bluuebunny/crossref_metadata_2025 huggingface dataset:
Dust-Filled Universes of Class II and Class III
Authors: Ozsváth István
Published: February 2004

I construct on the Lie group R × H3 two different families of left-invariant metrics which satisfy the Einstein field equations with incoherent matter, calling the Riemannian spaces M4, obtained this way, Class II and Class III universes. We discuss the geometry of these universes.
Unitary Irreducible Representations of the Groups SO(n, 1)
Authors: Schwarz Fritz
Published: February 2004

By SO0(n, 1) we denote the identity component of the group O(n, 1), by so(n, 1), the Lie algebra of SO0(n, 1). We determine all those representations of the Lie algebras so(n, 1) which can be extended to a unitary irreducible representation of the group and give explicit expressions for the generators. The general results are specialized to the cases n = 2, 3, 4, and 5.
A Mathematical Property of Dirac Plane Waves
Authors: Muraskin M.
Published: February 2004

From Dirac plane waves, we can define a gij, Γjki, and eαi. It is found that Dirac plane waves satisfy, in addition to the Dirac equation, a set of nonlinear field equations involving these quantities. General eαi plane waves do not satisfy these equations.
Statistical Group Theory and the Distribution of Angular Momentum States
Authors: Cleary J. G. , Wybourne B. G.
Published: February 2004

The problem of developing relations for the statistical distribution of the angular momentum states of an electron configuration lN, where l and N are large, has been considered. If D(L) is the number of times the orbital angular momentum L occurs, then, using the theory of partitions and groups, we find that the numbers D(L) are approximately distributed with respect to L according to the Wigner-type form D(L)=A(L+12) exp [−(L+12)2/2σ2]. A number of examples are examined.
New Approach to the Noether Theorems
Authors: Plybon Benjamin F.
Published: February 2004

The Noether theorems were derived by Noether for n-dimensional Euclidean spaces, but they have been used by many writers in relativistic theories where the geometry is not Euclidean. We give a derivation of the Noether theorems, assuming only a Riemannian space and following the method used by Noether as closely as possible. This requires new definitions of total variations for fields and integrals since a covariant total variation for tensor fields is required. The results have been applied to electromagnetic fields.
Application of Regge Calculus to the Schwarzschild and Reissner-Nordstro/m Geometries at the Moment of Time Symmetry
Authors: Wong Cheuk-Yin
Published: February 2004

Applied to 3-dimensional space, Regge calculus approximates a curved space by a collection of tetrahedrons or other simple solid blocks. Within each block the geometry is Euclidean. Curvature is idealized as concentrated at the edge common to two or more of these solids. We specialize to a static geometry endowed with spherical symmetry and to a radial electric field produced by the flux of electric lines of force trapped in a throat connecting two quasi-Euclidean regions of space. The one relevant Einstein field equation takes the form ∑ all edges which meet at a given vertex(length of edge of prism)(deficit between (1) sum of dihedral angles which meet at that edge and (2) normal value of 2π)=(factor proportional to square of electric field). In method (1) the space is decomposed into shells separated from one another by icosahedral surfaces, all having a common center. Method (2) is even simpler: Space is decomposed into successive spherical shells of area 4π ρi2 separated by a proper distance d. Regge calculus gives a recurrence relation relating the dimensions of the successive shells. The approximate geometries calculated by methods (1) and (2) are compared with the well-known exact Schwarzschild and Reissner-Nordstro/m geometries. Errors range from roughly 10% down to less than 1%, depending upon the method of analysis, the quantity under analysis, and the fineness of the subdivision.
Asymptotic Distribution of Eigenvalues of the Kernel in the Kirkwood-Riseman Integral Equation
Authors: Ukai Seiji
Published: February 2004

An asymptotic formula for the eigenvalue is presented for the kernel appearing in the integral equation of the Kirkwood-Riseman type. The method used here provides a procedure of successive iteration for solving the inhomogeneous integral equation as well as the eigenvalue equation.
Structure of the Generalized Veneziano Amplitudes. I. Radon Transforms
Authors: Wu Alfred C. T.
Published: February 2004

The (tree-graph) generalized Veneziano amplitudes are shown to be boundary values of a new class of generalized hypergeometric functions having the property that they are Radon transforms of products of linear forms.
Structure of the Generalized Veneziano Amplitudes. II. Possible Group Theoretic Content
Authors: Wu Alfred C. T.
Published: February 2004

An attempt is made to generalize a result of Vilenkin that the beta function (being adopted as Veneziano formula for four-particle processes) appears as the kernel (in the integral) of the irreducible representation (in the Mellin-transformed space) of the group of 2 × 2 unimodular triangular matrices. It is shown that with a modified multiplier in the Gel'fand-Naimark prescription for the representation of the group of (n + 1) × (n + 1) unimodular triangular matrices, the (tree-graph) generalized Veneziano amplitude for (n + 3)-particle processes is recovered by a limiting procedure.
Exact Solution of a Time-Dependent Quantal Harmonic Oscillator with a Singular Perturbation
Authors: Camiz P. , Gerardi A. , Marchioro C. , Presutti E. , Scacciatelli E.
Published: February 2004

