bluuebunny/crossref_metadata_2025 huggingface dataset:
Electromagnetic wave propagation in inhomogeneous multilayered structures of arbitrarily varying thickness-Generalized field transforms
Authors: Bahar E.
Published: February 2004

To provide a suitable basis for the expansion of electromagnetic fields in multilayered structures of arbitrarily varying thickness we derive, in this paper, the appropriate transform pairs for the transverse electric and magnetic field components. Applying the technique utilized earlier for two semi-infinite media, we first derive the transform pairs for the three-medium problem. Building on these expressions for the transform pairs, we systematically extend our results for structures with an arbitrary number of layers. The generalized transforms derived consist of two infinite integrals (continuous spectrum) which correspond to the radiation and the lateral wave terms as well as a finite number of terms (discrete spectrum) which correspond to the surface waves. Exact boundary conditions are employed rather than surface impedance boundary conditions. In the analysis, the sources and the observation point may be located in any of the structure's layers. Thus for instance, the derived field expressions are suitable for the study of antennas embedded in the earth's crust or submerged underwater.
Finite and infinitesimal canonical transformations. II
Authors: Testa F. J.
Published: February 2004

Linear differential equations generating finite canonical transformations are obtained for cases where the infinitesimal generator ω(q,p) is a homogeneous function of degree α in either one or both canonical variables.
On trace-class operators of scattering theory and the asymptotic behavior of scattering cross section at high energy
Authors: Martin Ph. , Misra B.
Published: February 2004

We investigate necessary and sufficient conditions under which the difference of the resolvents Rz − R0z of two self-adjoint operators of the form H01 ≡ F(P) and H ≡ F(P) + V(Q) is nuclear. Here F(P) denotes a positive and continuous function of the usual momentum observables P and V(Q) a function of the conjugate coordinate observables. Roughly speaking, we prove that Rz − R0z is nuclear if and only if F(P) increases faster than |P|3/2 at large |P| and V(Q) falls off to zero faster than 1/|Q|3 at large |Q|. (For a precise statement of this result Sec. 3.) In particular, it is noticed that if H0 = (|P|2 + m2)1/2 the relativistic free Hamiltonian, then Rz − R0z is not nuclear for any of the (suitably regular) potential V(QN.W.) where QN.W. denotes the usual Newton-Wigner position operator of the relativistic particle. We also investigate in Sec. 3 the necessary and sufficient conditions for Rzβ V Rz0β(β>0;β≠1) to be nuclear. The implications of these results for the asymptotic behavior of the total scattering cross sections at high energy is discussed in Sec. 4.
Theory of ground state correlations of closed shell nuclei: A density-matrix formulation
Authors: Krejs Franz , Klein Abraham
Published: February 2004

A general theory of long range correlations in the ground state of a closed shell nucleus is outlined, using a number of ideas introduced or adumbrated, but not always successfully developed, in previous work of the authors and others. These include the following: (i) Any operator can be formally expressed as a series in particle-hole (p-h) excitation and destruction operators which should converge rapidly for a suitable choice of single-particle basis at the closed shells. By means of these relations and with the help of sum rules all observables can be computed without the explicit use of wave functions. (ii) For a fixed choice of single-particle basis, the ground state energy can be computed from a variational principle in which in lowest nontrivial approximation, in consequence of (i), the parameters are amplitudes of the same type as occur in the random phase approximation (RPA). The precise relation to RPA is fully detailed. (iii) The single particle basis chosen is the natural orbital basis of Lowdin, which presents itself as the obvious choice both for formulation of the dynamics and for the algorithm of solution. (iv) Though the theory deals with pairs of fermion operators, particular attention is paid that all Pauli principle restrictions are satisfied. (v) It is verified that in the perturbation limit, known results are reproduced. The method is generally applicable to any system for which the correlations can be viewed as particle-hole excitations with respect to a reference Slater determinant.
Stochastic symmetry breaking of time reversal invariance
Authors: Fox Ronald Forrest
Published: February 2004

An equation for the time evolution of the density matrix for a nonrelativistic quantum mechanical system is presented. It involves a Hamiltonian which contains a stochastic contribution. Before stochastic averaging is performed, it is shown that the density matrix equation is time reversal invariant, whereas after stochastic averaging is performed, it is shown that the averaged density matrix equation is not time reversal invariant.
Eigenvalues of λx2m anharmonic oscillators
Authors: Biswas S. N. , Datta K. , Saxena R. P. , Srivastava P. K. , Varma V. S.
Published: February 2004

