bluuebunny/crossref_metadata_2025 huggingface dataset:
On the Interaction of the Electromagnetic Field with Heat Conducting Deformable Insulators
Authors: Tiersten H. F. , Tsai C. F.
Published: February 2004

The differential equations and boundary conditions describing the behavior of a finitely deformable, polarizable, and magnetizable, heat conducting continuum in interaction with the electromagnetic field are derived by means of a systematic application of the laws of continuum physics to a well-defined macroscopic model. The model consists of an electronic charge and spin continuum coupled to a lattice continuum, which in itself consists of two interpenetrating ionic continua, which can displace with respect to each other to produce ionic polarization. Since spin angular momentum and electronic and ionic linear momentum are taken into account, magnetic spin resonance and both ionic and electronic polarization resonances are included in the treatment. Magnetic interaction terms are obtained by regarding magnetization as a consequence of point circulating current densities. When material resonances are suppressed, a simpler model is applicable and a not only smaller but somewhat different system of equations turns out to be convenient.
Velocity-Dominated Singularities in Irrotational Hydrodynamic Cosmological Models
Authors: Liang E. P. T.
Published: February 2004

We consider irrotational perfect fluid solutions of the Einstein equations with an equation of state p = γρ. We define ``velocity-dominated'' singularities of these solutions, a notion previously introduced for dust models. We demonstrate explicitly that uniquely and invariantly defined inner metric tensor, extrinsic curvature tensor, and scalar bang-time function can be assigned to these singularities, as in the dust case. We study the effects of a time-varying equation of state and viscosities on these singularities, and show by order-of-magnitude estimates that they do not change the structure of the singularity provided γ > 0. Some known exact perfect fluid solutions, both homogeneous and inhomogeneous, are listed as examples.
A Method for Generating New Solutions of Einstein's Equation. II
Authors: Geroch Robert
Published: February 2004

A scheme is introduced which yields, beginning with any source-free solution of Einstein's equation with two commuting Killing fields for which a certain pair of constants vanish (e.g., the exterior field of a rotating star), a family of new exact solutions. To obtain a new solution, one must specify an arbitrary curve (up to parametrization) in a certain three-dimensional vector space. Thus, a single solution of Einstein's equation generates a family of new solutions involving two arbitrary functions of one variable. These transformations on exact solutions form a non-Abelian group. The extensive algebraic structure thereby induced on such solutions is studied.
Nonlinear Perturbation Operators
Authors: Andrews L. C. , Triffet T.
Published: February 2004

A systematic perturbation theory is presented for the analysis of nonlinear boundary-value problems. In particular, those equations are considered whose unperturbed form belongs to the class of linear special-function equations; the nonlinear terms are then regarded as perturbations of special-function operators. Utilizing the coordinate representation of quantum mechanics, a matrix representation is obtained for the perturbed operator, truncation and diagonalization of which will determine the perturbed eigenvalues and eigenvectors. In most cases the method is applicable even when the perturbation term is of the same order of magnitude as the remaining terms, perhaps even when it is larger. To illustrate this point the nonlinear Legendre-like equation (d/dx)(1 − x2)(du/dx) + λu + αx2u2 = 0 is solved for the cases when α = 1 and α = 5. Other examples include the Hartree equations for the helium atom, where a qualitative comparison of the ground-state energy is made with experimental data, and a detailed analysis of the van der Pol equation for α = 0.5 and α = 1.
The Angular Spectrum Representation of Electromagnetic Fields in Crystals. I. Uniaxial Crystals
Authors: Lalor Éamon
Published: February 2004

The electromagnetic field in a linear, nonmagnetic, nonabsorbing uniaxial crystal which fills the entire half-space z ≥ 0 and whose optic axis is perpendicular to the plane z = 0 is represented as an angular spectrum of plane waves. The angular spectrum representation consists of a superposition of plane electromagnetic waves expressed as the sum of two integrals. In general both homogeneous and evanescent plane waves are required in each integral. Each plane wave of the spectrum satisfies the identical equations obeyed by the entire field. The homogeneous plane waves of the first integral are all ordinary waves and those of the second integral all extraordinary waves. The spectral amplitudes of the field are explicitly expressed in terms of the Fourier transform of the field in the place z = 0. The method of stationary phase is applied to the integral representation and it is thereby shown that in the far zone the field may be expressed as the sum of an outgoing (nonuniform) spherical wave and an outgoing (nonuniform) ellipsoidal wave. The amplitude of these waves, at each point on the wave surface, is expressed in terms of the Fourier transform of the field in the plane z = 0.
Proof of an Existence Condition for Solutions of the Unitarity System of Equations
Authors: Eftimiu C.
Published: February 2004

A previously established set of conditions for the existence of solutions of a nonlinear system, expressing the unitarity of n × n symmetric matrices, is proven by means of the homotopy invariance theorem.
Geodesics and Classical Mechanics on Lie Groups
Authors: Hermann Robert
Published: February 2004

Hamilton-Jacobi Theory on Lie groups is discussed, and an error in a previous paper is corrected. A method for ``analytically continuing'' geodesics from compact to noncompact Lie groups is presented.
Nonpolynomial Lagrangians with Isospin
Authors: Delbourgo R.
Published: February 2004