The quantal problem of a particle interacting in one dimension with an external time-dependent quadratic potential and a constant inverse square potential is exactly solved. The solutions are found both in the Schrödinger representation, by using a generating function or a time-dependent raising operator, and in the Heisenberg picture. They depend only on the solution of the classical harmonic oscillator. The generalizations to the n-dimensional problem and to the problem of N particles in one dimension, interacting pairwise via a quadratic time-dependent potential and a constant inverse square potential, are finally sketched.
On the Martin-Newton Condition for Finite-Dimensional Unitary Matrices
Authors: Eftimiu C.
Published: February 2004

A prescription is formulated by means of which one can write conditions for the existence of solutions of a nonlinear system expressing the unitarity of n × n symmetric matrices. These conditions are less restrictive than those analog to the Martin-Newton condition for the nonlinear integral equation representing the unitarity condition in the elastic region. At least for n ≤ 4 these conditions are also necessary.
The T Matrix for the Hulthén Potential
Authors: Bahethi O. P. , Fuda M. G.
Published: February 2004

A closed-form expression for the s wave part of the Hulthén potential's T matrix is derived. This expression is used to obtain a simpler result for the terms in the Weinberg series for the T matrix than the results given previously by other authors.
Scalar Diffraction by a Curved Edge
Authors: Bailey Paul B. , Barr George E.
Published: February 2004

The Green's function is constructed for the problem of time-dependent scalar diffraction by a planar curved edge in a form which includes contributions to the field from nonlocal parts of the diffracting edge. The Green's function involves an elementary solution of the wave equation corresponding to the diffracted wave which is obtained in the form of a series connected with the geometric properties of the wave fronts. The half-plane, slit, and circular aperture are treated as particular cases.
Characteristic Identities for Generators of GL(n), O(n) and Sp(n)
Authors: Green H. S.
Published: February 2004

A hierarchy of tensor identities, satisfied by the generators of the general linear group GL(n), is obtained in terms of two different sets of invariants. An application to the identification of irreducible representations and the decomposition of reducible representations is described. Similar results are obtained for the generators of orthogonal, pseudo-orthogonal, and symplectic groups.
Moments of Solutions of a Class of Stochastic Differential Equations
Authors: McKenna J. , Morrison J. A.
Published: February 2004

This paper is concerned with the exact calculation of moments of solutions of the stochastic, ordinary differential equation d2udz2+β02 [1+nf(M(z))]u=0,where M(z) is an arbitrary, finite state space Markov process and f(·) is an arbitrary, real, single-valued function of its argument. The process f(M(z)) is in general not a Markov process. The calculation of the moments is reduced to the solution of a system of ordinary, first-order differential equations. In the special case where the process M(z) has a stationary transition mechanism, these systems of equations have constant coefficients, so that the moments must consist of sums of exponentials. A specific example of such an equation with M(z) stationary is analyzed in some detail. The results obtained provide an important nontrivial check of some useful approximate techniques.
Covariant Derivatives of Infinite-Dimensional Fields
Authors: Bender Carl M. , Griffiths David J.
Published: February 2004

We show that a field which transforms irreducibly under the homogeneous Lorentz group admits four kinds of covariant derivatives-gradient, divergence, and two species of curl. We construct these derivatives explicitly for both finite- and infinite-dimensional representations. Physical applications are discussed.
Radiation Scattering in Einstein-Maxwell Theory
Authors: Couch W. E. , Hallidy W. H.
Published: February 2004

A linearized Einstein-Maxwell field composed of a mass monopole, a radiating mass quadrupole, a Coulomb field, and radiating electromagnetic dipole and quadrupole fields is examined to second order. If the first-order radiation is a pulse of finite duration, then the only second-order radiation present after the pulse has turned off is due to interactions involving the mass monopole. All other interactions contributing to the second order produce no such scattered radiation. At third order, the dipole-dipolemass interaction is found to give rise to scattered radiation.
The Statistical Mechanical Derivation of the Stress Tensor and Heat Flux for a System of Spherical Molecules
Authors: Miller Bruce N.
Published: February 2004

The equations of hydrodynamics are derived from the principles of classical statistical mechanics for a single component system of spherical molecules. Exact expressions for the stress tensor and heat flux are obtained without resorting to any methods of approximation. The derivations are carried out for a system of molecules which interact through a continuous pair potential, and for a system consisting solely of rigid spheres. The ``long-wavelength'' expansion employed by Irving and Kirkwood [J. Chem Phys. 18, 817 (1950)] in their expressions for the stress tensor and heat flux is examined. It is demonstrated that this expansion converges only if the intermolecular potential goes to zero faster than any positive power of (1/r) in the limit of large r (r is the internuclear distance) and hence diverges for any realistic intermolecular potential. An elementary example is considered to demonstrate the effect of finite wavelength on the stress tensor.
The Riemannian Structure of Space-Time as a Consequence of a Measurement Method
Authors: Castagnino Mario A.
Published: February 2004