The ground state as well as excited energy levels of the generalized anharmonic oscillator defined by the Hamiltonian Hm = − d2/dx2+x2+ λx2m, m = 2,3, …, have been calculated nonperturbatively using the Hill determinants. For the λx4 oscillator, the ground state eigenvalues, for various values of λ, have been compared with the Borel-Padé sum of the asymptotic perturbation series for the problem. The agreement is excellent. In addition, we present results for some excited states for m = 2 as well as the ground and the first even excited states for m = 3 and 4. The behaviour of all the energy levels with respect to the coupling parameter shows a qualitative similarity to the ground state of the λx4 oscillator. Thus the results are model independent, as is to be expected from the WKB approximation. Our results also satisfy the scaling property that εn(m)(λ)/λ1/(m+1) tend to a finite limit for large λ, and always lie within the variational bounds, where available.
Structure of Ališauskas-Jucys form of the 9j coefficients
Authors: Wu Alfred C. T.
Published: February 2004

From the Ališauakas-Jucys triple summation expression, the Wigner 9j coefficients may be visualized as boundary values of a new generalized hypergeometric function φ(3)(αik ;βk,γm;wk) in three variables. Integral representations are given both for φ(3) in general and its boundary values as the 9j coefficients. The Radon structure is discussed. It is seen that φ(3) and the 9j coefficients in general do not belong to the class of hypergeometric functions whose Radon transforms are products of linear forms.
Ergodic properties of simple model system with collisions
Authors: Goldstein Sheldon , Lanford Oscar E. , Lebowitz Joel L.
Published: February 2004

We investigate the ergodic properties of the discrete time evolution of a particle in a two-dimensional torus with velocity in the unit square. The dynamics consists of free motion for a unit time interval followed by a baker's transformation of the velocity.
Construction of reproducing kernels for analytic Hilbert spaces
Authors: Cutkosky R. E.
Published: February 2004

The reproducing kernels of suitably chosen Hilbert spaces provide a simple but powerful way to generate approximations to functions on which linear data is given. These data may consist either of exact values (for the problem of interpolation) or of values subject to experimental error. For applications, it is important to be able to construct reproducing kernels which embody the information which is available from general considerations about the physics of the problem. Explicit methods are given here for construction of reproducing kernels for Hilbert spaces of analytic functions, these functions being characterized by various types of behavior on the boundary of their domain of holomorphy.
The gravitational influence of a beam of light. I
Authors: Nackoney Raymond W.
Published: February 2004

In this paper an exact solution is provided for the Einstein field equations of a beam of light. The beam is circular in cross section, infinite in length and duration, and considered in the geometrical limit with the flux being a function of only the radial coordinate. Null and timelike trajectories of this metric are considered in two classes: those with and without angular motion around the circular beam. The elements of the beam are initially without angular or radial motion and are found to follow a set of null trajectories which allows the beam to be in a state of equilibrium. A null trajectory, without angular motion, which is initially inclined slightly to the direction of the beam will curve away from the beam. Such a trajectory will continue to curve away until it is directed perpendicular to and then opposite to the beam direction, thereupon coming back into the beam upon the mirrored outgoing trajectory. Such trajectories are discussed with emphasis upon Lorentz transformations along the direction of the beam. Trajectories with angular motion include orbital cases. Beams of sufficient energy flux may allow closed null orbitals and regions of stable and unstable closed time-like orbits. Null helical trajectories which spiral back along the length of the beam can always occur; however, forward spiraling trajectories are restricted to large fluxes and are discussed in the light of Lorentz transformations.
Exact parastatistics for one-dimensional lattice space
Authors: McQuistan R. B.
Published: February 2004

Exact parastatistics are developed which describe the occupation of a one-dimensional lattice space by any arbitrary distribution of particles {gλ}, (λ=1,2,3,…,), where λ is the particle correlation distance, i.e., the number of contiguous lattice sites occupied by a particle.
Projection operator techniques for compact groups
Authors: Shapiro Joseph Y.
Published: February 2004

