bluuebunny/crossref_metadata_2025 huggingface dataset:
Interpretation of the Symmetry of the Clebsch-Gordan Coefficients Discovered by Regge
Authors: Bincer Adam M.
Published: February 2004

An interpretation is proposed for the intriguing symmetry of the Clebsch-Gordan coefficients discovered in 1958 by Regge. The interpretation is based on the observation that, in the reduction of the Kronecker product of two irreducible representations of an SU(2) group, there appears in a natural way another SU(2) group, which is almost independent of the original one. The Regge symmetry is interpreted as the symmetry under the interchange of these two SU(2) groups. In more picturesque language, the Regge symmetry is the symmetry under the interchange of the ``two-ness'' of the two angular momenta being added with the ``two-ness'' of SU(2). It follows from this interpretation that a symmetry of the same nature is present in the generalized Clebsch-Gordan coefficient that appears in the reduction of the Kronecker product of n (and not two, except when n = 2) irreducible representations of SU(n).
Properties of a Simplified Liquid 4He Ground State
Authors: Girardeau M. D.
Published: February 2004

A many-body wavefunction is constructed by antisymmetrization, with respect to the electron variables, of a product of 4He-atom wavefunctions, each in its individual ground state. This wavefunction is shown to have the following properties: (1) The pair distribution function D(Rij) vanishes at zero separation Rij = 0; part of the mutual repulsion of 4He atoms is built into the wavefunction as a result of the exclusion principle acting between the electron shells on different atoms. (2) Neither the nuclei nor the whole atoms undergo Bose condensation, but there is a ``Fermi condensation'' similar to that shown by Yang to characterize superconductivity, arising from off-diagonal long-range order of the appropriate reduced density matrix.
Transmission Properties of an Isotopically Disordered One-Dimensional Harmonic Crystal. II. Solution of a Functional Equation
Authors: Rubin Robert J.
Published: February 2004

The amplitude of a wave of frequency ω which is transmitted by a disordered array of N isotopic defects in a 1-dimensional harmonic crystal is investigated in the limit N → ∞. In particular, the ratio T̂N(ω) of the amplitude of the Nth defect to the amplitude of the first defect is represented as exp [−Nα̂N(ω,Q,{an})], where {an}, n = 2, ⋯, N, is the sequence of nearest-neighbor spacings and Q = (M − m)/m. It is known from earlier work that α̂N(ω,Q,{an}) is the logarithm of the Nth root of the magnitude of a continuant determinant of order N. The value of the continuant is expressed formally as a product of N factors ĝn which are recursively related. In the present case, the ĝn happen to lie on a circle K0 in the complex ĝ plane. Assuming that the spacings between defects are independent identically distributed random variables with the mean value c−1 and going to the limit N → ∞, a functional equation for the limiting distribution function of the ĝn on K0 is derived. The limiting value α(ω,Q,c)=limα̂N(ω,Q,{an}), as N → ∞, can be determined from the limiting distribution function of the ĝn. We determine the solution of the functional equation in three different ways for three different cases: (a) In the case of the special frequency of Matsuda, ω = 2−½ and Q = 1, we obtain exact values of the integral of the ĝ distribution function which are in excellent agreement with Monte Carlo estimates; (b) in the physically interesting case where the mean spacing between defects is small compared to the incident wavelength, i.e., c−1ω ≪ 1, we obtain the solution of the functional equation correct to first order in c−1ω and we calculate the lowest-order nonzero value of α(ω, Q, c); (c) for the general case of moderate values of ω, Q, and c, we develop a numerical method for solving the functional equation and present the results of the numerical calculations in several representative cases. These numerical results are in good agreement with Monte Carlo estimates. One of the principal results, obtained by solving the functional equation, is that α(ω, Q, c) > 0 for ω ≪ c < 1 and ω(|Q| + c−1) ≪ 1 with Q ≠ 0.
Unbounded Local Observables in Quantum Statistical Mechanics
Authors: Sewell G. L.
Published: February 2004

The algebraic formulation of quantum statistical mechanics is extended so as to include local unbounded observables. We start, in a usual way, with a C*-algebra U of quasilocal bounded observables in Fock space HF, an arbitrary, locally normal state φ on U, and a corresponding Gel'fand-Naimark-Segal (GNS) representation Rφ of U in a Hilbert space Hφ. We then construct a set QL of local, closed operators whose domains are dense in HF, such that QL includes all the local observables of the system. The representation Rφ is then extended so as to provide a *-homomorphism of HL into the closed, densely defined operators in Hφ. Correspondingly, a number of results previously established for the local bounded observables are extended to the unbounded ones. For appropriate classes of locally normal states, these extended results include the Kubo-Martin-Schwinger boundary conditions, the spatially asymptotic and ergodic properties of space-correlation functions, and the temporally ergodic properties of time-correlation functions. It is also shown that, for locally normal Gibbs states, the time correlations between elements of a specified subset of QL are thermodynamical limits of the corresponding correlations for finite systems.
Short Proof of a Conjecture by Dyson
Authors: Good I. J.
Published: February 2004