Following the graphical method of Marzke and Wheeler it is shown analytically that if we know the space-time paths of all particles and light pulses we can deduce the connection and the metric of the space-time manifold. Specifically if such space-time paths fulfill some reasonable physical hypotheses, it is proved that space-time is a Riemannian manifold. To reach this conclusion a new definition of parallelism is introduced, based only on ideal experiments. This parallelism is entirely different from the ordinary parallel transfers, if the manifold is non-Riemannian; therefore it opens new ways of modifying gravitational theory.
Perturbation Formulas
Authors: Mizushima Masataka
Published: February 2004

A simple form of perturbation formula is shown to be correct to the fifth-order of the perturbation. It also has the variational character, namely, it gives an upper limit for a correct eigenvalue when applied to a bound state. The formula is in the form of a Padé approximant. The next approximation is correct to the seventeenth order and has the same variational character. Some examples are given and compared to conventional theories.
Classical Adiabatic Perturbation Theory
Authors: Stern David P.
Published: February 2004

Methods of classical perturbation theory developed for small perturbations are extended to slowly (or adiabatically) perturbed systems, with slow dependence either on time or on dynamical variables. Specifically, the extension is performed for the canonical perturbation theory of Poincaré and Von Zeipel, for the Krylov-Bogoliubov-Kruskal method of eliminating angle variables, for the general form of direct near-identity canonical transformations and for two of its realizations, based on the ``conventional'' generating function and on the Lie transform. In addition, the concepts of slow (or adiabatic) perturbations and of an implicit ``small parameter'' ε are clarified, as is the distinction between two alternative definitions of adiabatic invariance, and as an example the solution of the slow perturbed harmonic oscillator up to and including O(ε3) is derived.
On the Inverse Scattering Problem at Fixed Energy For the Tensor and Spin-Orbit Potentials
Authors: Hooshyar M. A.
Published: February 2004

The main purpose of this work is to find an analog of the Regge-Newton equation for the problem of finding tensor and spin-orbit potentials, acting among particles of spin ½, from the knowledge of the S-matrix as a function of angular momentum at a fixed energy. We first find a transformation which makes the Schrödinger equation containing a central, a spin-orbit, and a tensor potential the matrix analog of the Schrödinger equation for spin-½ particle in a central and a spin-orbit potential. Next, guided by the work of Sabatier for the case of central and spin-orbit potentials, we are able to find the desired integral equation. The necessary existence and uniqueness of the solution to this integral equation is studied, and it is shown that indeed the wavefunctions for tensor and spin-orbit potentials can be represented in terms of the solution of this integral equation. A series representation of the wavefunctions, which are necessary for finding the potentials from the S matrix, is found, but the actual construction of the potentials from the S matrix is not considered in this work.
Integral Approximations in Potential Scattering
Authors: Burt P. B. , Woods F. J.
Published: February 2004

A development of the scattering amplitude in potential scattering which is based upon replacing a smooth potential by a sequence of potential steps is given. The Schrödinger equation is solved exactly in each interval over which the potential is constant and by matching boundary conditions an expression relating the coefficients of two linearly independent solutions at small radius to those at large radius is found. From this the scattering amplitude is calculated. The limits of validity are found to be dependent upon the value of the expression (r/2)ddrln(2mℏ2[E−V]). Limiting cases of the amplitude are shown to be a modified WKB approximation and the Born approximation. A particular application to the Yukawa potential is discussed. The discussion is restricted to attractive potentials.
The Unitary Group U(m) as the Symmetry Group of Curved Phase Space
Authors: Heskia Said , Sofroniou S. A.
Published: February 2004

By describing U(m) as the symmetry group of a curved phase space, namely, by describing U(m) as the group of holonomy of a Hamiltonian space endowed with a Riemannian metric, it is shown that the Lie algebra of such a group is prior to any explicit Hamiltonian assumption.
Correlation Length in a Nonequilibrium Gas
Authors: Pomeau Y.
Published: February 2004

We demonstrate on a gas model that, if three-body events are neglected, the nonequilibrium correlations extend over a distance proportional to the relaxation time of the one-body distribution function. For homogeneous perturbations this correlation length is the mean free path, the relaxation time being the mean free flight time. In the hydrodynamical limit both the relaxation time of nonhomogeneous perturbations and the correlation length become infinite. This resolves the apparent contradistinction between the recent claim of a finite correlation length for nonequilibrium (but homogeneous) gases and the occurrence of correlations with an infinite range leading to divergences in the virial expansion of transport coefficients which precisely describe hydrodynamical perturbations.
Variational Field Theory
Authors: Stacey Weston M.
Published: February 2004

Equations which define a ``consistent'' set of ``boundary'' conditions, and hence a field, for a given set of differential equations are derived from a variational principle. The equivalence of functionals defined over an entire domain and functionals defined over only a subdomain, but with a surface term added to account for the contribution of the excluded subdomain, is exploited. The appropriate surface term is found to satisfy the Hamilton-Jacobi equation. The formalism is specialized to neutron diffusion theory, and it is demonstrated that Stark's double sweep method follows as a natural consequence of this field theoretic formulation. The relation of this formalism to Pontryagin's Maximum Principle and Bellman's Dynamic Programming is demonstrated for problems which can be characterized by minimum variational principles.
Exact Equilibration of Harmonically Bound Oscillator Chains
Authors: Huerta M. A. , Robertson H. S. , Nearing J. C.
Published: February 2004

