bluuebunny/crossref_metadata_2025 huggingface dataset:
Relation between the Three-Dimensional Fredholm Determinant and the Jost Functions
Authors: Newton Roger G.
Published: February 2004

It is proved that the modified Fredholm determinant F of the three-dimensional Lippmann-Schwinger equation in the theory of scattering by spherically symmetric potentials is related to the Jost functions fl of angular momentum l by F= ∏ l=0∞{fl2i+1 exp[(2l+1) TrKl]},where Kl is the kernel of the lth radial Lippmann-Schwinger equation. The relation between the multiplicity of the zeros of F and the degeneracy is discussed, and a relevant theorem for Hilbert-Schmidt operators is proved.
Analytic Properties of the Free Energy for the ``Ice'' Models
Authors: Glasser M. L. , Abraham D. B. , Lieb E. H.
Published: February 2004

The calculation of the free energy for the two-dimensional lattice models which obey the ``ice'' condition is reviewed and summarized. The analytic properties of this function relevant to thermodynamics are obtained for the set of those models corresponding to the absence of external fields. Detailed complex temperature Reimann structures are presented for the KDP and F models.
Canonical Transformations and the Radial Oscillator and Coulomb Problems
Authors: Moshinsky M. , Seligman T. H. , Wolf K. B.
Published: February 2004

In a previous paper a discussion was given of linear canonical transformations and their unitary representation. We wish to extend this analysis to nonlinear canonical transformations, particularly those that are relevant to physically interesting many-body problems. As a first step in this direction we discuss the nonlinear canonical transformations associated with the radial oscillator and Coulomb problems in which the corresponding Hamiltonian has a centrifugal force of arbitrary strength. By embedding the radial oscillator problem in a higher dimensional configuration space, we obtain its dynamical group of canonical transformations as well as its unitary representation, from the Sp(2) group of linear transformations and its representation in the higher-dimensional space. The results of the Coulomb problem can be derived from those of the oscillator with the help of the well-known canonical transformation that maps the first problem on the second in two-dimensional configuration space. Finally, we make use of these nonlinear canonical transformations, to derive the matrix elements of powers of r in the oscillator and Coulomb problems from a group theoretical standpoint.
Lattice Wind-Tree Models. I. Absence of Diffusion
Authors: Gates D. J.
Published: February 2004

Some lattice versions of the wind-tree model of Ehrenfest are introduced and studied. They include two versions in which overlapping of tree particles is forbidden, a third in which it is allowed, and a fourth in which it is allowed but results in a finite repulsive force. In every case it is found that the mean-square displacement Δ(t) of the wind particles at time t is bounded independently of t at sufficiently high density of the trees. This is in sharp contrast with the Einstein relation Δ(t) = O(t) as t → ∞, which might be expected to hold at low densities. Randomization of the initial velocity of a wind particle is also shown to occur in a certain sense, and upper bounds on a recurrence time are obtained at high density. On the other hand, it is shown that thermalization does not occur even at low densities.
Thermodynamics and Hydrodynamics for a Modeled Fluid
Authors: Hardy J. , Pomeau Y.
Published: February 2004

This article presents a general study of a two-dimensional fluid model with microscopic discrete velocities. The rather unusual properties of this model lead to precise thermodynamical laws. The Navier-Stokes hydrodynamical equations are obtained, which contain a transport coefficient given by a Green-Kubo integral, and it is shown that this integral does not converge for a reason common to all two-dimensional fluids.
Poincaré and TCP Invariance in the Determination of Wave Equations for Particles of Arbitrary Spin
Authors: Seetharaman M. , Mathews P. M.
Published: February 2004

A brief outline is given of different types of approaches to the derivation of relativistic wave equations for free particles of arbitrary mass m and spin s. It is pointed out that all such equations can be subsumed in a standard form involving wavefunctions transforming according to the representation D (0,s) ⊕ D (s,0) of the Lorentz group. Generalizing earlier work employing this standard form, we determine all such equations (in a standard form) which are invariant under the Poincaré group and the combined operation Θ ≡ TCP. It is shown that the resulting equations are automatically invariant under T, C, and P separately.
Structure of the Gravitational Field at Spatial Infinity
Authors: Geroch Robert
Published: February 2004

A formalism is introduced for analyzing the structure of the gravitational field in the asymptotic limit at spatial infinity. Consider a three-dimensional surface S in the space-time such that the initial data on S is asymptotically flat in an appropriate sense. Using a conformal completion of S by a single point A ``at spatial infinity,'' the asymptotic behavior of fields on S can be described in terms of local behavior at A. In particular, the asymptotic behavior of the initial data on S defines four scalars which depend on directions at A. Since there is no natural choice of a surface S in a space-time, the dependence of these scalars on S is essential. The asymptotic symmetry group at spatial infinity, whose elements represent transformations from S to other asymptotically flat surfaces, is introduced. It is found that this group, which emerges initially as an infinite-dimensional generalization of the Poincaré group, can be reduced to the Lorentz group. A set of evolution equations is obtained: These equations describe the behavior of the four scalars under the action of the asymptotic symmetry group. The four scalars can thus be considered as fields on a three-dimensional manifold consisting of all points at spatial infinity. The notion of a conserved quantity at spatial infinity is defined, and, as an example, the expression for the energy-momentum at spatial infinity is obtained.
On the Equivalence of Dressing Transformations
Authors: Federbush Paul
Published: February 2004