We apply (Laplace, Fourier, …) transform methods to obtain compact representations of the perturbation S-matrix elements for interaction Lagrangians which are general nonpolynomial functions of isospin multiplets. In order to illustrate the power and simplicity of the method for coping with the isospin complications, we have treated several examples in detail, and these include the commonly used parametrizations of the unitary chiral SU(2)⊗SU(2) transformations.
A Class of Mean Field Models
Authors: Silver H. , Frankel N. E. , Ninham B. W.
Published: February 2004

A model of isotropically interacting ν-dimensional classical spins with an infinite range potential of the molecular field-type is solved. The partition function is represented as the integral of e−βHN over an appropriate weight function, which, for given ν, is the Pearson random walk probability distribution in ν dimensions. A molecular field-type phase transition is obtained for all ν.
Spectrum of Local Hamiltonians in the Yukawa2 Field Theory
Authors: Dimock Jonathan
Published: February 2004

It is proved that the local Hamiltonians constructed for the two-dimensional Yukawa model by Glimm and Jaffe have the same continuous spectrum as the free Hamiltonian. The proof depends on the construction of asymptotic creation and annihilation operators.
On the Mathematical Theory of Electromagnetic Radiation from Flanged Waveguides
Authors: Howard A. Q.
Published: February 2004

A mathematical technique particularly suited to describing the electromagnetic radiation from open-ended waveguide structures is discussed. As an example of the utility of the method, the exact solutions, for both wave polarizations corresponding to a uniform line source embedded in a dielectric filled slot in a ground plane, are given. The edge condition is used to estimate and partially correct for the truncation error resulting from approximating the infinite system of linear equations by a finite one. The truncation corrected field expressions are shown to recover the proper local field behavior in the vicinity of the aperture perimeter. Some numerical results, for both aperture and radiation fields are given and in the latter case compared with the Kirchhoff approximation to the radiation field.
On Uniqueness of the Kerr-Newman Black Holes
Authors: Wald Robert
Published: February 2004

It is proven that the Kerr-Newman space-times with e2 + a2 < m2 are the only electrovac black hole solutions of Einstein's equations which can be obtained by analytic variation of the space-time geometry starting from the Schwarzschild solution.
Light-Cone Singularities and Lorentz Poles
Authors: Ferrara S. , Rossi G.
Published: February 2004

The causal Meyer-Suura structure functions are projected into irreducible representations of the Lorentz group. A clarification of the connection between light-cone singularities and Lorentz poles is obtained: We find that in general a light-cone singularity of the type 1/(− x2 + iεx0)α, in the operator product of the hadronic electromagnetic current, is built up from a sequence of Lorentz poles at λn = 1 + α − n whose residues are polynomials of order n in the virtual photon square mass.
States, Minimizing the Uncertainty Product of the Oscillator Phase Operators
Authors: Ifantis Evangelos K.
Published: February 2004

The normalizable states that minimize the uncertainty product of the oscillator phase operators are determined and some of their physical properties are discussed. A physical classification of these states has been made and the class of ``analogous'' states to the well-known coherent states is physically defined.
On the Evaluation of the Multiplicity-Free Wigner Coefficients of U(n)
Authors: Chacón E. , Ciftan Mikael , Biedenharn L. C.
Published: February 2004

An explicit algebraic expression [containing the minimal number (n − 1) sums] for the general reduced Wigner coefficients associated with the multiplicity free Kronecker product [h1 … hn] × [p0 … 0] of irreducible representations of U(n), is determined. The calculation employs a combined use of recursive relations derived for the Wigner coefficients, and matrix elements (with respect to Gel'fand basis states) of a generator of U(n) raised to an arbitrary power. We also give an alternative procedure using the techniques of the ``pattern calculus.'' The method is illustrated first for the case of U(3) and then generalized to arbitrary U(n). It is found that the results can be expressed succinctly in terms of a new algebraic function Snm - thereby elucidating the structural details of the underlying algebra.
Exact Solutions to the Yang-Mills Field Equations
Authors: Rosen Gerald
Published: February 2004

New spatially localized solutions to the Yang-Mills classical field equations are reported.
On the Cauchy Problem for the Coupled Maxwell-Dirac Equations
Authors: Chadam John M.
Published: February 2004

The Cauchy problem for the coupled Maxwell-Dirac equations is solved within an arbitrary bounded region of space-time. An integral part of the proof is that the Cauchy problem for a cut-off version of these equations has a global solution. The analysis requires that the size of the Cauchy data or the coupling constant be suitably restricted.
Entropy Decomposition and Transfer-Matrix Problems
Authors: Falk H.
Published: February 2004