The approach to equilibrium of a finite segment of an infinite chain of harmonically coupled, harmonically bound oscillators is treated exactly, both when the initial description of the rest of the chain is canonical and when it is Gaussian. The necessary mathematical properties of the bound oscillator functions are developed and used to demonstrate exact equipartition of energy. The entropy of the finite segment, or system, is shown to evolve to a time-independent equilibrium state that is, in the limit of weak coupling, the correct one for a system of noninteracting harmonic oscillators.
Excited State Reduced Coulomb Green's Function and f-Dimensional Coulomb Green's Function in Momentum Space
Authors: Hostler Levere
Published: February 2004

An integral representation for the f-dimensional nonrelativistic Coulomb Green's function in momentum space and an expansion of this function in a series of Gegenbauer polynomials are obtained. It is shown that the momentum space representatives of the f-dimensional Coulomb Green's function and the related reduced Green's functions can be obtained by differentiation with respect to the momentum transfer of the corresponding functions in the one-dimensional (f odd) or two-dimensional (f even) case. Expressions in closed form are then obtained for the momentum space representatives in the one-dimensional case of the full Coulomb Green's function and of the general nth excited state reduced Coulomb Green's function.
Relativistic Scattering of Electromagnetic Waves by Moving Obstacles
Authors: Twersky Victor
Published: February 2004

The excitation for an obstacle moving with constant velocity in free space (Σ) is transformed to the scatterer's rest system (Σ′), and the corresponding far-field scattering U′∼Ua′(g) is transformed to Σ to obtain U ∼ Ua(G). A simple expression is derived for the scattering amplitude G in terms of the conventional g, and known functional forms U[G] give the scattered field in Σ as a complex integral and its inverse-distance expansion. In dyadic form, G̃ = p̃r·g̃·p̃, where p̃ corresponds to transforming the excitation from Σ to Σ′, and p̃r (a planar reciprocal) to transforming the scattering from Σ′ to Σ. Then we transform the Green's function surface and volume integral representations, and the multipole series for U′, and apply the results to spherically symmetric scatterers, arbitrary small scatterers, large tenuous scatterers, and to cylinders and slabs.
A New Approximation Method for Wave Theories
Authors: Persides S.
Published: February 2004

The scalar field due to a bounded source and obeying the wave equation is analyzed. As a result of this, a set of rules is derived for solving a class of ``wave theories,'' including electrodynamics and general relativity, by expanding the field in a power series of c−1 in null-spherical coordinates. The method is applied for the Maxwell equations to give all the well-known results without the use of Fourier analysis and Bessel functions.
3
F
2 Representations for Spin Projection Coefficients
Authors: Mano Koichi
Published: February 2004

It is shown that a variety of equivalent representations for the spin projection coefficient, given in terms of the generalized hypergeometric function with unit argument, 3F2[1], can be generated by applying Whipple's theory to the function.
Operator Algebras and Axioms of Measurements
Authors: Chen Etang
Published: February 2004

The axioms of measurements introduced by Ludwig are formulated and studied in the framework of operator algebras. It is shown that a concrete C*-algebra with identity satisfies the axiom of sensitivity increase of effects if and only if it is a von Neumann algebra; although a von Neumann algebra satisfies the axiom of decompossability of ensembles, however, the axiom of components of the mixtures of two ensembles is true only if a von Neumann algebra is a factor of type In (n < + ∞). It is also verified that the set of decision effects, which is proved to be a subset of projections of a von Neumann algebra, has similar lattice structure of quantum mechanics, and its connection with quantum logic in the sense of Varadarjan is also figured out.
On Vacuum Space-Times Admitting a Null Killing Bivector
Authors: Debney George C.
Published: February 2004

Starting with a vacuum space-time (Rab = 0) which admits a Killing vector field K, a study is made of the subclass where the Killing bivector (KBV) Ka; b is null. Reference is made to an earlier paper [J. Math. Phys. 12, 1088 (1971)] by the author which established some of the general approach and formalism used here. All space-times with the property above turn out to be in the class of expansion-free radiation fields, which are necessarily algebraically special. Of these only Petrov types II, D, and N are allowed; furthermore, those of type N are the pp waves. A result obtained from applying this approach is that expansion-free radiation fields are the only vacuum space-times which admit a geodesic Killing vector field; that field is necessarily lightlike. Finally, since the spaces with symmetry studied by R. P. Kerr and the author [J. Math Phys. 11, 2807 (1970)] had nonzero expansion, the associated bivector to each of those symmetries must necessarily be nonnull.
An Explicit Basis for the Reduction U(n + m) ↓ U(n) × U(m)
Authors: Mickelsson Jouko
Published: February 2004

We construct lowering operators associated with the multiplicity pattern obtained in a previous paper [J. Math. Phys. 11, 2803 (1970)] for the labeling of the basis vectors in the reduction of an irreducible representation of U(n + m) with respect to U(n) × U(m). Every basis vector can be written as a product of lowering operators acting on the highest-weight vector.
Exterior-Algebraic Derivation of Einstein Field Equations Employing a Generalized Basis
Authors: Ernst Frederick J.
Published: February 2004