The equivalence of the representations of the Weyl algebra for φ2+14 in a box induced by the dressing transformation of Glimm and the unitary dressing transformation is studied. Equivalence is shown for the simplified model in which only the most singular portion of the interaction is kept.
On Weyl and Lyra Manifolds
Authors: Sen D. K. , Vanstone J. R.
Published: February 2004

It is shown that Weyl's geometry and an apparently similar geometry suggested by Lyra are special cases of manifolds with more general connections. The difference between the two geometries and their relationship with Riemannian geometry are clarified by giving a global formulation of Lyra's geometry. Finally the outline of a field theory based on the latter geometry is given.
Solutions of a Class of Nonlinear Coupled Partial Differential Equations
Authors: Swenson Robert J.
Published: February 2004

A class of nonlinear coupled partial differential equations are solved. These are generalizations of the general relativistic equations arising for a static distribution of massive charged particles.
On Multigroup Transport Theory with a Degenerate Transfer Kernel
Authors: Silvennoinen Pekka , Zweifel P. F.
Published: February 2004

The multigroup transport equation is studied in plane geometry assuming that the transfer kernel is representable in a degenerate form. The eigenvalue spectrum is analyzed and the associated eigensolutions are obtained in terms of generalized functions. Full-range orthogonality relation is demonstrated. The full-range completeness of the eigensolutions is established under rather general conditions. For the half-range completeness to hold, it is additionally required that the scattering kernel be self-adjoint and possesses reflection symmetry.
Radial Moments of Folding Integrals for Nonspherical Distributions
Authors: Satchler G. R.
Published: February 2004

Simple relations are exhibited between the radial moments of two nonspherical distributions when one is obtained by folding a scalar function into the other. Some applications are mentioned, and the generalization to nonscalar functions is indicated.
Variational Estimates and Generalized Perturbation Theory for the Ratios of Linear and Bilinear Functionals
Authors: Stacey Weston M.
Published: February 2004

Variational functionals are presented which provide an estimate of ratios of linear and bilinear functionals of the solutions of the direct and adjoint equations (inhomogeneous and homogeneous) governing linear systems. These variational functionals are used as the basis for a generalized perturbation theory for estimating the effects of changes in system parameters upon these ratios of linear and bilinear functionals. The relation of the present theory to the variational theory of Pomraning and to the generalized perturbation theory of Usachev and Gandini is discussed. Potential applications of the theory to nuclear reactor physics are outlined.
Structure of Simplexes of Equilibrium States in Quantum Statistical Mechanics
Authors: Chen Etang
Published: February 2004

The structure of Choquet simplexes of equilibrium states of infinite system in quantum statistical mechanics is investigated. It is shown that a facial simplex is a Bauer simplex whenever its extreme points form a physically equivalent class; however, the simplex of KMS states for a given inverse temperature is not a Bauer simplex if it is not a singleton.
Is the Maxwell Field Local?
Authors: Avishai Y. , Ekstein H. , Moyal J. E.
Published: February 2004

Is the classical Maxwell field truly local? This question is raised by several observations, among them the Aharonov-Bohm effect; but the question cannot be answered without a systematic definition and characterization of local subalgebras of observables. This paper reformulates classical field theory in analogy to axiomatic quantum field theory and introduces a precise statement for local independence. (Synonyms for local independence are Einstein causality and principle of maximum signal velocity.) The formal answer of the analysis is: The free Maxwell field does not have local independence. This conclusion is critically discussed.
A Watson Sum for a Cubic Lattice
Authors: Glasser M. L.
Published: February 2004

The origin-origin value of the Green's function for a simple cubic lattice with axial anisotropy is evaluated exactly.
Multigroup Neutron Transport
Authors: Belleni-Morante A. , Busoni G.
Published: February 2004

We investigate the nature of the approximations involved in the multigroup treatment of the time-dependent neutron transport equation by using the method of approximating sequences of Banach spaces. We prove that solutions of the multigroup system converge, in a suitable sense, to the corresponding solutions of the exact transport equation. Moreover, we indicate the order of magnitude of the rate of convergence.
Conservation of Kinks and Spin in Nonlinear Quantum Field Theories
Authors: Williams J. G.
Published: February 2004

Certain nonlinear field theories exhibit particlelike structures called ``kinks'' that have fermionlike properties. This paper uses a Feynman path integral approach to show that, in the quantum theory, the number of kinks and the spin associated with them are both conserved quantities.
Rigorous Statistical Mechanics for Nonuniform Systems
Authors: Garrod Claude , Simmons Carver
Published: February 2004