For a system which may be partitioned into M subsystems A1, A2, …, AM, such that configurations of subsystems Ai, Aj correspond to realizations of discrete, random variables si, sj, not necessarily isomorphic, and such that the probability for a configuration of the total system is p(s1, s2, …, sM) = f1(s1) … fM(sM)g1(s1, s2) × g2(s2, s3) … gM−1(sM−1, sM), we prove that p(s1, s2, …, sM) = p1(s1 | s2)p2(s2 | s3) … pM−1(sM−1 | sM)pM(sM), where pi(si | si+1) is the conditional probability for si given si+1, and pi(si) is the reduced probability for si. This result yields a decomposition of the total entropy into ``single-subsystem entropies'' −Σ pi(si) lnpi(si) and ``nearest-neighbor'' cumulant-like terms −Σpj(sj,sj+1) ln[pj(sj,sj+1)/pj(sj)pj+1(sj+1)] only. This Markovian decomposition applies to systems with short-range interactions for which transfer-matrix methods are introduced.
Nonrelativistic Time-Dependent Scattering Theory and von Neumann Algebras. I. Single Channel Scattering
Authors: Zachary W. W.
Published: February 2004

For single-channel nonrelativistic time-dependent scattering we analyze the von Neumann algebras M± generated by the wave operators Ω± and the algebra B generated by the spectral projections of both the total and free Hamiltonians. Each of the algebras M± is the direct sum of an Abelian algebra and a factor of type I∞, but both summands need not occur. For a large class of central potentials B is the direct sum of a countable number of factors of type I∞ and its commutant the direct sum of a countable number of finite factors of type I. In the latter case the type of each direct summand is uniquely determined by the angular momentum of the corresponding partial wave. Similar decompositions are obtained for algebras related to B and B′ in a natural way that have certain connections with the absolutely continuous and point spectra of the total Hamiltonian. The structure of some algebras related to M± is connected with certain properties of the bound states.
On the Eigenvalues of the Invariant Operators of the Unitary Unimodular Group SU(n)
Authors: Partensky A.
Published: February 2004

By a purely infinitesimal method we derive the eigenvalues of the Biedenharn's invariant operators from I2 to I6 for the SU(n) group. We show that the general formula, quoted from the Racah's work by Baird and Biedenharn, to obtain the eigenvalues of the invariant operators, is valid only for the two first I2 and I3 operators and not for the higher order invariants. We give the correct values for the first invariants till I6.
The Spin Spectrum of an Unstable Particle
Authors: Fleming Gordon N.
Published: February 2004

A state vector (vector-valued distribution) of an unstable particle can be a 3-momentum eigenvector in at most one inertial frame as a consequence of the necessary width of the energy spectrum. We investigate this frame dependence of momentum eigenvectors of unstable particles and demonstrate that:

(i) It is compatible with the principle of relativity.

(ii) It leads to a distinction between two ways of defining the spin of the particle which are equivalent for stable particles.

(iii) One definition, called kinematical spin, yields a precise value, and is determined by considerations of detailed balancing and other means of counting the degeneracy of the momentum eigenvectors.

(iv) The second definition, called dynamical spin, need not yield a sharp value, is determined by the dynamics of the decay process, and is measured by observing angular distributions of decay products.

It is shown that an unstable particle with vanishing kinematical spin (pion) may have a small admixture of non-isotropic angular distribution of unpolarized decay products in the rest frame of the decay products. The order of magnitude of the effect is estimated and the coupling between the mass and spin spectrum is studied in the case of local interactions without derivative coupling.
Probabilistic Interpretation of the Quantum Scattering Cross Section
Authors: Babbitt Donald G.
Published: February 2004

The probabilistic interpretation of the quantum scattering cross section in the case of potential scattering is discussed in terms of Poisson random measures on the impact parameter plane and the sphere of outgoing directions.
Modified WKB Approximation Applied to the Solution of the Repulsive Singular Potential
Authors: Lu Pao , Wald Sheldon S.
Published: February 2004

The conventional WKB method for phase shift calculations is known to fail for singular repulsive potentials at small incident energies. We show in this paper that the modified WKB method due to Miller and Good can be used instead and that it gives better agreement with the exact results of the scattering phase shifts at small incident energies and in the small coupling constant limit, as more terms in ℏ2 are included.
Note on the Explicit Form of Invariant Operators for O(n)
Authors: Maekawa Takayoshi
Published: February 2004

A complete set of invariants of O(n) is constructed explicitly and a method of deriving the corresponding invariants of O(p, q) is briefly remarked.
Solution of Faddeev Equations for a One-Dimensional System
Authors: Majumdar Chanchal K.
Published: February 2004

Exact solutions are derived for the Faddeev equations for a one-dimensional system of three distinguishable particles of identical mass, interacting pairwise through a delta function potential. The method here employed uses scattering boundary conditions directly on the system of equations.
Spin-Dependent Operators in the Occupation-Branching Number Representation
Authors: Gouyet J. F.
Published: February 2004

In two preceding papers, a general method was given of building up open-shell wavefunctions which are eigen-functions of the spin operators S2. This method leads to a second quantizationtype formalism, where degenerate multiplets are described in what we call the occupation-branching number representation. In the paper referred to as Paper II, equivalent monoelectronic and bielectronic operators were defined and a diagrammatic technique was developed. In the present paper, the equivalent spin-dependent operators in the occupation-branching number representation are built up, in the cases of monoelectronic and bielectronic operators. The spin-orbit and the spin-spin coupling are the most important operators of this kind. The associated diagrammatic representation is given.
Analytic Unimodular Matrix Groups Containing the Image Dj of the Rotation Group: A Simple Derivation
Authors: Abellanas L. , Galindo A.
Published: February 2004