A tetrad vector formulation of Einstein's field equations is developed in which the orthogonality properties of the tetrad are permitted to vary in any prescribed smooth way from one space-time point to another. The components of the Riemann tensor with respect to such a basis are derived by means of exterior calculus. The approach facilitates a simple direct derivation of the Harrison-Ernst equations.
On Some Properties of Physical Symmetries
Authors: Lopuszanski Jan T.
Published: February 2004

It is shown that each symmetry of a field theory with interaction and with a mass gap, induced by a local current, is also induced by at least two other currents, local with respect to the asymptotic free fields and bilinear in these fields. The currents are asymptotic currents in the sense of Araki and Haag [H. Araki and R. Haag, Commun. Math. Phys. 4, 77 (1967)] of the original current. It is also shown that the charges, displaying spinorial transformation character with respect to the Lorentz group, vanish, while the tensorial charges are a linear combination of the scalar charges (internal symmetries) and the energy-momentum vector (translational symmetry).
Computation of the Cluster Coefficients of the δ-Function Gases through the U Functions
Authors: Servadio Sergio
Published: February 2004

It is shown that the wavefunctions of the δ-function l-body problem are simple enough to allow an explicit evaluation of the cluster operator Ul. Upon integration one can then obtain the general cluster coefficient bl. The l = 2 case is explicitly solved for particles of any statistics.
Classical Lorentz Invariant Particles
Authors: Arens Richard
Published: February 2004

A classical Lorentz invariant completely Hamiltonian elementary one-particle system is defined as having a state space K in which the Poincaré group acts transitively, its infinitesimal actions having generating functions relative to some Poisson bracket, such that there can be associated with each state k a world line Γ(k) in Cartesian 4-space. It is determined that there are nine families of such particles. Two have their speed in the usual range, three travel at the speed of eight, and four always faster. In each family the members are distinguished by one or two parameters such as mass and spin.
Irreducible Vector and Ray Representations of Some Cubic Crystal Point Groups in Four Dimensions
Authors: Chen Li-Ching , Birman Joseph L.
Published: February 2004

A new, and computationally simple, method is given for obtaining the characters of all the inequivalent irreducible vector representations of a finite group. The method was applied to determine the characters of the irreducible vector and ray representations of the four-dimensional cubic crystal point groups: group 47 and group 45. These groups are of order 384 and 1152, respectively, and contain the cubic point group in three dimensions Oh[3] as a subgroup. Tables are given of the irreducible representations of Oh subduced by the irreducible representations of group 47 and group 45. These tables may be useful in testing the conjecture that accidental degeneracy in problems in solid state physics in three dimensions reflects a higher symmetry in four dimensions.
Perturbation of Statistical Semigroups in Quantum Statistical Mechanics
Authors: Uhlenbrock D. A.
Published: February 2004

The perturbation theory of Hille and Phillips for semigroups of bounded linear operators on a Banach space is modified to apply to the semigroups of positive traceclass operators encountered in quantum statistical mechanics.
Minimal Uncertainty States for Bounded Observables
Authors: Ifantis Evangelos K.
Published: February 2004

The procedure of finding the states, which minimize the uncertainty product of two noncompatible observables, leads to the study of the approximate point spectrum of a non-self-adjoint operator. The spectrum of a large class of such bounded non-self-adjoint operators is studied. The results are applied to the theory of the oscillator phase operators.
The Phase Shift. II. As a Continuous Functional
Authors: Frank William M. , McLaughlin David W.
Published: February 2004

The continuity of the phase shift and S-wave scattering length as a functional of the potential is considered. The question is investigated in the present article for sequences of square wells which converge pointwise to zero. The results show certain conditions to be sufficient for convergence of the phase shift and scattering length to zero. These results are generalized to certain integral norms.
The Inverse Decay Problem
Authors: Horwitz L. P. , LaVita J. A. , Marchand J.-P.
Published: February 2004

Let UK(t) be a one-parameter operator family of positive type in a Hilbert space K and U(t) its minimal unitary dilation with infinitesimal generator H. If UK(t) is a contractive semigroup, then H is not positive. If in addition UK(t)→0 for t → ∞, then there exists a state φ∈K on which H is not defined. We interpret these and other results in the context of the quantum-mechanical theory of unstable particles and the scattering theory of Lax and Phillips.
Identity Satisfied by the Racah Coefficients of U(n)
Authors: Louck J. D. , Biedenharn L. C.
Published: February 2004

The origin of a well-known relation satisfied by the Racah coefficients of SU(2) is demonstrated to be the associative law of multiplication of the Wigner operators of SU(2). Recognition of this simple fact allows the immediate generalization of this identity to the Racah coefficients of U(n).
Boundary Conditions in the Pairwise Point Transformation Method
Authors: Witriol Norman M.
Published: February 2004

Using boundary conditions, one can eliminate the need of a transformation cutoff function in the pairwise point transformation method applied to the many-body problem.
New Generalized Bessel Transform and Its Relationship to the Fourier, Watson, and Kontorowich-Lebedev Transforms
Authors: Bahar E.
Published: February 2004

