dirac wavefunctions or special cases thereof are considered. These are investigated as functions of the momenta p of the particles. Branch cuts and the behavior along the branch cuts in the complex p plane are given. The formulas presented permit accurate calculation of the matrix elements also, when the parameters have values arbitrarily close to singular points. The prime concern, however, is to facilitate second- and higher-order perturbation calculations.
Evaluation of a Partial-Wave Unitarity Integral
Authors: Dilley James
Published: January 2005

The integral ∫s+∞ρ(s)f(s)ds, where ρ(s) = (1/s)[(s - s+)(s - s−)]½, 0 ≤ s− < s+, is evaluated for an arbitrary function f(s) which is meromorphic in the complex s plane and has the behavior at infinity |s1+εf(s)|→ lim |s|→∞ 0. Some applications to the N/D method of elementary particle physics are discussed.
Realization of Lie Algebras by Analytic Functions of Generators of a Given Lie Algebra
Authors: Chand P. , Mehta C. L. , Mukunda N. , Sudarshan E. C. G.
Published: January 2005

In this paper we discuss the problem of the Poisson bracket realization of various Lie algebras in terms of analytic functions of the generators of a given Lie algebra. We pose and solve the problem of realizing the general O(4), O(3, 1), and E(3) algebras in terms of analytic functions of the generators of a prescribed realization of an E(3) algebra. A similar problem is solved for the symmetric tensor realizations of SU(3) and SL(3, R). Related questions are discussed for O(n + 1), O(n, 1), E(n), SU(n), and SL(n, R). We study in some detail the finite canonical transformations realized by the generators of the various groups. The relation of these results to the reconstruction problem is briefly discussed.
Systems of First-Order Linear Ordinary Differential Equations as Canonical or Euler-Lagrange Equations
Authors: Rund H.
Published: January 2005

A simple but complete theory is given of the necessary and sufficient conditions which must be satisfied in order that a system of first-order linear ordinary differential equations, whose coefficients are functions of the independent variable, be the canonical or Euler-Lagrange equations of a variational principle.
Electro-Optical Effects. I
Authors: Carroll M. M. , Rivlin R. S.
Published: January 2005

The theory of Toupin and Rivlin for the propagation of electromagnetic waves in a centro-symmetric isotropic material to which static electric and magnetic fields are applied is specialized to the case when only a static electric field is applied. The reflection-refraction problem for an electromagnetic wave normally incident on the interface between free space and the material is studied for arbitrary direction of the applied electric field. It is found that, in general, there are two refracted rays and that these are not generally normal to the interface.
Formal Properties of the Solution to the Radiationless Relativistic Kepler Problem
Authors: Cawley Robert G.
Published: January 2005

Formal properties of the solution to the classical radiationless relativistic Kepler problem are discussed with particular attention to the strong coupling limit, a case rarely considered. It is found that fall to the origin can occur for potentials less strongly attractive than required nonrelativistically. One conclusion is that the relativistic centrifugal barrier is less ``effective'' than the nonrelativistic kind. It is possible to describe these effects in terms of a dimensionless parameter resembling a classical ``coupling constant.'' The quantum-mechanical case is also briefly treated.
Systems of Observables in Axiomatic Quantum Mechanics
Authors: Gudder Stanley
Published: January 2005

Systems of observables are considered in an axiomatic framework for quantum mechanics which generalizes the usual Hilbert space formulation. Familiar concepts such as complete systems of observables and superselection rules are generalized and it is shown that many of the Hilbert space theorems carry over to this abstract formalism. Also functions of observables are considered and some theorems due to John von Neumann are generalized.
A Class of Null Spectroscopic Coefficients
Authors: Judd B. R. , Wadzinski H. T.
Published: January 2005