Projection operator techniques for reducing the Kronecker product of N irreducible representations of a compact group are developed. Among the results are a generalized Clebsch-Gordan series and generalized Wigner-Eckart theorems. The methods developed here are easily applied to any compact group provided one can (a) compute the matrix elements, between product states, of the projector onto the identity representation, and (b) select a subset of product states such that their projections form a basis for the subspace belonging to the identity representation. For the case of angular momentum projection, methods are given for solving both these problems.
Quantum field theory in terms of sesquilinear forms
Authors: Wyss Walter
Published: February 2004

We propose to describe a quantum field theory by continuous positive sesquilinear forms; using positive linear functionals would then be a special case. Our formalism still can accommodate a scattering theory.
On the Lee model with dilatation analytic cutoff function
Authors: Weder R. A.
Published: February 2004

The spectrum of the Lee model Hamiltonian with Y interaction is studied; first of all we extend the work of Kato and Mugibayashi about the eigenvalues outside the essential spectrum and about the essential spectrum itself. Furthermore, it is proved that the singular-continuous spectrum is not present; properties of resonances and eigenvalues embedded in the continuous spectrum are obtained.
Unitary representations of SO(n, 1)
Authors: Wong M. K. F.
Published: February 2004

All unitary representations of SO(n, 1) have been obtained in the group chain SO(n,1)⊃SO(n)⊃SO(n−1)⊃⋯⊃SO(2). The branching laws have been explicitly formulated. These results follow from the observation that the matrix elements of the ``noncompact'' generators of SO(n, 1) differ from the corresponding matrix elements of the same generators of SO(n + 1) by a factor of −1. The branching laws then follow from the unitarity condition. It is also observed that the invariants of SO(n, 1) have the same eigenvalues as the invariants of SO(n + 1). Finally we show that the normalized raising and lowering operators in SO(n + 1), obtained by Pang and Hecht in graphs, and by Wong in algebraic form, can be similarly defined and applied to SO(n, 1).
Multipole moments of stationary space-times
Authors: Hansen R. O.
Published: February 2004

Multipole moments are defined for stationary, asymptotically flat, source-free solutions of Einstein's equation. There arise two sets of multipole moments, the mass moments and the angular momentum moments. These quantities emerge as tensors at a point A ``at spatial infinity.'' They may be expressed as certain combinations of the derivatives at A of the norm and twist of the timelike Killing vector. In the Newtonian limit, the moments reduce to the usual multipole moments of the Newtonian potential. Some properties of these moments are derived, and, as an example, the multipole moments of the Kerr solution are discussed.
An extension of Hamilton's principle to include dissipative systems
Authors: Kiehn R. M.
Published: February 2004

The key idea of conservative Hamiltonian systems is the fact that the closed line integral of action is an absolute invariant of the motion. Dissipation effects may be included by considering those systems for which the closed integral of action is a parameter-dependent, conformal invariant of the motion. An application of this idea to hydrodynamics is made, and the conditions required for the validity of the Liouville theorem with respect to conformal Hamiltonian flows are examined.
The Clebsch-Gordan problem and coefficients for the three-dimensional Lorentz group in a continuous basis. IV
Authors: Mukunda N. , Radhakrishnan B.
Published: February 2004

This is the last of four papers describing a new approach to the Clebsch-Gordan problem for the group SU(1, 1). Here we have related the Clebsch-Gordan series for products of the type C ⊗ C to properties of the group O(2, 2) and the structure of the series is thus seen to arise out of the properties of O(2, 2) spherical harmonics in an O(1,1) ⊗ O (1,1) basis. The Clebsch-Gordan coefficients in a continuous basis are also evaluated.
Matrix mechanics approach to a nonlinear oscillator
Authors: Halpern Francis R. , Yonkman Thomas W.
Published: February 2004

The system with Hamiltonian p2 + x4 is discussed. An approximation scheme is given for matrices x and p that satisfy the canonical commutation relation and diagonalize the Hamiltonian.
Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0
Authors: Kalnins E. G. , Miller W.
Published: February 2004

A detailed study of the group of symmetries of the time-dependent free particle Schrödinger equation in one space dimension is presented. An orbit analysis of all first order symmetries is seen to correspond in a well-defined manner to the separation of variables of this equation. The study gives a unified treatment of the harmonic oscillator (both attractive and repulsive), Stark effect, and free particle Hamiltonians in the time dependent formalism. The case of a potential c/x2 is also discussed in the time dependent formalism. Use of representation theory for the symmetry groups permits simple derivation of expansions relating various solutions of the Schrödinger equation, several of which are new.
Schrödinger equation and quantum state codons in discrete transform space
Authors: King Jean I. F.
Published: February 2004