The existence of closed connected subgroups X of SU(2j+1) such that Dj[SU(2)] lim ≠<X lim ≠<SU(2j+1) is investigated in terms of Lie algebras. We look for a more general solution to this problem. Besides the trivial (orthogonal or symplectic) candidates, Racah pointed out that X=G2 is another relevant example, for the case j = 3. This augmented chain made possible some very interesting theoretical calculations in the framework of atomic spectroscopy. Actually these are all possible solutions. We give a quite simple proof of this fact, using some well-known properties of the 6-j symbols.
A Functional Calculus Approach to the Ursell-Mayer Functions
Authors: Shen C. Y.
Published: February 2004

A more complete treatment of the Ursell-Mayer functions is given here by way of a functional calculus defined on the algebra of complex-valued functions on the exponential of a set. Through measure-theoretical considerations, we are able to establish relationships between these functions and certain linear operators which relate probability densities and correlation functions in statistical mechanics. Also we point out that these functions provide a way of representing states of an infinite system.
Another Set of Axioms for Classical Gas Dynamics
Authors: Schilder Michael
Published: February 2004

Another set of axioms is given for a nonequilibrium classical gas composed of hard, spherical, nonattracting molecules. It is shown that the thermodynamic functions of this type of gas can be expressed as multiple integrals. It is also shown in a certain limiting case that the thermodynamic functions of this type of gas can be expressed as Wiener integrals.
Topological Analysis of Self-Generating Interactions in Lagrangian Field Theory
Authors: Gunzig E.
Published: February 2004

We determine entirely the n-body nonlocal potentials, parameters of a given Lagrangian field theory, in terms of a set of independent functionals of the many-body propagators. These functionals are more suitable for the description of self-generating interactions than the many-body propagators themselves.
Constructing Examples in Relativistic Classical Particle Mechanics
Authors: Shukre C. S. , Jordan T. F.
Published: February 2004

A new method is proposed for constructing examples in relativistic classical particle mechanics, starting with the Poincaré group and space reflections as transformations of position and velocity variables for two free particles and deriving equations for Lorentz covariant position variables for two interacting particles. The advantages are that the equations do not couple the position variables of the two particles, and solutions yield the particle world lines directly. Solutions are obtained for a special case.
Identities Involving the Coefficients in the Asymptotic Expansion of the Outgoing Scattering Solution of the Schrödinger Equation
Authors: Gelman Donald
Published: February 2004

Scattering by a short-range potential is described by the wavefunction ψ having the asymptotic form Ψ→eik·r+Feikr,r→∞, where F has the series representation F=f(k,kr)/r+g(k,kr)/r2+…. When only the first term in this series is taken into account, the requirement that the particle current be conserved leads to the optical theorem. By taking into account all of the remaining terms, we obtain a sequence of identities involving the coefficients f, g, …. These identities are formally analogous to the optical theorem, which is seen to correspond to the first identity in the sequence.
Rank 1 Expansions
Authors: Gilmore Robert
Published: February 2004

A group expansion technique is presented which is valid for all homogeneous Riemannian symmetric coset spaces of rank 1. Examples are given.
Helicity and Canonical Spin Operators of the Poincaré Algebra
Authors: Beckers J.
Published: February 2004

In the study of the irreducible unitary representations [m, s] of the Poincaré group, we define an ``helicity'' spin operator through a fundamental connection between canonical and helicity bases. This operator, in covariant notation, is simply related to the well-known Bargmann-Wigner operator and to the canonical spin operator. Its spatial components generate an SU(2)-algebra and coincide with the elements of the Z-spin algebra recently proposed on different grounds by Braathen-Foldy. The very simple arguments developed here establish in a natural way the uniqueness of this algebra when helicity representations are studied.
Renormalization of the Hilbert Space in the Mass Shift Model
Authors: Rosen Lon
Published: February 2004

The (φ2)s+1 quantum field theory model can be solved exactly, where the number of space dimensions is s ≤ 3. Thus this model explicitly illustrates many properties of nontrivial models such as (φ2n)2 and Yukawa2. In particular we study hyperbolicity, the energy spectrum, local Fockness, and the change of Hilbert space as the spatial cut off is removed.
The Plasma Inverse Problem
Authors: Balanis George Nick
Published: February 2004

A simple and direct development of the theory of the plasma inverse problem is given, and it is shown that the time record of the reflected wave arising from a δ function electric field normally incident on a stratified plasma determines uniquely the plasma density through an integral equation.
General Theory of Spherically Symmetric Boundary-Value Problems of the Linear Transport Theory
Authors: Kanal Madhoo
Published: February 2004

A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the ``gray'' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.
Analytic Renormalization of the Exponential Interaction: The Three-Point Time-Ordered Product with Minimum Light Cone Singularity
Authors: Daniel M. , Mitter P. K.
Published: February 2004