The irreducible representations occurring in the decomposition of the Kronecker products U × U and W × W for irreducible representations U and W of the groups G2 and R7 are separated into symmetrical and antisymmetrical parts. Application of the Wigner-Eckart theorem yields new selection rules and explains many of the apparently accidental zeros in the tabulation by Nielson and Koster of the reduced matrix elements of various single-particle tensor operators for the electronic configurations fn. The method is applied in detail to the magnetic spin-spin interaction between electrons in the f shell, and the new selection rules are presented in tables.
Potential-Correlation Function Duality in Statistical Mechanics
Authors: De Dominicis C. , Englert F.
Published: January 2005

The Feynman path-integral formulation is used to analyze the grand-partition function Z and the n-body Green's function Gn or rather their cumulants (or connected parts) G̃n for a system governed by p-body interaction potentials vp. It is shown that the functional relationship expressing G̃n in terms of vp is invariant under the transformation exchanging −(−)mG̃m and vm everywhere. Under the same transformation log Z undergoes a change of sign. The content of these results is discussed in conclusion.
Finite-Range Effects in Distorted-Wave Born-Approximation Calculations of Nucleon Transfer Reactions
Authors: Sawaguri T. , Tobocman W.
Published: January 2005

A method for doing distorted-wave Born-approximation calculations for nucleon transfer reactions is presented. This method is designed to be used when the zero-range approximation cannot be made. The method has the advantage that only simple quadratures need be performed. When recoil effects are negligible, our method leads to a particularly simple form. The technique developed here can be applied to the evaluation of the six-dimensional integrals that result when the general two-body interaction is considered. Thus it may be usefully applied to nuclear-structure calculations when it is desired to use wavefunctions which are not harmonic-oscillator eigenfunctions.
Partial Group-Theoretical Treatment for the Relativistic Hydrogen Atom
Authors: Bacry H. , Richard J. L.
Published: January 2005

The Lie algebra of SU (1, 1) and its Hermitian representations are used together with spherical harmonics to solve the wave equations for the nonrelativistic q-dimensional oscillator and the relativistic Kepler problem.
Discontinuities in Nonideal Magnetogasdynamics
Authors: Friedel Helmut
Published: January 2005

An evolutionary condition is derived from generalized jump relations including dissipation terms and applied to the basic equations of magnetogasdynamics. Two contact discontinuities existing as solutions of these equations are found not to be evolutionary.
Effective Dielectric Tensor and Propagation Constant of Plane Waves in a Random Anisotropic Medium
Authors: Liu C. H.
Published: January 2005

Random anisotropic media are assumed to be characterized by dielectric tensors in which the components are random functions of position. A turbulent plasma in a static magnetic field is one example of such media. In this paper wave propagation in turbulent magnetoactive plasma is studied. The averages of electric field and dielectric displacement vectors over an ensemble of these media are found, assuming these average quantities are time-harmonic plane waves. The effective dielectric tensor is defined as the proportionality factor between the two average quantities. When this effective dielectric tensor is applied to the wave equation, a general dispersion relation for plane waves is derived. Expressions for propagation constants are obtained and some special cases are considered in detail. It is found that, because of random scattering, there are attenuations for both the ordinary and extraordinary waves for the average fields. The results reduce to those obtained by J. B. Keller and F. C. Karal when the anisotropy of the background media is removed
Tetrad Formulation of Junction Conditions in General Relativity
Authors: Estabrook Frank B. , Wahlquist Hugo D.
Published: January 2005

Explicit and complete junction conditions across internal boundaries are found for the Ricci rotation coefficients and Riemann tensor components in an arbitrary reference tetrad frame; the reference frame may be discontinuous at the boundary. The allowed jumps in inertial and gravitational field dyadics are given for the case of normal boundary motion. When the reference frame is chosen to be comoving with the matter distribution on either side of the boundary, the junction conditions include such immediately physical results as the relativistic Rankine-Hugoniot relations. It is expected that use of such comoving reference frames will be important in finding discontinuous exact solutions.
Analyticity in the Potential Strength
Authors: Masson D.
Published: January 2005