A generalized Bessel transform is postulated, and the corresponding inversion formula is deduced. This transform is used to show the direct relationship between the Fourier, Watson, and Kontorowich-Lebedev transforms. Thus, solutions of a certain class of boundary value problems can be expressed in terms of a single Bessel transform. Furthermore, the curvature of the boundary may range from zero to infinity.
Diffraction of Electromagnetic Waves by Cylindrical Structures Characterized by Variable Curvature and Surface Impedance
Authors: Bahar E.
Published: February 2004

The electromagnetic fields around a cylindrical boundary of variable curvature and surface impedance are expressed in terms of a complete set of local cylindrical modes, and Maxwell's equations are converted into coupled differential equations for the forward and backward wave amplitudes. The local cylindrical modes are shown to merge with the Fourier type expansion of the fields over plane surfaces. As an illustrative example, the launching of a surface wave over an infinite wedge with a rounded corner is considered in detail.
Recursive Method for the Computation of the SOn, SO
n,1, and ISOn, Representation Matrix Elements
Authors: Wolf Kurt Bernardo
Published: February 2004

We find a procedure whereby the matrix elements of the finite SOn,1 transformations (principal series) can be expressed as a single integral, over a compact domain, of two matrix elements of the SOn subgroup and a multiplier. In this way we automatically obtain their classification by the canonical chain SOn, 1⊃SOn⊃⋯⊃SO2. Analytic continuation yields the SOn+1 matrix elements in a recursive form. We obtain the asymptotic behavior of the boost matrix elements. The Inönü-Wigner contraction yields the ISOn representation matrix elements classified by the chain ISOn⊃SOn⊃⋯⊃SO2.
Iterated Integral-Transform Trial Functions
Authors: Somorjai R. L.
Published: February 2004

The concept of iterated integral-transform trial functions is introduced. Its formal correspondence with the iterative solution of integral equations is established. Extensions and generalizations are indicated, and some of the advantages of the approach are discussed. Ways are suggested to make tractable the multidimensional integrals that arise in the method.
``Short-Ranged'' Scalar Gravity in Einstein's Theory
Authors: Das A.
Published: February 2004

This paper deals with the class of conformally flat universes satisfying Einstein's field equations from a new point of view. It is shown that this class involves a scalar or pseudoscalar field that necessarily satisfies a meson-type field equation. This scalar gravity does not act at a distance, so to say, but supplies cohesive forces inside the source structure. Furthermore, the scalar field may involve spin-zero, massive quanta if quantized. Three exact solutions of this class are furnished here.
Zeros of the Partition Function for the Heisenberg, Ferroelectric, and General Ising Models
Authors: Suzuki Masuo , Fisher Michael E.
Published: February 2004

The Lee-Yang theorem for the zeros of the partition function of a ferromagnetic Ising model with real pair spin interactions is extended to general Ising models with complex many-spin interactions (satisfying appropriate ``ferromagnetic'' and spin inversion symmetry conditions). When many-spin interactions are present, all zeros lie on the imaginary Hz-axis for sufficiently low (but fixed) T, but, in general, some leave the imaginary axis as T → ∞. The extended Ising theorem is used to prove the same result for a Heisenberg system of arbitrary spin with the real anisotropic pair interaction Hamiltonian Hij=−(JijzSizSjz+JijxSixSjx+JijySiySjy)in an arbitrary transverse field (Hx, Hy) under the ``ferromagnetic'' condition Jijz≥|Jijx| and Jijz≥|Jijy|. The analyticity of the limiting free energy of such a Heisenberg ferromagnet and the absence of a phase transition are thereby established for all (real) nonzero magnetic fields Hz. The Ising theorem is also applied to hydrogen-bonded ferroelectric models to prove, in particular, that the zeros for the KDP model lie on the imaginary electric field axis for all T below the transition temperature Tc.
Quantum Many-Body Problem in One Dimension: Ground State
Authors: Sutherland Bill
Published: February 2004

We investigate the ground state of a system of either fermions or bosons interacting in one dimension by a 2-body potential V(r) = g/r2. In the thermodynamic limit, we determine the ground state energy and pair correlation function.
Quantum Many-Body Problem in One Dimension: Thermodynamics
Authors: Sutherland Bill
Published: February 2004

We continue our investigation of a system of either fermions or bosons interacting in one dimension by a 2-body potential V(r) = g/r2. We first present an approximation for the eigenstates of a general 1-dimensional quantum many-body system. We then apply this approximation to the g/r2 potential, allowing complete determination of the thermodynamic properties. Finally, comparing the results with those properties known exactly, we conjecture that the approximation is, in fact, exact for the g/r2 potential.
Some Properties of Cylindrically Symmetric Einstein-Maxwell Fields
Authors: Safko John L. , Witten Louis
Published: February 2004