A method of analytic renormalization is developed to define the three-point time-ordered product of massless fields of exponential type as a strictly localizable distribution. The uniqueness property, known for the two-point T-product, is verified for the three-point product, for a special choice of fine renormalization. It is characterized by minimum singularity on the light cone: There are no delta function type singularities concentrated on the surface x1 = x2 = x3.
Algebraic Solution for the Källén-Pauli State Vectors in the Vθ Sector by a Congruence Transformation
Authors: Nelson C.A.
Published: February 2004

From the representation of Bolsterli of the Vθ sector physical states in a basis having singular integral equations of the separable type, a congruence transformation carries the representation into the Källén-Pauli Heisenberg field components. This solves the Källén-Pauli singular integral equation algebraically. The resulting state vectors are proven explicitly to be both complete and orthonormal and furnish a new Möller wave matrix.
Incoherent Exciton Quenching on Lattices
Authors: Hemenger Richard P. , Pearlstein Robert M. , Lakatos-Lindenberg Katja
Published: February 2004

The time-dependent excitation function φ(t) for exciton quenching in lattices of any dimension is derived from a general master equation in terms of perfect lattice Green's functions. Attention is largely restricted to nearest-neighbor interactions for which the Green's functions have simple forms. The quenchers are characterized by three dimensionless rate parameters: λ, for nearest neighbor host-quencher energy transfer; μ, for back transfer from quencher to host; and Q, for irreversible degradation of excitation on the quencher. Simple expressions for the Laplace transform of φ(t) under two different initial conditions are given for low concentrations of periodically placed quenchers that have identical but arbitrary λ, μ, and Q. Randomly placed quenchers are treated by adapting the coherent potential approximation; in three dimensions, this method gives a φ(t) that is identical to that with periodic quenchers of the same low concentration. Lattices with two types of defects-one with μ = 0 and one with μ > 0, a case of particular interest in organic crystals-are treated in some detail. Finally, it is shown that energy transfer anisotropies have little effect on φ(t), unless the smallest relative transfer rate is at least as small as the quencher concentration.
On the Mathematical Characterization of the Breaking of Hadronic Internal Symmetry
Authors: Abellanas Lorenzo
Published: February 2004

The adjoint action of a semisimple complex Lie algebra G singles out some singular directions with special properties. The directions of breaking of the hadronic internal symmetry groups, e.g., SU(3) or SU(3) × SU(3), by the electromagnetic, semileptonic, and nonleptonic weak interactions, are of this type. They are Hermitian (Q,Y) or nilpotent (Cabibbo direction) elements in the corresponding complexified Lie algebra. Their mathematical characterization is provided by the adjoint action of G. In particular, they satisfy a generalized extremal property for every G−invariant polynomial.
Analytic Treatment of the Coulomb Potential in the Path Integral Formalism by Exact Summation of a Perturbation Expansion
Authors: Goovaerts M. J. , Devreese J. T.
Published: February 2004

A straightforward analytical calculation of the s-like energy spectrum of the hydrogen atom is performed entirely within Feynman's path integral formalism. For this purpose the integral transform W = ∫d3rβK(rβ,0), where K(rβ,0) is the density matrix of the hydrogen atom written as a path integral, is calculated by means of the exact summation of a ``modified'' perturbation expansion (W is expanded as a power series in β with β = 1/kT). Performing this summation is equivalent to solving a problem of moments with infinite moments. For a wide class of potentials the perturbation expansion for W converges faster than the power-series expansion for the exponential function (for the Coulomb potential the convergence rate of both expansions is the same). It is shown how the complete energy spectrum can be obtained by this method. It is also illustrated how the wavefunctions might be obtained by transforming W.
Generalized Lienard-Wiechert Fields
Authors: Couch W. E. , Newman E. T.
Published: February 2004

We show that a moving point multipole source for a spin-S field gives rise to radiation having (in the rest frame of the source) multipole structure of order S through 2L + S, where L is the highest order moment of the source.
Closed Rotating Cosmologies Containing Matter Described by the Kinetic Theory. Entropy Production in the Collision Time Approximation
Authors: Matzner Richard A.
Published: February 2004

A collision time approximation for the production of partly collisional particles (``neutrinos'') from a collision dominated fluid (``electrons and photons'') within closed anisotropic Bianchi type IX cosmologies is discussed. Two distinct, constant, times are introduced; the neutrino production rate te−1 is distinct from the neutrino destruction rate tv−1. The conservation of energy and momentum is discussed, and it is shown, for a subclass of rotating closed cosmologies and for Maxwell-Boltzmann neutrinos, that the local entropy production rate sμ;μ is positive, aside from ``rest entropy'' terms, i.e., terms representing a fixed amount of entropy permanently attached to each neutrino (which goes out of existence when the neutrino is destroyed and reappears when a neutrino is regenerated). The results here contain as appropriate limits the same conclusions within special relativity and within simpler (Bianchi type I) cosmologies.
Bounds for Solution of Nonlinear Wave-Wave Interacting Systems with Well-Defined Phase Description
Authors: Wang P. K. C.
Published: February 2004