Quantum states of simple systems are shown to have composite root-pole structure in the complex transform plane. The Schrödinger condition becomes the inverse of a continuity equation expressing invariance of the Ψ-transform codon under discrete displacement. Four distinct quotient polynomial solutions model the Legendre, Hermite, Laguerre, and Jacobi polynomial families. Schrödinger coefficients are identified with pole strengths of quotient polynomials and are geometrically interpreted in terms of universal root and pole interactions.
Quantization on hyperboloids and full space-time field expansion
Authors: diSessa A.
Published: February 2004

Beginning with free field quantization on hyperboloids in the forward lightcone, we extend field expansions to the full space-time. The role of boundary conditions on the propagator and of the particle-antiparticle distinction in establishing a unique field expansion is discussed. Some difficulties with the possibility of a surface to surface development of the S matrix are encountered in the massless case. Even in the massive case hyperboloids are unsuitable quantization surfaces when x2<0, and we develop in some detail an alternative set of surfaces for that region in two dimensions.
Propagation through an anisotropic random medium
Authors: Beran M. J. , McCoy J. J.
Published: February 2004

An expression is derived, Eq. (59), for the mutual coherence of an initial plane wave signal that has propagated a distance, z, into an anisotropic random medium. This expression is valid for cases in which the characteristic radiation wavelength divided by 2π .λ̄/2π is roughly speaking of the same order as, or greater than, all characteristic correlation lengths in the direction perpendicular to the mean propagation direction, which is taken to lie in a horizontal plane. The exact condition is given in Eq. (48). We require λ̄/2π to be much smaller than all characteristic correlation lengths in the horizontal plane. Two derivation procedures are used. One follows that introduced by Beran (J. Opt. Soc. Am. 56, 1475 (1966)] for cases in which λ̄/2π is much smaller than all characteristic correlation lengths and one is based on introducing simplifications in a Bethe-Salpeter equation. We discuss the problem of the loss of spatial coherence of an acoustic signal due to scattering by the ocean temperature microstructure in the light of the theory presented.
Multiplicative stochastic processes, Fokker-Planck equations, and a possible dynamical mechanism for critical behavior
Authors: Fox Ronald Forrest
Published: February 2004

A derivation of the Fokker-Planck equations for additive stochastic processes is given which involves treating the continuity equation in the configuration space representation of the additive stochastic process as a multiplicative stochastic process. The average of the continuity equation becomes the Fokker-Planck equation. A presentation of the ``multiplicative stochastic, Markov approximation'' follows. This approximation is applied to the analysis of the dynamics of a heavy particle in a molecular fluid as described by Hamilton's equations. The nonperturbative approximation technique leads to the Fokker-Planck equation for simple Brownian motion. As part of the analysis, ``intrinsic diffusion'' is discovered and used to show ergodicity for the autocorrelation formula which appears during the Brownian motion calculation. An account of how these methods might be used to study the dynamical origins of critical behavior is given.
Weyl tensor decomposition in stationary vacuum space-times
Authors: Glass E. N.
Published: February 2004

The electric and magnetic parts of the Weyl tensor are represented as symmetrized derivatives of gradient vector fields in stationary vacuum space-times. It is shown that a necessary and sufficient condition for a stationary vacuum space-time to be static is that the Weyl tensor be electric type. It is further shown that the only stationary vacuum space-time with vanishing electric type Weyl tensor is flat space.
Diffraction characteristics of a slit formed by two staggered parallel planes
Authors: Kashyap S. C.
Published: February 2004

The diffraction of a plane electromagnetic wave by a slit formed by two staggered parallel planes is investigated using an asymptotic Wiener-Hopf technique. By following a standard procedure the problem is formulated in terms of two coupled Wiener-Hopf equations. For large edge-edge separation, the decoupling of the equations is accomplished by evaluating certain integrals by the saddle point method of integration. The results thus obtained can be conveniently identified as rays emanating from the two edges. It is shown that various changes in transmission coefficient and diffraction pattern of a slit can be obtained by changing the angle of stagger of the planes. Plots of transmission coefficients and diffraction patterns are presented for various slit widths and angles of stagger to show these characteristics.
Bounds for effective thermal, electrical, and magnetic properties of heterogeneous materials using high order statistical information
Authors: Elsayed Mostafa A.
Published: February 2004