Some properties of static cylindrically symmetric universes consisting of gravitational and electromagnetic fields with a central axial mass, charge, or current density are discussed. Of three permissible distinct configurations, general solutions of the appropriate equations are given for two. The properties of the solutions of these two are then examined in greater detail. The equations of motion of test particles (both charged and uncharged) are described for some simple trajectories. The qualitative effect of the magnetic field on uncharged test particle behavior in some instances is noted as well as the qualitative distinction in the behavior of charged and uncharged test particles. The algebraically independent invariants of the Riemann tensor are calculated. A stability analysis is carried out for the two solutions when the system is subjected to radial perturbations. It turns out that both solutions are stable. The stability analysis is carried out by using the equations of the already unified field theory of Rainich, Misner, and Wheeler.
Hypergeometric Functions with Integral Parameter Differences
Authors: Karlsson Per W.
Published: February 2004

For a generalized hypergeometric function pFq(z) with positive integral differences between certain numerator and denominator parameters, a formula expressing the pFq(z) as a finite sum of lower-order functions is proved. From this formula, Minton's two summation theorems for p = q + 1, z = 1 are deduced, one of these under less restrictive conditions than assumed by Minton.
Analytic Properties of Nonstrictly Localizable Fields
Authors: Constantinescu F.
Published: February 2004

A class of test functions ``minimal with respect to causality'' is introduced. The corresponding fields are called local. Tempered and strictly localizable fields are local, but there is a large class of fields that are local but not strictly localizable. For local fields, the analytic properties of vacuum expectation values are studied. The local fields that are not strictly localizable are characterized by an arbitrary fast increase of Wightman functions near the light cone. With an adequate definition of local commutativity, other properties of tempered and strictly localizable fields seem to remain valid.
Group Theory of Superfluidity
Authors: Solomon A. I.
Published: February 2004

The method of using a dynamical group to generate the energy spectrum of a given Hamiltonian is applied to the case of a superfluid Bose system. Here the relevant group is found to be SU(1, 1) [or Πk⊗SU(1,1)k for a multilevel system]. The energy eigenvalues and eigenfunctions are obtained by means of the group.
Topology for Minkowski Space
Authors: Nanda S.
Published: February 2004

The purpose of this paper is to prove one of Zeeman's conjectures that the group of homeomorphisms of the finest topology on Minkowski space that induces the 3-dimensional Euclidean topology on spacelike hyperplanes is the one generated by the inhomogeneous Lorentz group and dilatations.
Gravitational Radiation Damping of Slowly Moving Systems Calculated Using Matched Asymptotic Expansions
Authors: Burke William L.
Published: February 2004

This paper treats the slow-motion approximation for radiating systems as a problem in singular perturbations. By using the method of matched asymptotic expansions, we can construct approximations valid both in the near zone and the wave zone. The outgoing-wave boundary condition applied to the wave-zone expansion leads, by matching, to a unique and easily calculable radiation resistance in the near zone. The method is developed and illustrated with model problems from mechanics and electromagnetism; these should form a useful and accessible introduction to the method of matched asymptotic expansions. The method is then applied to the general relativistic problem of gravitational radiation from gravitationally bound systems, where a significant part of the radiation can be attributed to nonlinear terms in the expansion of the metric. This analysis shows that the formulas derived from the standard linear approximation remain valid for gravitationally bound systems. In particular, it shows that, according to general relativity, bodies in free-fall motion do indeed radiate. These results do not depend upon any definition of gravitational field energy.
Stochastic Theory of Quantum Mechanics for Particles with Spin
Authors: de la Peña-Auerbach L.
Published: February 2004

The stochastic theory of quantum mechanics is further developed to include the problem of extended rigid particles, thus allowing the introduction of spin. It is demonstrated that the stochastic equations for the system's center of mass give rise to a generalized Schrödinger equation for integral or half-integral spin; in the particular case of spin ½, upon elimination of the internal variables, Pauli's equation is obtained. A formal simplified relativistic extension of the theory is worked out and shown to lead to Dirac's equation in the case of spin ½ and for a gyromagnetic ratio equal to 2; in the case of arbitrary spin, the theory gives an equation of the Feynman-Gell-Mann type.
Almost Periodic Functions and the Theory of Disordered Systems
Authors: Romerio M. V.
Published: February 2004

The Schrödinger equation appropriate to a potential described by an almost periodic function (in the sense of representation theory) is examined. The Bloch-Floquet theorem is generalized to almost periodic functions and some properties of the density of states and spatial localization of the electrons are obtained. Some qualitative aspects of band structure are discussed.
Equations of Motion in Nonequilibrium Statistical Mechanics. III. Open Systems
Authors: Robertson Baldwin , Mitchell William C.
Published: February 2004

A simple hypothesis on the effect of the interaction between a system and its surroundings is used to generalize nonequilibrium statistical mechanics to apply to open systems. Thermal driving of a system by its surroundings is defined in statistical mechanics by analogy with the first law of thermodynamics, which describes exchange of heat between the system and an external source. The assumption that an isolated system is thermally driven is used to derive a Liouville equation with an additional term that is linear in the external source strength. The generalized Liouville equation is used to derive closed equations of motion that are the same as for an isolated system except for an additional term, which is just the source strength. This formalism is attractive because the source strength, which is assumed known, appears in the equations linearly just as in classical thermodynamics or hydrodynamics. A microscopic expression for the source strength is obtained by comparing the thermal driving formalism with an exact dynamical analysis of the system interacting with its surroundings.
Current-Stress Tensor Commutators
Authors: Deser Stanley , Morrison L. Kent
Published: February 2004