Dyson made a mathematical conjecture in his work on the distribution of energy levels in complex systems. A proof is given, which is much shorter than two that have been published before.
Quantum Theory of the Generalized Wave Equations. I
Authors: Tripathy Kishor C.
Published: February 2004

We have made a systematic analysis of the quantum theory of the infinite-component fields that transform under the combined representations of SL(2, C)(Majorana)⊗Dirac. A complete set of solutions of the wave equation includes solutions with timelike and spacelike momenta. We have explicitly calculated the mass spectra for the timelike and spacelike cases. Our method makes use of the decomposition of the product representation into reducible representations of the ``little'' groups SU(2) and SU(1, 1). Finally, the quantization of the generalized fields is presented.
Convolution Approximation for the n-Particle Distribution Function
Authors: Wu F. Y. , Chien M. K.
Published: February 2004

The convolution approximation introduced by Jackson and Feenberg for the 3-particle distribution function is extended to the n-particle distribution function gn. It is shown that the generalized convolution form satisfies the limiting and the recursion relations connecting gn and gn+1.
Instantaneous Interaction Relativistic Dynamics for Two Particles in One Dimension
Authors: Hill Robert Nyden
Published: February 2004

Differential conditions which guarantee the Lorentz invariance of instantaneous action-at-a-distance relativistic dynamics have been given by Currie and by Hill. The present paper obtains the general solution of these conditions for the special case of two particles in one dimension. The resulting equations of motion are integrated to obtain the world lines. World-line invariance is explicitly demonstrated. The equations of motion are cast into Hamiltonian form with the transformations of the inhomogeneous Lorentz group canonical. The Hamiltonian formulation is made unique up to canonical transformation for those forces which fall off faster than the inverse square of the interparticle separation by the demand of asymptotic reduction to free particle form. The special case of the inverse-square-law forces of electrodynamics is considered; the constant of the motion associated with Lorentz invariance is found to have an interaction piece which survives asymptotically as in the relativistic mechanics of Van Dam and Wigner. The Poisson bracket [x1, x2] between the physical coordinates also has an interaction piece which survives asymptotically for electrodynamics.
Scattering in General Higher Sectors of the Lee Model
Authors: Liu Tsu-Huei , Zimmerman Robert L.
Published: February 2004

The technique of an iterative expansion in terms of the 2-body solution used in V−2θ sector of the Lee model has been extended to the general higher sector, i.e., V−nθ sector with n > 2 so that S matrices for the general cases of scattering (n − 1)θ particles off the (Vθ) bound state can be calculated. Again, as in V−2θ sector, each term of the expansion preserves the properties of the (Vθ) bound state, the analytic structure, and symmetries of the τ functions.
Multipole Moments. I. Flat Space
Authors: Geroch Robert
Published: February 2004

There is an intimate connection between multipole moments and the conformal group. While this connection is not emphasized in the usual formulation of moments, it provides the starting point for a consideration of multipole moments in curved space. As a preliminary step in defining multipole moments in general relativity (a program which will be carried out in a subsequent paper), the moments of a solution of Laplace's equation in flat 3-space are studied from the standpoint of the conformal group. The moments emerge as certain multilinear mappings on the space of conformal Killing vectors. These mappings are re-expressed as a collection of tensor fields, which then turn out to be conformal Killing tensors (first integrals of the equation for null geodesics). The standard properties of multipole moments are seen to arise naturally from the algebraic structure of the conformal group.
Initial-Value Problem for the Equation(∂∂t + a(t,x,y)∂∂x + b(t,x,y)∂∂y + c(t,x,y) + d(t,x,y)∂2∂x∂y)u=f(t,x,y) in the Complex Domain
Authors: Mülthei Heinrich N.
Published: February 2004

The initial-value problem ut+a(t,x,y)ux+b(t,x,y)uv+c(t,x,y)u+d(t,x,y)uxv=f(t,x,y), u(0,x,y)=φ(x,y)is first considered in a complex polycylinder Q whose center is the origin. All functions appearing are holomorphic in Q. On the one hand, this problem has at most one holomorphic solution in Q, while on the other hand, the strong assumptions of holomorphy do not in general guarantee even the existence of a local holomorphic solution. We then treat the special initial-value problem of Lambropoulos [J. Math. Phys. 8, 11 (1967)]ut+axux+byuv+cxyu+uxv=0, u(0,x,y)=φ(x,y),where a, b, and c are complex constants. We are able to derive an infinite series as the formal solution, which is easy to examine. Moreover, some statements on the existence of a local holomorphic solution are given.
Internal Symmetry Cannot Be Concealed
Authors: Kantor Paul B.
Published: February 2004

We consider the problem of determining whether a given ``particle'' is elementary or is some member of a degenerate multiplet corresponding to an exact symmetry. We discuss a double-scattering experiment which can make this determination unless the members of the multiplet are unable to distinguish one another. Finally, such an inability is shown to be incompatible with the usual relation between spin and statistics and known analyticity properties of scattering amplitudes for strongly interacting particles.
Massive Vector Field: Covariant Definition of Independent Components and Quantization
Authors: Mathews P. M.
Published: February 2004