The thermodynamic limit of a classical system with many-body interactions and under the influence of an external potential is investigated for the canonical ensemble. By scaling the external potential to a sequence of domains which are isotropic expansions of an initial domain confining the system, it is shown that the canonical free energy per particle has an infinite system limit. Moreover, by restricting consideration to internal interactions which have the property that separated groups of particles have negligible mutual attractive energy as the system becomes infinite, it is proven that the free energy per particle limit is precisely the free energy per particle obtained by minimizing the integral ∫[φρ + f(ρ, β)] with respect to all properly normalized functions ρ(r). φ is the external potential; f(ρ, β) is the free energy per unit volume for a uniform system of density ρ and inverse temperature β. The only technical complication is the above-mentioned restriction on the allowed internal interactions. It is demonstrated that there exists a wide class of many-body interactions which have the required separation properties. The simplest example is a two-body interaction which includes a hard core.
Exactly Soluble Model of Interacting Electrons
Authors: Mattis D. C. , Nam S. B.
Published: February 2004

We diagonalize a many-fermion Hamiltonian consisting of terms quadratic as well as quartic in the field operators. A dual spectrum of eigenstates is an interesting result. We also derive a formula for obtaining the free energy at finite temperature.
Unbounded Solutions of Coupled Mode Equations
Authors: Jackson E. Atlee
Published: February 2004

A number of sufficient conditions for the existence of unbounded solutions of two and three coupled mode equations are obtained when some modes are linearly unstable and all initial amplitudes are arbitrarily small. The difficulty of obtaining sufficient conditions for boundedness of all solutions is discussed, and only two such conditions are obtained. In certain cases it is proved that the unbounded solutions are not more rapid than exponential, whereas they can be shown to be singular (``explosive'') in other cases.
Study of Differential Equations of Physics in the Hardy-Lebesgue Space
Authors: Ifantis Evangelos K. , Kouris Christos B.
Published: February 2004

The problem of polynomial solutions of differential equations which are of interest in physics is studied by the Hardy-Lebesgue space technique.
Contributions to the Theory of Multiplicative Stochastic Processes
Authors: Fox Ronald Forrest
Published: February 2004

The theory of multiplicative stochastic processes is contrasted with the theory of additive stochastic processes. The case of multiplicative factors which are purely random, Gaussian, stochastic processes is treated in detail. In a spirit originally introduced by theoretical work in nuclear magnetic resonance and greatly extended by Kubo, dissipative behavior is demonstrated, on the average, for dynamical equations which do not show dissipative behavior without averaging. It is suggested that multiplicative stochastic processes lead to a conceptual foundation for nonequilibrium thermodynamics and nonequilibrium statistical mechanics, of marked generality.
Long-Wavelength Normal Modes of Crystals with Coulomb Interactions
Authors: Davies John A.
Published: February 2004

An investigation is made of the behavior of the normal modes of vibration in the long-wavelength limit for infinite crystal lattices in which Coulomb interactions are present. The work is applicable to point ion models with any crystal structure. Rules are derived which are helpful in determining the long-wavelength behavior of the normal modes from symmetry considerations. A study is made of the conditions under which the branches of the phonon dispersion relations will approach definite frequencies in the long-wavelength limit. Finally, a number of examples are presented which illustrate the preceding analysis.
On the Finite Transformations of SU(3)
Authors: Akyeampong D. A. , Rashid M. A.
Published: February 2004

The finite transformations in an arbitrary irreducible representation of the SU(3) group are obtained by considering the reduced matrix elements of the operator e−iνλ4. The special case of ν = ½π is also worked out and shown to be in agreement with earlier derivations. Symmetry properties and addition theorems for the resulting matrix elements are explicitly stated. As a useful application of the method, the finite transformations of the Weyl subgroup on the basis vectors of an arbitrary irreducible representation of SU(3) are also given.
Applications of Function Space Integrals to Problems in Wave Propagation in Random Media
Authors: Chow Pao-Liu
Published: February 2004

Two problems in wave propagation governed by the reduced wave equation with a random refractive index are studied. Problem (a) is concerned with radiation from a source in an infinite medium, and problem (b) pertains to the scattering by a random half-space at high frequencies. By transforming the reduced wave equation into a generalized heat equation, it becomes possible to express the moments of solutions in terms of Wiener integrals. Concrete results are obtained for certain special cases. By systematically approximating the functional integral representation for the moments, various perturbation equations come forth. Among them is Kraichnan's direct interaction approximation. By examining the errors involved, the accuracy in each approximation is ascertained and the nature of the approximation becomes transparent.
A Model for Dissipative Behavior in Nonlinear Quantum Optics
Authors: Emch Gérard G. , Wolfe John C.
Published: February 2004

The compatibility of mechanistic, microscopic dynamics with dissipative, macroscopic behavior is proved by solving rigorously a model. This model consists of an infinite chain of two-level atoms interacting with an electromagnetic mode via two-photon emission and absorption.
Lattice Green's Function for the Diatomic Lattices
Authors: Morita Tohru , Horiguchi Tsuyoshi
Published: February 2004