In this paper, upper and lower bounds for the solutions of nonlinear three-wave interacting systems with well-defined phase description are established. The results are used to deduce a sufficient condition for the non-existence of explosive instabilities.
Some Comments on the Behavior of Acceleration Waves of Arbitrary Shape
Authors: Bowen Ray M. , Chen Peter J.
Published: February 2004

This work concerns an application of the general results of Bailey and Chen to the study of acceleration waves of arbitrary shape. A modification of one of their main theorems is also presented; it applies to converging waves. For both converging and diverging waves, general expressions are given in terms of the initial principal curvatures. For diverging waves, a necessary and sufficient condition is given for the initial critical amplitude to be nonzero. In addition, Bailey and Chen's asymptotic formulas are specialized so as to apply to acceleration waves of arbitrary shape.
Scattering Theory in Fock Space
Authors: Prugovečki Eduard
Published: February 2004

It is shown that the wave operators which can be introduced in quantum field theories with cutoff interactions can be represented by wave transformers acting on states represented by statistical operators. Integral representations can be found for these wave transformers, which then form the basis of a time-independent scattering theory for such quantum field theories. It is pointed out that this leads to a time-independent perturbation theory in Fock space.
A Tachyon Dust Metric in General Relativity
Authors: Foster J. C. , Ray J. R.
Published: February 2004

Special relativity allows the possibility of a class of particles, called tachyons, which travel with speeds greater than the speed of light in vacuum. These particles have spacelike 4-velocities. Since tachyons have energy and momentum, they will contribute to the gravitational field through the energy-momentum tensor. One question then is what types of solutions to the Einstein field equations will tachyons yield. We consider a metric which admits a four-parameter isometry group. When this metric is used in the field equations using a dust energy-momentum tensor, solutions exist only for spacelike 4-velocity of the dust. We interpret these as solutions for a tachyon dust. Exact solutions to the field equations are obtained.
Time-Dependent and Time-Independent Potential Scattering for Asymptotically Coulomb Potentials
Authors: Marchesin Dan , O'Carroll Michael L.
Published: February 2004

We consider the three-dimensional quantum mechanical problem of nonrelativistic potential scattering, where the Hamiltonian is H2 = H1 + V = H0 + Vc + V;H0 is the free particle Hamiltonian, Vc is the Coulomb potential, and V(x) is a real-valued potential function defined for x ∈ R3. We show the existence of the wave operators W±(H2,HD) = s-lim eiH2t e−iHD(t) on L2(R3) for V = V2 + V′, where V2∈L2(R3),V′∈L∞(R3)∩Lp(R3)(p<3),and e−iHD(t) is the family of unitary operators used by Dollard to show the existence of the wave operators W±(H1,HD) appropriate for the pure Coulomb case. If V is spherically symmetric then W±(H2,HD) are shown to be absolutely continuous complete. If in addition V(r) is continuous in (0,∞), then W±(H2,HD) are continuous complete. In both cases S=W+*W− is unitary. The connection between the more physical, time-dependent wave operator approach and the traditional time-independent method is made, and phase shift formulas are obtained for the wave and scattering operators.
Perturbations of Gibbs States. I. Grand Canonical Formalism for Self-Interacting Fermion Systems
Authors: Uhlenbrock D. A.
Published: February 2004

The perturbation series for the statistical operators of quantum statistical mechanics developed earlier is applied to provide a perturbation theory for the grand canonical Gibbs states of a self-interacting fermion system. Explicit formulas for an interaction Hamiltonian which is a polynomial in creation-annihilation operators are provided.
Complex Time, Contour Independent Path Integrals, and Barrier Penetration
Authors: McLaughlin David W.
Published: February 2004

By developing an analogy between the Feynman path integral and contour integral representations of the special functions, we obtain WKB formulas for barrier penetration from a path integral. We first show that there exists for the path integral a notion of contour independence in the time parameter. We then select an appropriate contour to describe the physical situation of barrier penetration and obtain asymptotic formulas from the function space integral. The method is interpreted as a path integral derivation of the complex ray description of barrier penetration. In the last three sections we investigate several canonical problems of the theory of complex rays with these path integral techniques.
Hypergeometric Structure of the Generalized Veneziano Amplitudes
Authors: Mano Koichi
Published: February 2004

A multiple integral representation for a function of n(n − 1)/2 variables, which reduces to the (n + 3)-point generalized Veneziano amplitude for unit values of the variables, is integrated out once to obtain a recurrence formula for the amplitude. The result of complete integration obtained through repeated use of the recurrence formula is shown to belong to a class of generalized hypergeometric functions of many variables which are similar to but are more complex than the Lauricella functions. It is shown also that the (n + 3)-point amplitude for n ≥ 3 can be represented as a linear combination of an infinite number of n+1Fn[1] series with varying parameters.
On the Reduction of the Generalized RPA Eigenvalue Problem
Authors: Ullah Nazakat , Gupta K. K.
Published: February 2004

The 2n-dimensional eigenvalue problem, which arises when the random phase approximation (RPA) matrix is not real, is reduced to an n-dimensional eigenvalue problem. Some properties of the reduced eigenvalue problem are studied. A numerical example is considered for illustrative purposes.
Lattice Wind-Tree Models. II. Analytic Property
Authors: Gates D. J.
Published: February 2004