The partial-wave S-matrix element is examined as a function of potential strength g. It is shown to be related to a series of Stieltjes in g. This is accomplished by looking at the zeros of the Jost function below threshold and the zeros and poles of tan δι above threshold. The series of Stieltjes property is used to establish the convergence of the Padé approximant method of summing the Born series.
Some New General Relativistic Dust Metrics Possessing Isometries
Authors: Farnsworth David L.
Published: January 2005

In a four-dimensional Lorentzian manifold in which Einstein's gravitational field equations hold with the field produced by pressure free dust, a significant set of new solutions is found. Assuming that the manifold possesses a four parametric group of isometries of type 5 in Bianchi's classification, which act on a three-dimensional negative definite subspace, all metrics are found. The solutions are unusual in that the geodesics which the particles follow are not orthogonal to the three-dimensional negative-definite subspace so that the space will not appear homogeneous to these observers. The isotropic expansion is nonzero for almost all these solutions.
Statistical Mechanics of Dimers on a Quadratic Lattice
Authors: Ferdinand Arthur E.
Published: January 2005

The partition function for the square lattice completely filled with dimers is analyzed for a finite n × m rectangular lattice with edges and for the corresponding lattice with periodic boundary conditions. The total free energy is calculated asymptotically for fixed ξ = n/m up to terms o(1/n2−δ) for any δ > 0. The bulk terms proportional to nm, the surface terms proportional to (n + m) which vanish with periodic boundary conditions, and the constant terms which reveal a parity and shape dependence are expressed explicitly using dilogarithms and elliptic theta functions.
Generalization of the Determinantal Method to Continuous Channels
Authors: Newton Roger G.
Published: January 2005

The procedure by which all elements of the S matrix in multichannel scattering problems are expressed in terms of the Fredholm determinant of the Lippmann-Schwinger equation, is generalized to the case of ``continuous channels.'' This is a preliminary step toward its generalization to three (or more)-particle problems, in which the possibility of ``ionizing'' an initial bound state always introduces such a continuum. It is found that, whereas in the case of discrete channels the necessary functions can be obtained from the Fredholm determinant either by analytic continuation in the total energy, or by a ``substitution rule,'' for continuous channels only the latter procedure works, and it is not equivalent to an analytic continuation.
Existence and Bifurcation Theorems for the Ginzburg-Landau Equations
Authors: Odeh F.
Published: January 2005

The second-order transition of a superconducting material from normal to superconducting state according to the Ginzburg-Landau theory is rigorously discussed. The bifurcation of a superconducting state is proved for both the Abrikosov mixed state and the case of a film in a parallel magnetic field when the flux or external field is slightly less than critical. The existence of a mixed state for all values of flux below the critical value is also proved.
Results on the Analyticity of Many-Body Scattering Amplitudes in Perturbation Theory
Authors: Federbush Paul
Published: January 2005

The problem of analytic continuation of the many-body scattering amplitude associated with a perturbation-theory diagram under the rotation of the final momenta from real to complex momenta, k → (1 + iθ)k, is studied. It is shown that the contour of integration over internal momenta can be distorted avoiding singularities of the integrand, as θ varies for small enough θ. If the diagram is connected enough, the potentials are Yukawa-type, Re E > 0, and Im E < 0. The rotation angle can be picked independently of Im E.
Daughter Regge Trajectory in a Field Theory Model
Authors: Swift Arthur R.
Published: January 2005