Attention is called to the fact that the lattice Green's function for a diatomic alternating lattice (regular or irregular) can be calculated from the lattice Green's function for the corresponding monatomic lattice. The definition of the lattice Green's function is given in such a fashion that the imaginary part of the trace of the function gives the level density. The values at the origin are shown by graphs for the square, sc, and bcc diatomic lattices; the sc and bcc diatomic lattices are of the sodium-chloride and cesium-chloride type crystal structures, respectively. Discussions are given of the analytic behaviors and symmetry properties. The real part of the lattice Green's function is used to discuss the localized state of the one-impurity problem in the diatomic lattices. Some symmetry properties for the monatomic alternating lattice are given in the Appendix.
The Reproducing Kernel Method. I
Authors: Devooght J.
Published: February 2004

The use of operator-valued reproducing kernels is introduced in order to solve Cauchy problems, ∂N/∂t = HN. A series development of the solution is obtained in terms of the orthogonal functions φν(z) in a domain G containing the spectrum of the bounded operator H. The optimal character of the approximate solution is stressed.
Representations of the Invariance Group for a Bloch Electron in a Magnetic Field
Authors: Boon M. H.
Published: February 2004

The invariance translation-operator group for the Hamiltonian of an electron in a periodic electric field and a uniform magnetic field is examined in the context of the theory of infinite-dimensional representations. It is shown that this group is of Type I if and only if the magnetic field has rational components relative to the lattice. The case of a nonrational field along a lattice vector direction is studied in detail. Here, the group is the direct product of a factor involving the translations along the field and a factor expressible as a semidirect product in a way that depends on the choice of basic lattice vector pair for the translations across the field. For each choice, Mackey's theory of induced representations is applied to obtain an infinite set of physical irreducible representations (based on both transitive and strictly ergodic measures); it is found that for different choices the sets are different unless the vector pairs are related in a simple way. The representation carried by the state space L2(R3) is decomposed into a direct integral of primary representations, using Landau functions for a basis in L2(R3). These primary representations are not of Type I, for it is shown explicitly that each has an infinite number of direct integral decompositions into irreducible representations, such that representations from any two decompositions are inequivalent. Here, different decompositions involve Landau functions for propagation along different lattice vector directions. The invariance translation-operator group for a system with a uniform magnetic field only is also discussed; it is of Type I, and its physical irreducible representations are given.
Invariant Cones and Uniqueness of the Ground State for Fermion Systems
Authors: Faris William G.
Published: February 2004

A perturbation theory is developed for self-adjoint operators whose resolvents leave a cone invariant. The Perron-Frobenius theory may be applied to the perturbed operator to conclude that its lowest eigenvalue has multiplicity one. In quantum field theory this gives uniqueness of the vacuum for a class of fermion interactions different from that considered by Gross.
An Analytic Approximation Method for the One-Dimensional Schrödinger Equation. I
Authors: Hecht W.
Published: February 2004

A mathematical method for approximating the solutions of the one-dimensional Schrödinger equation is suggested which leads to a classification scheme identical to that of ``classical turning points.'' In this paper problems with at most two classical turning points are studied. Physical examples are chosen in such a way as to clarify especially the role of complex conjugate turning points and of others which do not belong to the physical region of the position variable. It is shown that, in general, those turning points must be taken into account and can be neglected only if their distances from the physical region of the position variable, as measured in units of a local wavelength, is large. The problem with three classical turning points, which turns out to be of special importance for intermolecular and internuclear forces will be treated in a later paper.
The Dielectric Ring in a Uniform, Axial, Electrostatic Field
Authors: Love J. D.
Published: February 2004

The exact solutions for the fields inside and outside a dielectric ring in a uniform, axial, electrostatic field are derived in the system of toroidal coordinates. Comparison is made with the perturbation solution generated by inverse aspect ratio expansion, and it is shown how the exact solution may be truncated to any desired accuracy. The cylindrical limits of the exact and truncated solutions are obtained.
Unitary Representations of the Homogeneous Lorentz Group in an O(1,1)⊗O(2) Basis and Some Applications to Relativistic Equations
Authors: Kalnins E. G.
Published: February 2004

Unitary irreducible representations of the homogeneous Lorentz group O(3, 1) belonging to the principal series are reduced with respect to the subgroup O(1,1) ⊗ O(2). As an application we determine the mixed basis matrix elements between O(3) and O(1,1) ⊗ O(2) bases and derive recurrence relations for them. This set of functions is then used to obtain invariant expansions of solutions of the Dirac and Proca free field equations. These expansions are shown to have the correct nonrelativistic limit.
Exact Nearest Neighbor Statistics for One-Dimensional Lattice Spaces
Authors: McQuistan R. B.
Published: February 2004

It is shown that A(n11,q,N), the number of ways of arranging q indistinguishable particles on a one-dimensional lattice space of N compartments in such a way as to create n11 nearest neighbor pairs is A(n11,q,N)=(N−q+1q−n11) × (q−1n11). A similar expression is also derived for n00, the number of pairs of vacant nearest neighbors. The normalization, first moment, and most probable value of these statistics are also discussed.
Anharmonic Oscillator with Polynomial Self-Interaction
Authors: Banks Thomas I. , Bender Carl M.
Published: February 2004