The model independent components of current-stress tensor equal time commutators are derived for arbitrary spin 0 and 1 systems.
Random Walks with Nonnearest Neighbor Transitions. I. Analytic 1-D Theory for Next-Nearest Neighbor and Exponentially Distributed Steps
Authors: Lakatos-Lindenberg Katja , Shuler Kurt E.
Published: February 2004

We present here exact analytic results for random walks on one-dimensional lattices with nonnearest neighbor transitions. After deriving the generating function for such lattices with and without boundaries, we have calculated a number of moment properties (mean first passage times to absorption, mean recurrence times and their dispersion, mean excursion from the origin, etc.) for random walks with next-nearest neighbor transitions and for random walks with exponentially distributed step length. In the latter case, variation of one of the parameters permits us to cover the whole range of step lengths from nearest neighbor transitions to steps of any finite length l. Since we have obtained explicit expressions for the generating function for these walks, any additional desired moment properties can readily be calculated. Among the interesting results of this study are: (1) The moment results for random walks with next-nearest neighbor transitions differ from the analogous nearest neighbor results at most by a factor of O(1); (2) the one-dimensional moment results for walks with arbitrary step length differ from the analogous one-dimensional results for walks with nearest neighbor transitions by several orders of magnitude; (3) the mean time to absorption for a random walker with equal probabilities for steps of arbitrary length in one dimension agrees to within a factor of O(1) with the mean time for absorption for a random walker with nearest neighbor steps in three dimensions; (4) the mean time to absorption for a random walker with equal probabilities for steps of arbitrary lengths is independent of the dimensionality of the lattice.
A Class of Type [4] Perfect Fluid Space-Times
Authors: Oleson M.
Published: February 2004

The existence of gravitational fields of Petrov-Penrose type [4] in the presence of a perfect fluid is established. In particular, the general type [4] solution of the Einstein field equations with a perfect fluid as source is obtained subject to the restriction that the repeated principal null congruence of the Weyl tensor is geodesic. The line element is expressed in terms of four arbitrary functions of a single variable, and in general admits no Killing vectors. The fluid flow is irrotational, but has nonzero shear, expansion, and acceleration. The physically reasonable requirement 0 < p ≤ A, where p is the fluid pressure and A the rest energy density, is imposed, and restricts the domain of validity of the solutions to a certain extent. In addition, it is shown that the stronger condition 0 < p ≤ A/3 excludes certain of the above solutions and further restricts the domain of validity of the remaining ones.
Consequences of a Field-Source Identity in a Spin-2 Meson Theory
Authors: Raman K.
Published: February 2004

We discuss the restrictions imposed on a spin-2 meson theory when the source is related to the stress tensor. We consider a spin-2 meson theory with a field-source identity, which postulates that the traceless part of the stress tensor is proportional to the irreducible part of the spin-2 meson field. We examine the consequences of imposing the field-source identity and Lorentz covariance on the spin-2 meson theory. We show that the field-source identity determines the parts of the singular terms in the stress-tensor equal-time commutation relations which are the most singular in the coupling strength g. It further requires that some of the singular terms be q-numbers. We obtain the constraints imposed on the field-dependence of the source Jμν(x) by the field-source identity and the Lorentz covariance conditions. We show that as a consequence of some of these, the interaction term gJμν(x) must be nonlinear in the coupling strength g.
Singularities in Forward Multiparticle Scattering Amplitudes and the S-Matrix Interpretation of Higher Virial Coefficients
Authors: Dashen Roger , Ma Shang-Keng
Published: February 2004

The role of singular forward multiparticle scattering amplitudes in S-matrix formulas for the higher virial coefficients is studied in detail. It is shown that by means of a simple limiting process one can give a precise, unambiguous meaning to the traces over on-shell scattering amplitudes which appear in our previous formulas for the virial coefficients. The general arguments, in which we maintain a reasonable level of rigor, are supported by explicit calculations for the third and fourth virial coefficients. Also, the angular momentum expansion used in earlier work is shown to converge.
Gauge Fields with Positive-Definite Energy Density
Authors: Uzes C. A.
Published: February 2004

The relationship between the couplings of the non-Abelian gauge field and the internal holonomy group is investigated on the classical level, under the requirements of full local gauge invariance and positive definiteness of the gauge field's energy density. For the free gauge field it is found that each solution to the gauge field equation with self-coupling is associated with a simple compact internal holonomy group. When the gauge field is coupled to other multiplet fields, an internal symmetry group is present in addition to the holonomy group H. In this case the internal holonomy group must also be simple and compact. In addition, homogeneity and isotropy of event space for closed systems of fields require that H be identical in group structure with either the symmetry group or a subgroup of the symmetry group and that all the field equations can be decoupled into sets of equations acting on multiplet fields transforming under irreducible representations of H. Thus, in local gauge theory, multiplet fields can be classified with respect to simple and compact internal holonomy groups. Some comments are offered on the relationship between internal holonomy and symmetry groups.