A new approach to the theory of the vector field is presented in which inelegant features like negative terms in the energy do not make an appearance at any stage. All components of the field are handled in a completely symmetric fashion and the explicitly covariant appearance of the theory is preserved in the process of quantization as well as in earlier stages. Though the special features which arise when the mass vanishes are pointed out, a detailed treatment of that case is not included here and will be given separately.
Boundary-Value Problems for the Integro-Differential Equations of Nonlocal Wave Interaction. I
Authors: Kalaba Robert
Published: February 2004

It is shown that the linear 2-point boundary-value problems for the integro-differential equations of nonlocal wave interaction may be reduced to Cauchy systems. This provides new equations for the study of solid state plasmas, electron-electron interactions, the anomalous skin effect, and helicon propagation near doppler-shifted cyclotron resonance. The Cauchy system is of analytic interest and computational utility.
Mandelstam Representation in Potential Scattering
Authors: Chela-Flores Julian
Published: February 2004

A simpler and more general proof of the Mandelstam representation based on Hartog's theorem is presented within the framework of potential scattering; the potential is chosen to be a superposition of the Yukawa type with no further restrictions.
De Sitter Symmetric Field Theory. III. Quantization in the Tung-Weinberg Basis
Authors: Bakri M. M.
Published: February 2004

The de Sitter symmetric fields, satisfying the field equations (Sμνpν + κγμ)ψ = pμψ, are quantized in the Tung-Weinberg basis. The properties of the associated Green's and causal functions are studied. Transformations of the Hilbert space under CPT and inhomogeneous Lorentz transformations are given. A simple closed expression is obtained for the Shaw-Weinberg matrix tensor tm1m2α1⋯α2s.
Peratization of a Class of Exponentially Singular Potentials
Authors: Frank William M. , Land David J.
Published: February 2004

First, second, and third peratizations are performed for evaluation of the scattering length for repulsive potentials of the form V(r) = gr−m exp (λ/r) with m an integer ≥4. For m = 4 a nontrivial result is found in second and higher peratization which has the same weak-coupling limit as the exact answer and agrees with the result of Calogero and Cassandro. For m > 4 one finds a zero result in both first, second, and third peratization, suggesting the inadequacy of the procedure as generally applied. The procedure of separate peratization of numerator and denominator of a ratio which is employed in this work is discussed at length. The optimum n method is introduced in the course of this discussion as a powerful and convenient method of evaluating the scattering length without summing the appropriate series. It also clarifies the limitations of the peratization approximation. A modification of the peratization procedure is suggested which has promise of being a more successful approximation scheme.
Approximate Solutions of the Unitarity Equation
Authors: Eftimiu C.
Published: February 2004

The possible use of the classical Newton approximation method, as extended by Kantorovich to Banach spaces, is discussed in connection with the problem of solving the unitarity equation for the phase of a scattering amplitude, in terms of the corresponding differential cross section.
Clebsch-Gordan Series and the Clebsch-Gordan Coefficients of O(2, 1) and SU(1, 1)
Authors: Wang Kuo-Hsiang
Published: February 2004

The Clebsch-Gordan series of the O(2, 1) group and its covering group SU(1, 1) are derived for all cases except that of the supplemental series. The continuable Clebsch-Gordan coefficients (or equivalently, the Wigner coefficients) are explicitly expressed in terms of the generalized hypergeometric function 3F2. The spectra in the decomposition of the product of the two principal series are discussed. The applications to the UIR of O(2, 2) are also studied.
Foundations for Quantum Mechanics
Authors: Giles Robin
Published: February 2004

A discussion is given of the structure of a physical theory and an ``ideal form'' for such a theory is proposed. The essential feature is that all concepts should be defined in operational terms. Quantum (and classical) mechanics is then formulated in this way (the formulation being, however, restricted to the kinematical theory). This requires the introduction of the concept of a mixed test, related to a pure test (or ``question'') just as a mixed state is related to a pure state. In the new formulation, the primitive concepts are not states and observables but certain operationally accessible mixed states and tests called physical. The notion of a C*-system is introduced; each such system is characterized by a certain C*-algebra. The structure of a general C*-system is then studied, all concepts being defined in terms of physical states and tests. It is shown first how pure states and tests can be so defined. The quantum analog of the phase space of classical mechanics is then constructed and on it is built a mathematical structure, called a q-topology, which is a quantum analog of the topology of classical phase space. Mathematically, a q-topology is related to a noncommutative C*-algebra as an ordinary topology is related to a commutative C*-algebra. Some properties of the q-topology of a C*-system are given. An appendix contains some physically motivated examples illustrating the theory.
Photoelectron Shot Noise
Authors: Picinbono B. , Bendjaballah C. , Pouget J.
Published: February 2004

The instants of time emission of photoelectrons generated by a detector immersed in an optical field constitute a point compound Poisson process. A complete definition of such a process is introduced to calculate some average values of the distribution. The shot noise due to this point process is also considered and we study the difference between the ``deterministic'' and the ``random'' shot noises. They are completely defined by the set of their characteristic functions. We consider also the asymptotic properties of the shot noise and we show that for large mean density of the point process the fluctuations are not described by a Gaussian, but by a Gaussian compound random function. Thus the central limit theorem is not strictly valid. An experimental setup to obtain these fluctuations is described and some statistical properties of the asymptotic shot noise are presented.
Anholonomic Bases in the Study of the Spin Connection and Gauge Potentials in a Riemann Space
Authors: Treat Richard P.
Published: February 2004