Bounds have been developed for the effective thermal, electrical, and magnetic properties (K*) of a two phase statistically homogeneous and isotropic material. These bounds came in terms of the ratio of the properties of the two phases, volume fractions, and the constants G, G2, G3, M1, and M2. Bounds on the values of these constants are obtained. It is shown that the constants G, G2, and G3 are geometric parameters. They are calculated in the general case of spheroidal inclusions in terms of the axial ratio A. The constants M1 and M2 are packing parameters. General expressions of these constants in terms of packing information are obtained. It is found that certain combinations of the constants M1 and M2 for spheres and plates give exact solutions for the effective property K*. The exact solutions were shown in some cases to be equal to Miller's upper bound and in other cases to Miller's lower bound. A self-consistent scheme for the case of spheres is carried out. The corresponding values of M1 and M2 were identified and used to plot the bounds. The bounds for plates are also calculated. It is found that these bounds introduce a great improvement over Miller's bounds. The small perturbation limit was considered. It is found that our bounds coincide to order η5 and all values of v (η = K1/K2− 1, Ki is the property of material i). Moreover, they include Miller's bounds to order η3 and Hashin bounds to order η2.
Representations of multidimensional symmetries in networks
Authors: Harter W. G.
Published: February 2004

Physical systems that have resonances corresponding to representations of multidimension symmetry groups can be constructed from electric circuit elements. Examples involving symmetries of two four-dimensional polytopes are shown. Also a group theoretical analysis of linear constraints is described.
On irreducible corepresentations of finite magnetic groups
Authors: Rudra P.
Published: February 2004

We have obtained a set of homogeneous linear equations in the Clebsch-Gordan coefficients for the Kronecker inner direct product of two irreducible corepresentations of a finite magnetic group. The solutions of these equations give the Clebsch-Gordan coefficients even when the group is not simply reducible. The nontrivial Clebsch-Gordan coefficients for the magnetic group C4ν(C2ν) have been evaluated. We have also investigated the criterion determining whether a particular irreducible corepresentation is equivalent to its complex conjugate representation. A projection operator has been constructed for obtaining the basis pertaining to a particular irreducible corepresentation.
Clebsch-Gordan coefficients and special functions related to the Euclidean group in three-space
Authors: Rno Jung Sik
Published: February 2004

In this paper the Clebsch-Gordan coefficients of the Euclidean group in 3-space are explicitly and rigorously determined. The results are used to give elegant derivations of identities involving Wigner D functions and spinor functions.
Summation of regularized perturbative expansions for singular interactions
Authors: Bessis D. , Epele L. , Villani M.
Published: February 2004

In this paper we give a first application of a general method whose mathematical aspects will be fully developed in a forthcoming article. We are concerned with strongly singular perturbative series. Here we shall restrict ourselves to the most general two-body repulsive singular potential for which a regularization exists. Various extensions of this case are discussed in the conclusion. We show that, knowing only a finite number of regularized Born terms, it is possible to construct an upper bound to the exact phase shifts and that this upper bound is the best possible for the given regularization. The method uses the construction of the [N/N] Padé approximation indifferently on the regularized partial waves of the K or T matrix and exploits the fact that the approximate corresponding phase shifts have an absolute minimum as a function of the regularization parameter (cutoff). Three numerical examples are provided which show, even for very large phase shifts, an excellent convergence.
Power statistics for wave propagation in one-dimension and comparison with radiative transport theory. II
Authors: Kohler W. , Papanicolaou G. C.
Published: February 2004

We consider the one-dimensional problem of a slab having a random index of refraction and illuminated from within by a point source. We compute the expected value and the fluctuations of both the total power and power flux. These quantities, which are functions of the slab width, source location, and observation point, are determined in the limit of weak refractive index fluctuations and large slab thickness. We compare the expected values of total intensity and flux with the predictions of radiative transport theory. We also compare the results of both theories with numerical simulations.
A scalar-tensor theory of gravitation
Authors: Dunn K. A.
Published: February 2004