All contributions of ladder diagrams in a λφ3 theory with unequal masses which are asymptotically of order t−2 lnm t are summed to give a family of secondary Regge trajectories. The analysis is carried out with the Mellin transformed scattering amplitude. The daughter Regge trajectory predicted by Freedman and Wang is identified. For equal internal masses on the sides of the ladder, the daughter pole has the following properties: (i) The trajectory function α(s) is constant when calculated to lowest order in the coupling constant; that is, the pole is fixed. (ii) The pole moves in higher order, but the trajectory function has no two-particle cut. (iii) The residue of the pole has no two-particle cut, and vanishes to all orders for equal external masses. The amplitude with unequal internal masses is considered in lowest order, and it is shown that three-particle scattering should continue to dominate the daughter trajectory function although there is a two-particle cut. The daughter pole moves towards the physical region less rapidly than the leading pole, and it develops a smaller imaginary part at the two-particle threshold. It is concluded that a detailed statement about the motion of the daughter pole requires an accurate treatment of three-particle scattering. As a by-product of this work an earlier error in a treatment of the mixing of Regge poles and cuts is corrected.
Exact Occupation Statistics for One-Dimensional Arrays of Dumbbells
Authors: Lichtman D. , McQuistan R. B.
Published: January 2005

Exact relationships are developed which describe the occupation statistics for one-dimensional arrays of dumbbells. It is shown that in the limit, as the number of compartments per array tends to infinity, these relationships reduce to those calculated, using the Bethe approximation when the number of nearest neighbors is two. A partition function, which includes the influence of the configurational correlation inherent in a one-dimensional array of dumbbells, is also derived and discussed.
Infinite Systems of Classical Particles
Authors: Katz Amnon
Published: January 2005

In this paper, infinite translation-invariant and periodic systems of classical particles are treated directly—not as limits of finite systems. A formalism of classical creation and annihilation operators that create and destroy classical identical particles at points of phase space is employed. By use of this formalism, classical dynamical variables are expressed without reference to the canonical coordinates and momenta of individual particles, or to the number of particles. Different physical situations are described by different representations of the algebra of creation and annihilation operators. The concept of thermal equilibrium is generalized so as to be meaningful in infinite systems. Stationary states and thermal-equilibrium states for an infinite system of noninteracting particles (possibly in a periodic external potential) are exhibited explicitly.
Structure of the Crossing Matrix for Arbitrary Internal Symmetry Groups. II. Matrices in SU (n)
Authors: Fairlie D. B.
Published: January 2005

It is shown that in SU(n) two distinct processes can give rise to identical crossing matrices in general. In SU(2) and SU(3), however, the crossing matrix corresponds to a unique scattering process, and thus the dynamical equations in the elastic channel are sufficient to discriminate between different processes. Some SU(n) crossing matrices, which generalize the work of Cook, Muturza, and Rashid, are given.
Theory of the Linear Fokker-Planck Collision Operator
Authors: Su C. H.
Published: January 2005

The linearized Fokker-Planck collision integral with coulomb interaction is expanded in terms of surface spherical harmonics. The radial part of the distribution function is shown to be governed by a set of decoupled differential-integral equations. The differential operators are shown to be self-adjoint while the integral operators are symmetric and completely continuous. The spectrum of the eigenvalues contains, on top of discrete points, a continuous part ranging from zero to minus infinity. The discrete part of the spectrum is obtained by requiring that the corresponding eigenvectors have a definite asymptotic behavior at large velocity. A variation principle is constructed for the computation of the discrete spectrum.
Maximal Analytic Extension of the Kerr Metric
Authors: Boyer Robert H. , Lindquist Richard W.
Published: January 2005

Kruskal's transformation of the Schwarzschild metric is generalized to apply to the stationary, axially symmetric vacuum solution of Kerr, and is used to construct a maximal analytic extension of the latter. In the low angular momentum case, a2 < m2, this extension consists of an infinite sequence Einstein-Rosen bridges joined in time by successive pairs of horizons. The number of distinct asymptotically flat sheets in the extended space can be reduced to four by making suitable identifications. Several properties of the Kerr metric, including the behavior of geodesics lying in the equatorial plane, are examined in some detail. Completeness is demonstrated explicitly for a special class of geodesics, and inferred for all those that do not strike the ring singularity.