A quantum anharmonic oscillator with a polynomial self-interaction is defined in coordinate space by a Hamiltonian of the form H = −d2/dx2 + ¼x2 + g[(½x2)N + a(½x2)N−1 + b(½x2)N−2 + ⋯]. Using WKB techniques we derive a secular equation which determines the eigenvalues of H for small |g|. We find that the qualitative analytic structure of these eigenvalues as functions of complex g remains unchanged for all fixed values of a, b,…, including a = b = ⋯ = 0. The secular equation also implies an elegant theorem which predicts how the a,b,⋯ terms in H affect the large-order growth of perturbation theory. We use this theorem to compare the perturbative behavior of non-Wick-ordered and Wick-ordered field theories in one-dimensional space-time. In particular, we show that the perturbation series ∑Angn and ∑Bngn for the energy levels of the (gψ2N)1 and (:gψ2N:)1 field theories differ in large order by an over-all multiplicative constant limn→∞An/Bn = exp[N(2N − 1)/(2N − 2)].
On the Symmetric Tensor Operators of the Unitary Groups
Authors: Ališauskas S. J. , Jucys A.- A. A. , Jucys A. P.
Published: February 2004

The algebraic expressions for the matrix elements of symmetric tensor operators (the powers of infinitesimal operators) of the unitary groups in the Gel'fand basis have been studied. The expressions for the isoscalar factors of the related Clebsch-Gordan coefficients, one of the two representations to be coupled being symmetric, as well as the elements of a special recoupling matrix have been found. The supplementary symmetry properties of the isoscalar factors corresponding to the Regge symmetries of the Wigner and 6j coefficients of SU2 have been examined.
Procedures in Quantum Mechanics without Von Neumann's Projection Axiom
Authors: Benioff Paul A.
Published: February 2004

The results of previous work are generalized to include procedures whose measurement operations correspond to expectations as defined by Davies. For such procedures Von Neumann's projection axiom is not in general applicable. Finite and infinite sequences of measurements and transformations as well as finite and infinite decision procedures are considered. It is shown that with each such procedure there is associated in a unique manner a probability operator measure.
Ward-Takahashi Relations in Massive Yang-Mills Theory
Authors: Barnebey T. A.
Published: February 2004

The equivalence of massive Yang-Mills theory in the simplest gauge to a theory of vector electrodynamics is reviewed. The resultant Feynman rules and SU(2) invariance are used to derive Ward-Takahashi relations among the corrected vertices which are valid to all orders. One of these is employed to find a new Ward identity. A brief discussion of divergence problems is given.
Quantum Dynamics of Higher-Derivative Fields
Authors: Riewe F. , Green A. E. S.
Published: February 2004

The generalized quantum field theory which follows from Lagrangians containing arbitrarily high-order derivatives is formulated in an indefinite metric space. Particular attention is given to conservation laws and canonical commutation relations. The Heisenberg equations of motion are derived.
The Symmetric Group and the Gel'fand Basis of U(3). Generalizations of the Dirac Identity
Authors: Lezuo K. J.
Published: February 2004

It is shown that the symmetrization of N particle states by means of the orthogonal units of the algebra of the symmetric group SN yields the Gel'fand basis states of the irreducible representations of U(3). The existence of generalizations of the Dirac identity is demonstrated, and a connection between the symmetrized two- and three-body exchange operators and the invariants of U(3) is established.
Lie Theory and the Lauricella Functions FD
Authors: Miller Willard
Published: February 2004

It is shown that the Lauricella functions FD in n variables transform as basis vectors corresponding to irreducible representations of the Lie algebra sl(n+3,C). Group representation theory can then be applied to derive addition theorems, transformation formulas, and generating functions for the FD. It is clear from this analysis that the use of SL(m,C) symmetry in atomic and elementary particle physics will lead inevitably to the remarkable functions FD.
Averages of the Components of Random Unit Vectors
Authors: McDonald J. F.
Published: February 2004

It is shown that a parametrization of the orthogonal and unitary groups due to Hurwitz can be used to evaluate averages of components of random unit vectors for those two spaces. Explicit results are given for moments which are general enough to include most cases of interest in applications.
Wave Propagation in a Random Lattice. I
Authors: Chow Pao-Liu , Keller Joseph B.
Published: February 2004

The small amplitude periodic classical motion of a lattice of particles about their equilibrium positions in a lattice is considered. The effect of random masses and random spring constants upon the coherent or mean motion is treated by using an equation for the coherent motion derived previously by Keller and others. From this equation the dispersion equation for coherent wave motion is determined. It is solved for the case in which the spring constants are not random but the masses are random. Explicit results are obtained in the one-dimensional case for both uncorrelated and exponentially correlated mass defects. They show an alteration of frequency or of wavelength and of phase velocity, as well as an attenuation due to scattering by the defects. In addition new highly attenuated modes are found. These results are utilized in Part II in which various reflection and Green's function problems are treated.
Lattice Green's Functions for the Triangular and Honeycomb Lattices
Authors: Horiguchi Tsuyoshi
Published: February 2004

The lattice Green's function for the triangular lattice at an arbitrary lattice site is expressed in terms of the complete elliptic integrals of the first and second kind. The lattice Green's function for the honeycomb lattice is shown to be expressed in terms of the one for the triangular lattice. The results obtained are shown by graphs.
An Approximation Technique for Solving Multiparticle and Bound-State Scattering Processes
Authors: Liu Tsu-huei
Published: February 2004