A scalar-tensor theory of gravitation is constructed using a non-Riemannian geometry in which both the metric tensor and the scalar function have an unambiguous geometric interpretation. The scalar function is introduced by defining a linear connection with nonvanishing torsion. The field equations of the theory, and the Lagrangian from which they are derived, are identical to those given by Dicke in an alternate formulation of the Brans-Dicke theory. By using the static spherically symmetric solution to the field equations it is found that, with a proper choice of parameter, this theory agrees with experimental results in the three classical tests of a gravitational theory.
The uniqueness of the Bertotti-Robinson electromagnetic universe
Authors: Tariq N. , Tupper B. O. J.
Published: February 2004

By employing the spin coefficient formalism of Newman and Penrose a direct proof is obtained that the Bertotti-Robinson electromagnetic universe is the only conformally flat solution of the source-free Einstein-Maxwell equations for nonnull fields.
On the higher order theories of piezoelectric crystal surfaces
Authors: Dökmeci M. Cengiz
Published: February 2004

This paper presents a higher order theory of crystal finite surfaces within the frame of the three-dimensional theory of linear piezoelectricity. First, by modifying Hamilton's principle, a variational theorem is deduced. Then, this theorem together with a method of series expansion is employed to establish the theory in a systematic and consistent manner. The theory consists of a hierarchy of two-dimensional equations of motion, charge equations of electrostatics, initial and boundary conditions, strain-displacement and electric field-electric potential relations, and macroscopic constitutive equations. It governs the extensional and flexural as well as torsional motions of piezoelectric crystal shells and plates of uniform thickness. Further, theorems of uniqueness in this theory are presented.
The discrete inverse scattering problem in one dimension
Authors: Case K. M.
Published: February 2004

A discrete version of the inverse scattering problem in one dimension is considered. While the natural formulation is somewhat different from the three-dimensional problem with spherical symmetry, the equations of solution turn out to be almost identical. Indeed, in the continuous limit (Schrödinger equation) even the slight differences disappear. Two equivalent treatments corresponding to considering incidence from left or right are given. For actual computation a combination of the two seems most efficient.
Lie algebra of the hypergeometric functions
Authors: Kyriakopoulos E.
Published: February 2004

It is shown that six operators forming the Lie algebra D2 can be introduced in order to treat the hypergeometric functions by Lie theory techniques. The relation of these operators to the three operators of the Lie algebra s l(2), which were used previously in treating the hypergeometric functions by Lie theory techniques, is discussed.
Bose-Einstein condensation in the presence of impurities. II
Authors: Kac M. , Luttinger J. M.
Published: February 2004

An alternative discussion, based on function space integration, is given of results given in our preceding paper.
Multipole expansions and plane wave representations of the electromagnetic field
Authors: Devaney A. J. , Wolf E.
Published: February 2004

A new and conceptually simple derivation is presented of the multipole expansion of an electromagnetic field that is generated by a localized, monochromatic charge-current distribution. The derivation is obtained with the help of a generalized plane wave representation (known also as the angular spectrum representation) of the field. This representation contains both ordinary plane waves, and plane waves that decay exponentially in amplitude as the wave is propagated. The analysis reveals an intimate relationship between the generalized plane wave representation and the multipole expansion of the field and leads to a number of new results. In particular, new expressions are obtained for the electric and magnetic multipole moments in terms of certain components of the spatial Fourier transform of the transverse part of the current distribution. It is shown further that the electromagnetic field at all points outside a sphere that contains the charge-current distribution is completely specified by the radiation pattern (i.e., by the field in the far zone). Explicit formulas are obtained for all the multipole moments in terms of the radiation pattern.
Green's function for electromagnetic scattering from a random rough surface
Authors: DeSanto John A.
Published: February 2004

The stochastic Green's matrix is calculated for a random rough surface with Gaussian statistics and a magnetic boundary condition. The techniques we use are similar to those developed for the scalar and elastic cases. The coupled surface integral equations which are derived are the Green's function version of the Franz formulas. These integral equations are represented in k-space in a certain gauge and a Feynman-diagram-like interpretation is given to each term in the equations. The diagram rules have many formal similarities with the scalar and elastic rules. By using partial summation techniques, the mean and second moment of this Green's function are shown to be solutions to Dyson and Bethe-Salpeter equations respectively. The Green's function is applied to a scattering problem. Some approximations and simple examples are presented. The lowest order approximations agree with the standard literature results. The main advantage of the diagram method, its systematic presentation of higher order approximations, is stressed.
Time-dependent multichannel Coulomb scattering theory
Authors: Chandler Colston , Gibson A. G.
Published: February 2004