Three lattice versions of the wind-tree model of Ehrenfest are studied. It is shown that various moments, including the recurrence time and the Cesaro limits limT→∞ (1/T)∑t=1TΔ(t) of the mean-square displacement Δ(t) and of the one-particle distribution ρ(t, x) at time t, are analytic functions of the reciprocal of the fugacity of the trees, or equivalently of the deviation 1-ρ of the density ρ of the trees from their close packing density 1, in certain disks in the complex plane. Two of the models were considered in Paper I, but the third is new.
Quantum Electromagnetic Zero-Point Energy of a Conducting Spherical Shell
Authors: Davies B.
Published: February 2004

The quantum zero-point energy of a conducting spherical shell was first calculated by Boyer [Phys. Rev. 174, 1764 (1968)]. Because of the importance of this calculation and also of Boyer's uncertainty about the analytical dependence of the energy on the cutoff function, we have checked the calculation independently. We determine an analytic continuation of the energy function using the Mellin transform, and thereby show how an exact value of the self-energy can be obtained from the divergent series. We also compute an approximate value of the self-energy by extrapolating a direct numerical evaluation of the cutoff integrals. These calculations confirm Bover's result.
Deformable Magnetically Saturated Media. II. Constitutive Theory
Authors: Maugin Gérard A. , Eringen A. Cemal
Published: February 2004

This article is devoted to the development of constitutive equations of deformable magnetically saturated media in three dimensions. In Sec. 1 we recapitulate the local balance laws and jump conditions derived previously. A thorough study of the consequences of the objectivity requirement is given in Sec. 2. In the following sections, the material symmetry restrictions are examined and exact and approximate constitutive equations are obtained for a variety of material classes.
Scattering by Two Charged Centers
Authors: Li Ming Chiang
Published: February 2004

The scattering of a charged particle by two fixed charged centers is discussed. The scattering potential is long-range and spheroidal. It is pointed out that the general method for handling the short-range spheroidal potential is not directly applicable here. The integral differential equation for the Coulomb spheroidal phase shift is given in the text. The behavior of the phase shift is discussed in Born's approximation. A method for solving for the radial spheroidal Coulomb wavefunction is also given.
On the Decomposition of Direct Products of Irreducible Representations
Authors: Litvin Daniel B.
Published: February 2004

A lemma concerning irreducible representations contained in the decomposition of a direct product of irreducible representations of simply reducible groups is generalized to arbitrary decomposable unitary and nonunitary groups.
Energy of Gravitational Shock Waves
Authors: Robinson David C. , Winicour Jeffrey
Published: February 2004

A model of a gravitational shock wave is developed using the null hypersurface approach to the initial value problem. Interior to the shock front is a flat Minkowski region. This is joined to a shear-free but curved exterior. The geometric properties of the shock front determine the physical properties of the wave. The gravitational energy measured at null infinity is a functional of the 2-geometry of the shock front. The positive energy conjecture reduces to a simple statement concerning the geometry of 2-surfaces. Explicit numerical calculations carried out for various 2-surfaces have led to positive energy. However, no inequality is known to show that the energy is positive for all 2-surfaces.
A model for peaking of galactic gravitational radiation
Authors: Campbell Gerald A. , Matzner Richard A.
Published: February 2004

Geometrical optics is used to calculate the radiation pattern from a source in orbit in a strong gravitational field. No specific mechanism is postulated for the radiation itself, and only the field's effect on the radiation enters. (The model proposes a ``black hole'' at the galactic center.) Besides the Doppler peaking expected in these orbits, we find that the gravitational lens effect can enhance the radiation (regardless of how the radiation is produced). If the radiation arises from individual short events, the gravitational lensing leads to a scatter in the observed intensity. Formulas are presented for the probability a certain pulse will exceed the average by a given factor for a detector of finite sensitivity. Enhancement as found here, if present in the galaxy, would lower the overall galactic mass loss implied by Weber's gravitational radiation measurements.
A model of field theory treated in the Fock-Cook formalism
Authors: Schroeck Franklin E.
Published: February 2004

We present an alternative to the usual formalism for quantum field theory by generalizing the Fock-Cook formalism. We illustrate the method by applying it to a generalization of a familiar model of quantum field theory.
Differential solutions of the biharmonic Poisson and first order Stokes equations
Authors: Love J. D.
Published: February 2004

For coordinate systems with rotational symmetry it is shown that particular solutions of the biharmonic Poisson and first order Stokes equations exist and can be expressed in terms of simple derivatives and algebraic functions of the corresponding solutions of the Laplace and Stokes equations.
Kerr geometry as complexified Schwarzschild geometry
Authors: Schiffer Menahem M. , Adler Ronald J. , Mark James , Sheffield Charles
Published: February 2004