A modified version of the Lee model by Bronzan is investigated by the LSZ formalism approach. The existence of (Vθ) bound state in the Bronzan's model is discussed. An iterative technique is applied for solving the tau functions in the V-2θ sector. Each term in the series preserves (a) (Vθ) bound state properties, (b) analytic structure, and (c) symmetry properties of the tau function. The S-matrix elements for both nonbound-state and (Vθ) bound state scattering processes in the V-2θ sector are obtained. Comparison of the result obtained by our iterative expansion method with that obtained by Bronzan's variational principle method is made.
Two-Time Spin-Pair Correlation Function of the Heisenberg Magnet at Infinite Temperature. III. bcc Lattice and Arbitrary Spin
Authors: Morita Tohru
Published: February 2004

The expansion coefficients in powers of time of the two-time spin-pair correlation function are obtained up to terms of order t8 for the bcc Heisenberg magnet of spin ½ at infinite temperature and up to terms of order t6 for the linear, square, sc, and bcc Heisenberg magnets of an arbitrary spin at infinite temperature. The result is applicable to the isotropic as well as the anisotropic Heisenberg magnet where the exchange integrals in the z direction and in the orthogonal plane are assumed to be different. Analysis of the results are given in separate articles.
Ether flow through a drainhole: A particle model in general relativity
Authors: Ellis Homer G.
Published: February 2004

The Schwarzchild manifold of general relativity theory is unsatisfactory as a particle model because the singularity at the origin makes it geodesically incomplete. A coupling of the geometry of space-time to a scalar field φ produces in its stead a static, spherically symmetric, geodesically complete, horizonless space-time manifold with a topological hole, termed a drainhole, in its center. The coupling is Rμν=2φ,μφ,ν; its polarity is reversed from the usual to allow both the negative curvatures found in the drainhole and the completeness of the geodesics. The scalar field satisfies the scalar wave equation □φ=0 and has finite total energy whose magnitude, expressed as a length, is comparable to the drainhole radius. On one side of the drainhole the manifold is asymptotic to a Schwarzschild manifold with positive mass parameter m, on the other to a Schwarzschild manifold with negative mass parameter m̄, and − m̄ > m. The two-sided particle thus modeled attracts matter on the one side and, with greater strength, repels it on the other. If m is one proton mass, then − m̄/m ≈ 1+10−19 or 1+10−39, according as the drainhole radius is close to 10−33cm or close to 10−13 cm; the ratios of total scalar field energy to m in these instances are 1019 and 1039. A radially directed vector field which presents itself is interpreted, for purposes of conceptualization, as the velocity of a flowing ``substantial ether'' whose nonrigid motions manifest themselves as gravitational phenomena. When the ether is at rest, the two-sided particle has no mass on either side, but the drainhole remains open and is able to trap test particles for any finite length of time, then release them without ever accelerating them; some it can trap for all time without accelerating them. This massless, chargeless, spinless particle can, if disturbed, dematerialize into a scalar-field wave propagating at the wave speed characteristic of the space-time manifold.
Spectral properties of the linearized Balescu-Lenard operator
Authors: Merchant Allan H. , Liboff Richard L.
Published: February 2004

The spectrum of the linearized Balescu-Lenard operator is studied in detail. It is found to be continuous, to range from zero to minus infinity, and to have no point spectrum. Analytic expressions are obtained for the l = 1 spherical harmonic eigenfunctions in the velocity domain ≳2.5, where x is microscopic speed, nondimensionalized through the thermal speed. Sketches showing the typical behavior for all x of this; l-mode eigenfunction are also given.
The anisotropic Kepler problem in two dimensions
Authors: Gutzwiller Martin C.
Published: February 2004

The classical trajectories are investigated for a particle with an anisotropic mass tensor in an ordinary Coulomb potential. For negative energies (bound states) these trajectories are isomorphic with the geodesics on a Riemannian surface which can be immersed in a Euclidean space and which looks like a ``double snail.'' For vanishing energy (or near a collision) the equations of motion can be reduced to an autonomous system whose trajectories can be fully discussed. On the basis of extensive numerical computations, it has been possible to give a simple, yet complete description of all trajectories with negative energy. A binary sequence is associated with any trajectory where each term gives the sign of the position coordinate for the consecutive intersections with the ``heavy'' axis. If the binary sequence is represented by two real numbers, a one-to-one and continuous map from them to the initial conditions can be constructed. Thus, the Poincaré map for the trajectories is equivalent with a shift of the binary Bernoulli scheme (tossing a coin), and all the periodic orbits can be obtained systematically. A number of these are discussed to illustrate the consequences of the isomorphism with the binary sequences. Finally, the baker transformation and its use for finding the trajectories which connect any two given endpoints, is mentioned.
Locality conditions on form factors
Authors: Andersson Bo
Published: February 2004