If parameters of a spin connection have a holonomy group which is the Lorentz group or a subgroup thereof and if a certain algebraic restriction involving the Riemann tensor, say R, is satisfied, then there is a one-to-one relation between the spin connection sΓμab and parameters of a Riemannian event connection Γμκλ, in a neighborhood of an assumed solution of the equations which establish the correspondence [see H. G. Loos, Ann. Phys. 25, 91 (1963)]. We have, by the use of anholonomic bases in the Riemann space, simplified the equations which determine the map and have shown that if the algebraic condition R is satisfied, a one-to-one correspondence holds also in the large. The same method, involving anholonomic bases, has also been used to study the map between gauge potentials acting in the internal space formed by generators of local Lorentz transformations and parameters of connection of a Riemannian event space. An analogous theorem is proved which asserts that if R is satisfied, then the correspondence between the gauge potential and the parameters of the event connection is one-to-one.
Tensor Harmonics in Canonical Form for Gravitational Radiation and Other Applications
Authors: Zerilli Frank J.
Published: February 2004

An analysis is made of the relation between the tensor harmonics given by Regge and Wheeler in 1957 and those given by Jon Mathews in 1962. This makes it possible to use the Regge-Wheeler harmonics, which are given in terms of derivatives of scalar spherical harmonics, for calculations while using Mathews' form of the harmonics [linear combinations of the elements of the product basis formed from a basis for scalar functions on the 2-sphere and a basis for symmetric tensors such that the product basis is split into sets which transform under the irreducible representations of SO(3)] to elucidate the properties of tensor harmonics. Thus, a convenient orthonormal set of harmonics is given which is useful in studying, for example, gravitational radiation.
Wave Equations for Unstable Particles
Authors: Humi Mayer
Published: February 2004

A model is presented for the kinematical description of unstable particles in terms of equations which are invariant under broken IO(4, 1). This model agrees with the current models of unstable particles, both those treating lifetimes and mass spectrum. It is shown that the concepts of generalized eigenfunction expansions and complex Fourier transforms enable us to deduce rigorously some of the guesses and assumptions made in these models. Finally, we deal with multiplets of unstable particles and discuss some of the predictions of the theory.
Another Note on Two Binomial-Coefficient Identities of Rosenbaum
Authors: Srivastava H. M.
Published: February 2004

This paper aims at providing a direct and unified approach to two binomial-coefficient identities proved recently by Rosenbaum [J. Math. Phys. 8, 1973 (1967)], who made use of rather long and involved considerations of commutation relations. The analysis presented here verifies the existence of the wider ranges of validity of these identities, as was subsequently pointed out by Gould [J. Math. Phys. 10, 49 (1969)].
New Integral Formulation of the Schrödinger Equation
Authors: Baird L. C.
Published: February 2004

The 1-dimensional Schrödinger equation is replaced by a pair of coupled integral equations. The equations are solved by iteration. The zeroth-order solution is the WKB approximation. The solutions are valid even in the presence of classical turning points and discontinuous potentials. Thus, connection formulas are not required. Low-order calculations are carried out in several cases of interest. In each case, a first-order calculation gives results comparable to or better than those obtained with connection formulas.
Solution of Mathieu's Type of Secular Equations
Authors: Chan Yau W.
Published: February 2004

A discussion is given for the general solution of a secular equation with all other matrix elements equal to zero except Hii, Hi i+h, and Hi+h i. Both the eigenvalue and the amplitudes of the corresponding eigenfunction are expressed in terms of continued fractions of the matrix elements. A solution of Mathieu equation is used as an example to compare the present method with other methods.
Diffraction Theory of Holography
Authors: Wolf E. , Shewell J. R.
Published: February 2004

A diffraction theory of side-band holography for transmission objects is formulated. Conditions are derived under which good quality images are formed. A simple geometrical construction is found by means of which the location of the images may be determined. It is also shown that, under conditions that are often satisfied in practice, one of the two images will be completely absent. This effect is entirely caused by diffraction (conversion of a homogeneous wave into evanescent waves on diffraction by the hologram) and has nothing to do with the finite resolving power or the finite thickness of the photographic plate. Numerical examples illustrating this phenomenon are given.
Classical and Quantum Mechanical Correlation Functions of Fields in Thermal Equilibrium
Authors: Keller Joseph B.
Published: February 2004

The two-point, two-time correlation functions of classical and quantum mechanical fields in thermal equilibrium in an arbitrary domain are considered. For classical fields that satisfy linear equations of motion, the correlation functions are expressed in terms of certain Green's functions of the domain. It is also shown, by evaluating the characteristic functional of the field, that a classical field is Gaussian distributed, so that all higher-order correlations can be expressed in terms of the second-order correlations. Then the second-order correlations are evaluated in various cases, and the classical and quantum mechanical results are compared. They are found to agree except within layers, about a thermal wavelength wide, near the boundaries of the domain and near the characteristic surface or light cone emanating from either of the two points. Thus the quantum mechanical correlation function can be approximated by the classical one with quantum-mechanical boundary-layer corrections.
Summability of the Many-Fermion Perturbation Series with Attractive Forces
Authors: Baker George A.
Published: February 2004