We present a simple derivation of the Schwarzschild and Kerr geometries by simplifying the Einstein free space field equations for the algebraically special form of metric studied by Kerr. This results in a system of two partial differential equations, the Laplace and eikonal equations, for a complex generating function. The metric tensor is a simple explicit functional of this generating function. The simplest solution generates the Schwarzschild geometry, while a displacement of the origin by ia in this solution generates the Kerr geometry.
Conformal group in a Poincaré basis. II. Principal discrete series
Authors: Macfadyen N. W.
Published: February 2004

In the second of this series of papers we study the six principal discrete series of unitary irreducible representations of SU(2,2). The same techniques are used as before, except that to examine the reducibility we are forced to use complexifications of all of our spaces. It is found that when restricted to the Poincaré group, two of the series contain only timelike momenta—with positive and negative masses, respectively — and a finite number of spins; the remaining four series contain spacelike momenta and spins which allow a certain helicity. A point of interest is that these two classes require entirely different scalar products.
Coordinate independent dyadic formulation of wave normal and ray surfaces of general anisotropic media
Authors: Lindell Ismo V.
Published: February 2004

Dyadic algebra has been applied to the problem of propagation of an electromagnetic discontinuity in a general lossless anisotropic medium (ε̿ and μ̿ positive definite symmetric dyadic quantities). It is seen that the wave normal and ray equations and, hence, the equations of the wave normal and ray surfaces, take a coordinate-independent explicit form. The optical axes of the medium are also discussed.
Perturbation theory for nonderivative nonpolynomial Lagrangians
Authors: Taylor J. G.
Published: February 2004

We present a regularization scheme for deriving finite, unitary, and causal amplitudes to each order in the major coupling constant for nonderivative nonpolynomial Lagrangians for the self-interaction of massless neutral scalar particles. The results are shown to contain no arbitrary constants, though these may be introduced consistently into the superpropagator, the second-order contribution.
Method of calculating quasiaverages
Authors: Bogolubov N. N.
Published: February 2004

Some features of quasiaverages for model systems with four-fermion interaction are considered. A new method of defining quasiaverages for the systems under consideration is proposed.
U and V sectors in the Bronzan-Lee model
Authors: Choudhury A. L.
Published: February 2004

The Lehmann-Symanzik-Zimmermann (LSZ) formalism is used in the Bronzan-Lee model to investigate the scattering processes in the lowest sectors. In this model, there are three heavy recoilless particles U, V, and N interacting with a θ particle. The processes allowed are U⇄Vθ and V⇄Nθ. In U and V sectors of this model all τ functions have been calculated, and relevant scattering and production amplitudes are evaluated. The mass, wavefunction, and vertex function renormalization constants have been found and they agree with the results previously obtained by Bronzan and later also by Liossatos.
Diagrammatic methods and renormalization in the Iwamoto-Yamada cluster expansion
Authors: Schäfer Lothar
Published: February 2004

We develop diagrammatic methods which give the explicit expression for the n th order term of the linked Iwamoto-Yamada cluster expansion in terms of the cluster integrals. The method applies independently of the number A of particles of the system. We carry through partial summations which for finite A result in a representation of the expansion by skeleton diagrams, whereas in the limit A → ∞ the expansion is reduced to two analytical equations. In addition, for finite A the renormalization establishes a connection between the expectation value of an arbitrary operator and the probability to find n hole states, 1 ≤ n ≤ A, occupied. Simple considerations raise some doubts concerning the convergence of the unrenormalized expansion.
On the utility of separable expansions for the t matrix
Authors: Levinger J. S.
Published: February 2004

Osborn used the property of compactness to show that there is an infinite mean square deviation between the t matrix for a local potential and any separable t matrix of finite rank. I present an alternate proof, using only the property of square integrability. The divergence of the mean square deviation arises from very large momenta. I argue that a separable t matrix can give a good approximation to the trinucleon energy, which is insensitive to values of the t matrix at very large momenta.
Transition from time-dependent to time-independent multichannel quantum scattering theory
Authors: Chandler Colston , Gibson A. G.
Published: February 2004

Rigorous proofs are given of several theorems establishing the connection between time-dependent and time-independent multichannel scattering theory. The method of proof involves a two-Hilbert-space formulation of time-dependent multichannel theory and the theory of spectral integrals. In particular, the time-independent theory in the form proposed by Alt, Grassberger, and Sandhas is derived.
On the structure of the canonical tensor operators in the unitary groups. III. Further developments of the boson polynomials and their implications
Authors: Louck J. D. , Biedenharn L. C.
Published: February 2004

Three structurally distinct and explicit expressions are developed for the boson polynomials. The relationship of these polynomials to the representations of the general linear group and the Gel'fand-Graev generalized beta functions is noted. A by-product of these results is a new, closed expression for the irreducible representations of the symmetric group. Some similarities, as well as dissimilarities, between the boson polynomial forms and the canonical tensor operator forms are presented and discussed, the origin of these properties being traced to the similarities and distinctions between Wigner coefficients and Racah coefficients. One of the boson polynomial expressions is used to prove an important new relation in the Racah-Wigner calculus: the identity of the set of extended projective coefficients to a subset of Racah coefficients. This relationship becomes one-to-one for SU(2) and establishes a pattern calculus for the Racah coefficients of angular momentum theory.