We derive a set of integral equations which are necessary and sufficient conditions on the form factors of local field theory, i.e. on the matrix elements of local operators. The basic idea is that out of the set of all (distribution-valued) functions defined on the boundary of an analyticity domain, in general only a subset are boundary values of functions which are analytic within the domain. The form factors are boundary values of a vertex function which, due to the general assumptions of locality, reasonable energy, and mass spectrum and Poincaré covariance, is analytic at least in the domain constructed by Källén and Wightman. The characteristic boundary of the domain (``the distinguished boundary'') is the set of physical values of the arguments of the form factors, and the integral equations in that way only involve such values. The main advantages in formulating the locality conditions in this way are that (1) only the physical quantities of the field theory, i.e., the matrix elements between the field operators, enter into the equations and (2) the frustrating complications which are met in the construction of the domains of analyticity for n-point functions with n > 3 might hopefully be avoided because the distinguished boundary can be constructed even if the whole domain is not known. The integral equations have naturally no unique solutions, because, e.g., all perturbation-theoretical form factors must, of course, fulfill them. The equations may, however, function as a convenient starting point for approximations and ``model building'' for form factors outside the presently used perturbation theories. The integral equations are straightforward generalizations of the notion of ``weak local commutativity'' for the two-point function. This condition means that the two spectral functions connected to two locally commuting operators should be equal. The conditions on the form factors (which are the generalizations of the two-point spectral functions) are that the difference should vanish when integrated over certain physical sets of mass space.
Position operators in a (3+1) de Sitter space
Authors: Mallett R. L. , Fleming G. N.
Published: February 2004

Earlier studies of covariant position operators in special relativistic quantum theory are generalized here to the case of a de Sitter universe of positive curvature. The hyperplane formalism previously employed undergoes a natural generalization in this case to a spacelike hypersphere formalism. In the analysis of the underlying geometry, the minimal pseudo-Euclidean embedding space for the de Sitter universe plays a dominant role and suggests an intrinsic coordinate system of special interest for the representation of geodesics. The de Sitter analogs of the Minkowski space center of energy, center of spin, and center of inertia are constructed, and we find that de Sitter-center of spin to retain commuting components in our intrinsic coordinate system.
Radiation fields in the Schwarzschild background
Authors: Bardeen James M. , Press William H.
Published: February 2004

Scalar, electromagnetic, and gravitational test fields in the Schwarzschild background are examined with the help of the general retarded solution of a single master wave equation. The solution for each multipole is generated by a single arbitrary function of retarded time, the retarded multipole moment. We impose only those restrictions on the time dependence of the multipole moment which are required for physical regularity. We find physically well-behaved solutions which (i) do not satisfy the Penrose peeling theorems at past null infinity and/or (ii) do not have well-defined Newman-Penrose quantities. Even when the NP quantities exist, they are not measurable; they represent an ``average'' multipole moment over the infinite past, and their conservation is essentially trivial.
A stochastic Gaussian beam
Authors: Papanicolaou G. C. , McLaughlin D. , Burridge R.
Published: February 2004

We consider the propagation of a Gaussian beam in a strongly focusing medium with random deviations from uniformity. We compute the intensity and intensity fluctuations on the beam axis and the mean power of the fundamental mode when the random inhomogeneities are weak and the distance between source and observation point is large. We also compute the mean power transferred to each higher mode.
Neutron transport equations with spin-orbit coupling
Authors: Tannenwald L. M.
Published: February 2004

An ab initio derivation of the transport equations is given for fast neutrons traversing a material having spin zero nuclei. The resulting set of equations agrees with the equations of Bell and Goad except for the treatment of the coherent terms. Application of the equations to asymmetric situations is suggested.
Schrödinger equation with a random potential: A functional approach
Authors: Eggarter Thomas P.
Published: February 2004

We present a new functional integral approach to the average density of states of a quantum particle in a random potential. As an illustration of the method, the formulas are explicitly evaluated for some one-dimensional problems; results previously obtained by other methods are recaptured. The formalism for the study of wavefunction localization is also derived.
The relativistically invariant expansion of a scalar function on imaginary Lobachevski space
Authors: Kalnins E. G.
Published: February 2004

Using the previous analysis of Gel'fand and Graev a new relativistically invariant expansion of a scalar function on three-dimensional imaginary Lobachevski space L3(I) is given. The coordinate system used corresponds to the horospherical reduction SO(3,1)⊃E2⊃SO(2) and covers all of L3(I).
Exact motion in noncentral electric fields
Authors: Hautot André
Published: February 2004

We study the problem of the motion of a charged particle in noncentral potentials of the type f(θ)/r2 + V(r). Newton's and Schrödinger's mechanics are considered. Exact solutions exist if V(r)=−H/r or Kr2 (i.e., Coulomb or harmonic oscillator potentials) while f(θ) may have at least three different expressions as a function of θ if the problem is three-dimensional and seven expressions if it is two-dimensional. The classical trajectories are computed and the energy levels in the corresponding quantum problem are given. Analogies between the two treatments are discussed.
Scattering by a spin-dependent spheroidal potential
Authors: Li Ming Chiang
Published: February 2004

The scattering by a spin-dependent spheroidal potential is studied. For this potential the scattering amplitude is considerably simple. The simplification is accomplished through the use of ``reccurence relations'' among the spheroidal functions. An iteration procedure is used for solving the infinitely coupled integral equations of the radial functions. The convergence of the solutions is proved.
Renormalized oscillator equations
Authors: Friedman Charles N.
Published: February 2004