The summability of the many-fermion perturbation series in the presence of attractive forces is considered. We find that, although it is an asymptotic series, the potential-strength perturbation series is summable. We find that some rearrangements to handle the hard-core potentials also lead to the correct sum; however, the ``hole-line'' summation procedure using Brandow's choice for intermediate state energies is either wrong or deceptive in its convergence.
Theory of Particles with Variable Mass. II. Some Physical Consequences
Authors: Greenberger Daniel M.
Published: February 2004

The formalism of the previous paper, in which mass and proper time are treated as independent dynamical variables in a canonical formalism, is shown to imply certain physical consequences. There will exist a mass vs proper time uncertainty relation; trajectories and proper time will be exactly determinable in an external gravitational field, while mass will be determinable in an external electromagnetic field; and conventional quantum mechanics will imply that equivalence is invalid for low-lying quantum states. This leads to a second possible way to quantize a system in a gravitational field, which introduces a fundamental length. It is shown that it is possible to test for quantum interference effects of gravitational systems with present technology and conventional techniques, using the earth's gravitational field.
Canonical Unit Adjoint Tensor Operators in U(n)
Authors: Louck James D. , Biedenharn L. C.
Published: February 2004

A complete, fully explicit, and canonical determination of the matrix elements of all adjoint tensor operators in all U(n) is presented. The class of adjoint tensor operators—those transforming as the IR [1 0̇ −1]—is the first exhibiting a nontrivial multiplicity. It is demonstrated that the canonical resolution of this multiplicity possesses several compatible (or equivalent) properties: classification by null spaces, classification by degree in the Racah invariants, classification by limit properties, and the classification by conjugation parity. (The concepts in these various classification properties are developed in detail.) A systematic treatment is presented for the coupling of projective (tensor) operators. Six appendices treat in detail the explicit evaluation of all Gel'fand-invariant operators (Ik), the structural properties of Gram determinants formed of the Ik, the zeros of the norms of the adjoint operators, and the conjugation properties of the canonical adjoint tensor operators.
Derivation of the Wave and Scattering Operators for an Interaction of Rank One
Authors: Grubb M. Anthea , Pearson D. B.
Published: February 2004

Expressions for the wave and scattering operators in terms of singular integral operators are rigorously derived for a simple scattering system, for which the interaction Hamiltonian V is of rank 1. The wave operators, defined by the strong limits, lim eiHte−iH0t as t→∓∞, are known to exist for this interaction, and the existence of these limits is assumed throughout the paper. Using complex contour integrals to write down representations for certain operators, we find an identity for the evolution operator in terms of a family of bounded operators, from which singular integral operators are obtained in the limit as t → ∞. The analysis differs from previous applications of time-dependent scattering theory to this system in that at no stage need ``smoothness'' or Hölder conditions be assumed for the element of L2(− ∞, ∞) from which V is constructed.
Rotation in Closed Perfect-Fluid Cosmologies
Authors: Matzner Richard A.
Published: February 2004

A Lagrangian is presented which describes the evolution of anisotropy in rotating closed (Bianchi type IX) cosmologies. It is assumed that the matter is a perfect fluid with an adiabatic equation of state p = P(ρ) such that 0 < dp/dρ < 1 − γ, γ > 0. The matter terms enter the Lagrangian as a potential which for large anisotropy is essentially identical to one found previously for dust. Because the dust potential has been thoroughly investigated by Ryan, we confine our discussion of the dynamics to a few brief remarks. The matter terms are crucial for the rotation since the constraint equations require matter for the presence of rotation. The chief effect of the rotation is the appearance of centrifugal terms in the Lagrangian which exclude certain parameter values to the system. An appendix gives a proof that R = 0 is a true infinite-density singularity.
Curvature Collineations for Gravitational pp Waves
Authors: Aichelburg P. C.
Published: February 2004

Vacuum fields which admit a covariant constant vector are investigated in order to find ``curvature collineations,'' i.e., £Rklji=0. For all discussed types of pp waves it is shown that proper curvature collineations exist. We state the explicit form of these transformations.
Analytic Function Method for the Many-Body Problem
Authors: Anderson J. T.
Published: February 2004

The equivalence of analytic functions in complex variable representations with conserved functions in real variable representations is utilized to write eigenvalue equations for the energy and momentum on the complex planes. A self-consistent field method is then developed and used to study the scalar interactions of a particle gas with arbitrary coupling strength. The eigenvalue equations for momentum and energy yield equilibrium solutions which are functions only of the initial values and a renormalized coupling strength. The results are applied to the electron gas and to the Bose gas.
When Is an Ising Magnet a Ferromagnet?
Authors: Sherman S.
Published: February 2004