The formulation by Mulherin and Zinnes of two-particle Coulomb scattering theory is extended to the multichannel case. The wave operators so obtained are proved by a direct method to be identical with those of Dollard.
On nonlinear transformations in vector spaces. Colineation and conformal groups
Authors: Tilgner Hans
Published: February 2004

The sets of special colineations and conformal transformations of a pseudo-orthogonal vector space can be given only a Lie groupoid structure, rather than a Lie group structure because of the non-vanishing denominators. With every such groupoid one can associate a unique Lie group, which, however, no longer consists of transformations. For one-parameter subgroups one can define infinitesimal transformations and a bilinear composition, called Lie bracket, which reduces for linear transformations to the commutator. In the special cases of colineations and conformal transformations on pseudo-orthogonal vector spaces of arbitrary finite dimension and signatures, covering homomorphisms onto matrix groups are given together with the corresponding Lie algebra isomorphisms.
A model unified field theory
Authors: Mirman R.
Published: February 2004

The geometry of space is probed by using a quantum mechanical wavefunction, which allows the introduction of the ordinary curvature tensor, and also provides room for a vector which is identified with the electromagnetic vector potential. The coordinates of space are taken as complex. Thus the electromagnetic field is geometrized and its presence is found to affect the gravitational field equations.
Noncompact Lie-algebraic approach to the unitary representations of SU∼(1,1): Role of the confluent hypergeometric equation
Authors: Montgomery W. , O'Raifeartaigh L.
Published: February 2004

The continuous unitary irreducible representations of the covering group SU∼ (1,1) of SU(1,1) are studied using the self-adjoint representations of the Lie algebra in the case that one of the noncompact generators is diagonal. The study can be carried out for all the representations simultaneously and is shown to reduce to a study of the self-adjointness of the compact element of the Lie algebra, which in this basis turns out to be the confluent hypergeometric operator. Several basic results, such as the classification of the representations, and a formula for the transformation coefficients from the compact to the noncompact basis which is valid for all representations, emerge quite simply.
Some useful properties of a theory of variable mass particles
Authors: Greenberger Daniel M.
Published: February 2004

By a simple extension of the canonical formalism, one can include mass and proper time as dynamical variables in mechanics. Such a theory allows one to treat particles with variable mass and also classically decaying particles. The theory has other properties which offer a fresh approach to classical dynamics. For example, the inertia of a system becomes an active concept, and the rest mass of an interacting particle changes to include its binding energy. Also, the proper time as measured by a clock on a decaying particle runs at a different rate from a clock on a stable particle. This effect causes a ``decay red shift'' to be present in classically decaying systems, over and above other red shift effects. The effect could be used to remove the acausal properties of ``pre-acceleration'' in radiative reaction, and it is suggested that for rapidly decaying massive objects, like quasars, this effect might be responsible for part of their red shift.
Two-particle approximation for the quantum third virial coefficient: Comparison of two approaches
Authors: Johnson R. E. , Pope N. K. , Barrett A. J.
Published: February 2004

Two distinct approaches have been followed to produce an approximate expression for the third virial coefficient of a quantum system in terms of the pertinent two-particle quantities (standard T matrix elements and bound state eigenvalues and eigenstates): One approach is based on the T approximation for the self-energy in the theory of temperature Green functions, and the other uses the diagrams which represent the various terms in the multiple-scattering expansion of the three-particle T operator. It is shown that the result given by the former method is reproduced exactly by the contribution of a small number of selected diagrams. The Green function method requires the evaluation of the Kadanoff and Baym generalized T matrix to one order in the activity higher than its familiar low-density limit. The common result can be written entirely in terms of the lowest order self-energy and should give a reasonable approximation to the third virial coefficient for systems with short-range forces.
Occupation statistics from exact recursion relations for occupation by dumbbells of a 2 × N array
Authors: Rashid M. A.
Published: February 2004

Starting from an exact recursion relation of the form A(q,N)=Σi,jA(q−i,N−j)Cij, we present a recursion method for calculating the various moments μN(m)=Σq=0NqmA(q,N). These results are applied to obtain the occupation statistics for occupation of a 2 × N array by parallel and not necessarily parallel dumbbells.
On the existence of solutions to S matrix models
Authors: Greenman J. V.
Published: February 2004