Let {H=L2(R,dx), q=x,p=−id/dx} be the standard Schrödinger representation of the canonical commutation relations for one degree of freedom. For a, b, c, real scalars, put Habc = ½p2 + q4 + aq3 + bq2 + cq and q(t) = exp(itHabc)q exp(− itHabc). Then q(t) satisfies the operator equation q̈(t) = − 4q3(t) − 3aq2(t) − 2bq(t) − c. For n = 0, 1, 2, 3 we define renormalized (or Wick-ordered) nth powers of q, denoted q(n); these are polynomials of degree n in q and are characterized by the conditions: {q(0)=1 [q(n+1),p]=i(n+1)q(n)for n>0,∫G*q(n)Gdx=0,where G=ground state of Habc}. In terms of these powers the equation for q(t) can be written q̈(1) = − 4q(3) − Aq(2) − Bq(1) − C, for some real A, B, C which are functions of a, b, c. This has the form of a much studied prototypical nonlinear quantum field equation in the somewhat (physically) trivial case of one space-time dimension. Basically, we prove two results concerning this equation which we feel are of interest, because they may provide some basis for conjecture about the behavior of nonlinear field equations in a higher number of dimensions. First we determine a nontrivial condition which the renormalization constants A, B, C must satisfy and which implies that the set of points (A, B, C) assumed as a, b, c vary is of measure zero in R3. We study in somewhat more detail the situation when a = c = 0. The associated renormalized equation then has the form q̈(1) + Bq(1) = − 4q(3), where B = B(b). We determine the qualitative behavior of the function B(b) as b → ± ∞ and show for example that B(b) is not one-to-one. As a corollary, for many values of B, there exist at least two equations of the form q̈(1) + Bq(1) = − 4q(3) with the same B, but which are not unitarily equivalent in a sense, to be precised. Such nonunicity cannot occur for linear equations, as has been known for some time.
Perturbation method for a nonlinear wave modulation. III
Authors: Taniuti Tosiya , Yajima Nobuo
Published: February 2004

The perturbation method for the nonlinear, slow modulation of a rapidly oscillatory plane wave, which was given in the first paper of this series for a class of systems of nonlinear partial differential equations, is now established for a general system of nonlinear integro-partial differential equations. It is shown that the system can be reduced to simpler nonlinear equations which in certain cases become the nonlinear Schrödinger equation. The reduction proceeds as in the first paper, and the result is then applied to nonlinear optics.
Tensor operators of finite groups
Authors: van Zanten A. J. , de Vries E.
Published: February 2004

Irreducible tensor operators of a finite group G are discussed as elements of the group algebras of G⊗n (n=1,2,3,…). Formulas are given for the number of times that an irreducible tensor operator of a certain rank can be constructed in these algebras and more specifically how often they can be constructed from the elements of a fixed class of conjugate elements in G⊗n (n=1,2,3,…). Some of results are interpreted in the framework of the duality between classes and irreducible representations in finite groups.
Similarity transformation for the compressible Jeffery-Hamel flow of dissipative plasmas
Authors: Wilhelm H. E.
Published: February 2004

A similarity transformation is presented which transforms the nonlinear, partial differential equations describing a compressible plasma flow across an azimuthal magnetic field between plane inclined walls (Jeffery-Hamel flow with viscous momentum transfer, Ohmic and viscous heating, and thermal heat conduction) into one linear and two nonlinear ordinary, coupled differential equations. By elimination, the nonlinear boundary-value problem of this compressible plasma flow is reduced to a boundary-value problem for (i) two ordinary, coupled differential equations or (ii) a single functional integro-differential equation. The characteristic parameter ``m'' of the similarity transformation is shown to be an eigenvalue of the nonlinear boundary-value problem.
Kinetic theory of a one-dimensional model
Authors: Anstis G. R. , Green H. S. , Hoffman D. K.
Published: February 2004

The kinetic theory of a model previously studied by Jepsen and others is reformulated in terms of the theory of the grand partition function and the hierachy of equations satisfied by the distribution functions derived therefrom. It is shown that the principle of molecular chaos implies an exact factorization of the two- and many-body distribution functions, which allows the equations of the hierachy to be solved exactly, with the recovery of results obtained by other methods. The methods of the present paper also allow examination of the origin of the divergences generated by well-known approximations, and suggest alternative approximations in which such divergences do not appear.
Generalized isoperimetric inequalities. II
Authors: Luttinger J. M.
Published: February 2004

Continuing the development of a previous paper on generalized isoperimetric inequalities (i.e., rearrangement inequalities for Green's functions), we extend the theory to the case of Green's functions for a potential which approaches zero at infinity. Specialization to domain potentials and long times gives Pólya and Szegö's isoperimetric inequality for the electrostatic capacity. Long times and a more general potential give a new isoperimetric inequality (for the ``scattering length'' of a potential). We also obtain from another specialization a curious isoperimetric inequality for the trace of the phase shift operator of scattering theory (for a given energy).