A subcollection of the correlation inequalities recently obtained by Ginibre for Ising ferromagnets is shown to be enough to guarantee that an Ising magnet in an external magnetic field with only 2-body interactions is a ferromagnet. Thus, one has a necessary and sufficient set of correlation inequalities to guarantee that an Ising magnet in a nonnegative external magnetic field with only 2-body interactions is a ferromagnet.
Equal-Time Commutation Relations and Divergence Conditions
Authors: Bergström K.
Published: February 2004

The connection between divergence conditions for currents or generalized currents and equal-time commutation relations is investigated in terms of the response of physical systems to external fields. We give a simple method of constructing physical amplitudes and of obtaining generalized Ward identities and equal-time commutation relations for currents. In order to set up this scheme, we have to make an assumption about the response of the physical system to a change of the external parameters and also consider the gradient terms. In this way, we try to reproduce the current algebra formalism. It is hoped that, when this has been done, we will have made it plausible that a certain representation of the algebra exist. However, we do not discuss the formal reconstruction of the field theory of strong interactions in terms of electromagnetic, weak, and gravitational scattering data. The discussion in this paper is mostly restricted to finite-dimensional algebras, but a generalization of the method to infinite-dimensional situations is briefly outlined.
General Theorem on Bifurcation and Its Application to the Hartree Equation of the Helium Atom
Authors: Reeken M.
Published: February 2004

The existence of a globally extended branch of pointwise positive solutions of a class of nonlinear eigenvalue problems is established. The branch bifurcates from the lowest eigenvalue of the associated linearized problem. The general theorem is then applied to the Hartree equation of the helium atom, giving a rigorous proof for the existence of a solution of this equation.
Generalized Racah Tensors and the Structure of Mixed Configurations
Authors: Butler P. H. , Wybourne B. G.
Published: February 2004

Generalized Racah tensors are defined after the manner of Elliott and Feneuille. The linear combinations ±w(κk)(l, l′) used by them are redefined to permit the correct embedding of the group R4 in the higher groups that may be used to classify the states of mixed configurations. A number of points regarding the transformation properties of states and operators are clarified and related to the problem of the symmetrization of the Coulomb repulsion in mixed configuations.
Some Aspects of the Relationship between Mathematical Logic and Physics. I
Authors: Benioff Paul A.
Published: February 2004

Quantum mechanics has several deficiencies as a complete theoretical description of the measurement process. Among them is the fact that the quantum mechanical description of correlations between the single measurements of a sequence is quite problematic. A single measurement is defined to be a preparation followed by an observation. In particular, one feels that an infinite sequence of such single measurements which corresponds to the measurement of a question O on a state η where η does not lie entirely in an eigenspace of O should generate a random output sequence. However, quantum mechanics seems to say nothing about this. In this paper, physical theories are defined in such a manner that correlations between single measurements are explicitly included. In particular, a physical theory is considered to be a mapping U, with domain in the set [Qsτ] of infinite instruction strings for carrying out infinite sequences of single measurements and range in the set of probability measures defined on A, the usual σ algebra of subsets of Ω. Ω is the set of all infinite sequences of natural numbers. A fundamental property which any valid physical theory must satisfy is that it agrees with experiment. It is proposed and discussed here that much of the intuitive meaning of agreement between a theory U and experiment with respect to H is given by the statement ∀Qsτ [U(Qsτ) defined⇒E(H,U(Qsτ),ψQsτ)],where U(Qsτ) is the probability measure U associates with the infinite instruction string Qsτ and ψQsτ is the outcome sequence obtained by carrying out Qsτ. E(H, U(Qsτ),ψQsτ) is the statement that all formulas in H with one free sequence variable which are true on Ω almost everywhere with respect to U(Qsτ) are true for ψQsτ. H is a subclass of the class of all formulas in a formal language L. A theorem is proved which states that, if U(Qsτ) corresponds to a nontrivial product probability measure and U H-agrees with experiment, then the outcome sequence ψQsτ is H-random. H-randomness is defined here in terms of the statement E(H, P, φ). Another property of a valid physical theory, which is defined here, is that, for some Qsτ, U(Qsτ) must be determinable on much of AH from ψQsτ. Sufficient conditions for this property to hold are given. AH is the class of all H definable subsets of Ω. Some properties of the statement E(H, P, φ) are given. Among other things, it is proved that, if E(H, P, φ) holds and P is a nontrivial probability measure on A, then φ is not definable in H.
Multipole Moments. II. Curved Space
Authors: Geroch Robert
Published: February 2004

Multipole moments are defined for static, asymptotically flat, source-free solutions of Einstein's equations. The definition is completely coordinate independent. We take one of the 3-surfaces V, orthogonal to the timelike Killing vector, and add to it a single point Λ at infinity. The resulting space inherits a conformal structure from V. The multipole moments of the solution emerge as a collection of totally symmetric, trace-free tensors P, Pa, Pab, ⋯ at Λ. These tensors are obtained as certain combinations of the derivatives of the norm of the timelike Killing vector. (For static space-times, this norm plays the role of a ``Newtonian gravitational potential.'') The formalism is shown to yield the usual multipole moments for a solution of Laplace's equation in flat space, the dependence of these moments on the choice of origin being reflected in the conformal behavior of the P's. As an example, the moments of the Weyl solutions are discussed.
Theory of Electrodynamics in Media in Noninertial Frames and Applications
Authors: Mo Tse Chin
Published: February 2004

The theory of local electrodynamics of media in given noninertial frames, within the Maxwell-Einstein theory, is constructed in terms of local observable EM fields and physical media parameters of its comoving frame. Localization of tensors to observables for and their relations among observers in different frames are introduced; local and global constitutive tensors and local Maxwell equations are obtained and interpreted. Also, a Lagrangian formulation for both lossless and lossy media is constructed, and boundary conditions, local conservation laws, and energy tensors are obtained. The applications concern linear accelerational and rotational media in flat space-time for which local Maxwell equations in comoving frames are obtained. Then an EM wave propagating in the direction of acceleration is studied in the accelerating frame. The first-order propagation shows a frequency shift and amplitude change which have very simple physical significances of instantaneous Doppler shift and photon density in media and which agree with familiar results in the vacuum limit. A particle model for this wave shows that the ``mass-dressed'' photon is dragged by the medium and does not follow a geodesic path. In the case of a rotating medium, a plane wave scattered by a rotating sphere is solved by an integral iteration method in the laboratory frame. The scattered field which is associated only with the rotation of the medium is separated from the Mie scattering. Its first-order amplitudes are found for incidences perpendicular and parallel to the rotation axis. Particular symmetry and shapes of scattering amplitude in the results agree with intuition and resemble radiation patterns of appropriately induced traveling electric and magnetic dipole sheaths.
Quantum Theory of the Electromagnetic Field in a Variable-Length One-Dimensional Cavity
Authors: Moore Gerald T.
Published: February 2004

The quantum theory of linearly polarized light propagating in a 1-dimensional cavity bounded by moving mirrors is formulated by utilizing the symplectic structure of the space of solutions of the wave equation satisfied by the Coulomb-gauge vector potential. The theory possesses no Hamiltonian and no Schrödinger picture. Photons can be created by the exciting effect of the moving mirrors on the zero-point field energy. A calculation indicates that the number of photons created is immeasurably small for nonrelativistic mirror trajectories and continuous mirror velocities. Automorphic transformations of the wave equation are used to calculate mode functions for the cavity, and adiabatic expansions for these transformations are derived. The electromagnetic field may be coupled to matter by means of a transformation from the interaction picture to the Heisenberg picture; this transformation is generated by an interaction Hamiltonian.
Intermediate Statistics
Authors: Katsura Shigetoshi , Kaminishi Katsuji , Inawashiro Sakari
Published: February 2004

The distinctions between intermediate statistics, parastatistics, and Okayama statistics are discussed and it is pointed out that the distribution function of the intermediate statistics does not follow from the para-Fermi statistics. The partition function, the pressure, and the specific heat of free particles which obey intermediate statistics are calculated in one, two, and three dimensions.
Finite and Infinitesimal Canonical Transformations
Authors: Testa Francis J.
Published: February 2004

The general relation between the infinitesimal generator of a 1-parameter subgroup of canonical transformations and the usual finite generating functions is obtained. This relation is found to be simply a generalization of the Hamilton-Jacobi equation. When the latter relation is solved for the finite generating function, the connections for a finite transformation can be determined without the need for integration of the associated infinitesimal transformation.
Zeros of the Grand Partition Function for a Lattice Gas
Authors: Heilmann Ole J.
Published: February 2004

The following three statements about the zeros of the grand partition function of a lattice gas with negative (attractive) interactions are proved: (1) Not all the zeros will be on the unit circle in the high-temperature limit if forces of higher order than 2-body are included; (2) in the low-temperature limit they will, in general, lie on the unit circle; (3) it is possible to have the zeros dense in the complex plane. It is also shown that not all polynomials with positive coefficients and roots on the unit circle are a grand partition function of a lattice gas.
Exactly Solvable Electrodynamic Two-Body Problem
Authors: Rudd R. A. , Hill Robert Nyden
Published: February 2004

The equations of motion of the physical 2-body problems of relativistic electrodynamics are differential-difference equations. However, in the unphysical 2-body problem in which one particle responds only to retarded fields and the other only to advanced fields, the equations of motion are differential equations. These differential equations are solved in the center-of-momentum frame by the elementary method of finding integrating factors. Solutions in an arbitrary Lorentz frame are found by a method which parametrizes the world lines on the particle velocities. All of the constants of the motion contain interaction contributions; this appears to be a characteristic feature of relativistic particle dynamics.
Comparison of SCF and kν Functions for the Helium Series
Authors: Bishop David M. , Schneider Barbara E.
Published: February 2004

Wavefunctions for He, Li+, Be2+, and O6+ are presented. They were determined by using reduced modified Bessel functions of the second kind, kν(qr). The z dependence of energies calculated using such functions for high values of z is found to be the same as for the Hartree-Fock functions.
Stark Effect in Hydrogen Atoms for Nonuniform Fields
Authors: Bekenstein J. D. , Krieger J. B.
Published: February 2004

The correction for the energy eigenvalues of the Schrödinger equation for a hydrogenic atom in a non-uniform field resulting from the inhomogeneity of the field is expressed in terms of expectation values involving the eigenfunctions of the system for a uniform field. Only the first-order terms in the inhomogeneity of the field are retained. An examination of the symmetry of the eigenfunctions for the uniform field, followed by an application of Gauss' law, shows that the correction depends only on one component of the field gradient tensor, regardless of the symmetry of the field, except for states with magnetic quantum number m = ±1. For the latter states we find the degeneracy is removed provided that the field is not cylindrically symmetric. We evaluate the correction by applying Feynman's theorem to a pair of 1-dimensional eigenvalue equations similar to those obtained in the separation of the uniform field problem in parabolic coordinates. All the necessary eigenvalues are calculated by the WKB method that has been previously employed in obtaining the eigenvalues for the uniform field problem. As the final result we present an expression for the zz component of the quadrupole tensor of the electron labeled according to parabolic quantum numbers. Finally, we discuss the use of this expression in the study of line broadening caused by interatomic interactions (pressure broadening).
Proper Orientation of Space-Time
Authors: Enosh M.
Published: February 2004

An observer determining space-time around his world line by various measurements may encounter the problem of not being able to define a unique time order and a spatial orientation along world lines of other objects. The problem is discussed and resolved with the aid of geometrical considerations.
Physical-Region Discontinuity Equation
Authors: Coster Joseph , Stapp Henry P.
Published: February 2004

A Cutkosky-type formula for the discontinuity around an arbitrary physical-region singularity is derived from precisely formulated S-matrix principles.
Some Topological Properties Connected to the Parametrized Feynman Amplitudes
Authors: Liu C. J. , Chow Yutze
Published: February 2004

An approach first developed by one of the present authors for computation involving Poincaré incidence matrix is now carried over to the so-called ``loop-matrix'' formalism. A matrix τ lim ↔{l}{ν} is introduced to prove some important properties of transformations among different sets of basic loops. Several properties in the form of lemmas and theorems are presented here. In particular, a formula of very concise form is found for the total number of possible tree graphs of a given Feynman graph in terms of its corresponding Poincaré incidence matrix. Also derived here is the formula for the total number of tree graphs in terms of any loop matrix. Their proofs show that the previously developed approach for Poincaré incidence matrix can be nicely generalized to a surprising extent to the loop matrix formalism and thus demonstrate the duality between the two formalisms.
Labeling and Multiplicity Problem in the Reduction U(n + m) ↓ U(n) × U(m)
Authors: Mickelsson Jouko
Published: February 2004

A labeling for the basis vectors in a general unitary irreducible representation of U(n + m) is introduced with the Casimir operators of the subgroup U(n) × U(m) diagonal. The multiplicities are calculated in the reduction U(n + m) ↓ U(n) × U(m) for some special cases.
Einstein Spaces with Symmetry Groups
Authors: Kerr R. P. , Debney G. C.
Published: February 2004

In this paper, we construct all possible groups of motion (symmetry groups) for empty Einstein spaces admitting a diverging, geodesic, and shear-free ray congruence. (Minkowski space is excluded throughout the discussion.) It is proved that any such Einstein space cannot admit a symmetry group with dimension greater than four. Although the field equations are not solved completely for spaces with groups of dimension one or two, a generalization of the Kerr spinning-mass solution is obtained from the 2-dimensional class. It is shown that all such spaces with 4-dimensional symmetry groups are well known: Schwarzschild, NUT (Newman, Unti, and Tamborino), and a particular hypersurface orthogonal Kerr-Schild metric. The only member of these spaces admitting a 3-dimensional symmetry group is a Petrov Type III hypersurface orthogonal metric.
Scalar-Tensor Theory in Canonical Form. II. Exact Solutions for a Static Spherically Symmetric Charged Mass Distribution
Authors: Toton Edward T.
Published: February 2004

In this part variational techniques are used to generate the differential equations determining the static fields of a charged mass distribution. The equations are solved external to the source by the Hamilton-Jacobi method under the conditions of spherical symmetry. Solutions for a charged mass shell are investigated, the rigorous solution for the electron in general relativity is given and, by limit arguments, it is shown that the same external solution arises for the electron in the scalar-tensor theory.
Hyperplane Independence of the Scattering Amplitude
Authors: Fleming Gordon N. , Miller James T.
Published: February 2004

In the context of the formal theory of scattering the scattering amplitude on the energy-momentum shell is shown to be hyperplane independent even in the presence of hyperplane-dependent interaction ``potentials.'' Also, a formal field-theoretic example of consistent hyperplane-dependent potentials is presented.
Spatially Homogeneous World Models
Authors: Ozsváth István
Published: February 2004

We obtain the field equations of Einstein for spatially homogeneous spaces as the Euler-Lagrange equations of a variational problem. We write these equations in Hamiltonian form and regularize them. In this way, we obtain a class of solutions without rotations. We derive, in particular, the Lagrangian function for the rotating model with the S3 group first computed by Gödel. We suggest that the corresponding Hamiltonian equations can be regularized.