We analyze the charged scalar Low equation and show that, in this case at least, the breakdown of the standard fixed point theorems occurs because of their inherent weakness rather than through some topological change in the structure of the family of solutions. We also show that unless we reformulate the equation the Schauder principle only handles the basic solution, that solution without CDD poles. We discuss methods, alternative to the N/D method, to handle the other solutions.
Solving linear stochastic differential equations
Authors: Brissaud A. , Frisch U.
Published: February 2004

The aim of this paper is to provide the user with tools for the solution of linear differential equations with random coefficients. Only analytic methods which lead to expressions in closed form for first and second order moments and probability distributions of the solution are considered. The paper deals both with approximate methods which require the existence of a small (or large) dimensionless parameter and with the method of model coefficients, where the true coefficients of the stochastic equation are replaced by random step functions with the same first and second order moments and probability distributions, chosen in such a way that the equation can be solved analytically. The second procedure does not rely on the existence of a small parameter.
An action principle for superconductivity
Authors: Chela-Flores J.
Published: February 2004

We study a Lagrangian theory of superconductivity which, for slowly varying field variables, is shown to be equivalent to the BCS theory; we obtain the conservation of pairs, clearly showing its relation with the second kind of gauge invariance of the Euler-Lagrange equations. Finally, by treating the gauge function as a further field variable, we generalize the Maxwell-type Ginzburg-Landau equation and use it to discuss flux quantization.
The general solution to Einstein-Maxwell equations with plane symmetry
Authors: Letelier P. S. , Tabensky R. R.
Published: February 2004

The general solution to Einstein-Maxwell equations with plane symmetry is obtained. This solution has an extra Killing vector ξa not assumed a priori. The solution may be classified in two classes depending on the sign of an integration constant. The first class depends only on the time; ξa is spacelike. In the second class ξa is spacelike, lightlike, and timelike in different regions like Schwarzschild's metric.
On the moments of the distribution of widths corresponding to an ensemble of random matrices
Authors: McDonald J. F.
Published: February 2004

In this work, we discuss the moments of the width distribution corresponding to an ensemble of random matrices. The ensemble considered is one where the real and imaginary parts of the Hamiltonian matrices have Gaussian distributions with different widths. In particular, we give exact expressions for the moments when N = 2 (N = dimension of the Hamiltonian submatrix with a fixed set of quantum numbers) and give a method for obtaining a power series representation when N is arbitrary.
Prequantization of charge
Authors: Śniatycki Jȩdrzej
Published: February 2004

It is shown that a necessary and sufficient condition for quantization of relativistic dynamics of a particle with charge e moving in an external electromagnetic field F is that (e/2π)F should define an integral de Rham cohomology class on the space-time manifold.
Theory of multibin tests: Definition and existence of extraneous tests
Authors: Lubkin Elihu
Published: February 2004

Dirac's sets of commuting observables, in the guise of lists of mutually orthogonal projections which add to the unit matrix, are readily extended to a convex completion. But, furthermore, there exist lists of nonnegative Hermitian matrices which sum to the unit matrix which do not even belong to this convex completion. It is shown that these ``extraneous'' lists appear as tests in ordinary quantum-mechanical experiments. This circumstance leads to simpler rules for injecting measurement theory into the social sciences than might otherwise be proposed. Various relationships between lists of orthogonal projections and more general tests are given. The problem of devising rules of inference by direct computation is very briefly engaged.
Eigenvalue problem for Lagrangian systems. VII
Authors: Barston E. M.
Published: February 2004

Minimax principles for a subset of the real eigenvalues of the quadratic eigenvalue problem (ω2A +ω B + C)ξ = 0 are presented, where A, B, and C are formally self-adjoint operators mapping a dense subspace Δ of a complex Hilbert space E into E, and A >0. These results are applied to the problems of the small oscillations about equilibrium of a vertically stratified, viscous, heterogeneous incompressible fluid in a gravitational field and the oscillations of a rotating thin annular disk, and it is shown that the minimax principles characterize infinitely many eigenvalues of these systems.
Heat conduction and sound transmission in isotopically disordered harmonic crystals
Authors: O'Connor A. J. , Lebowitz J. L.
Published: February 2004

We investigate some kinetic properties of an isotopically disordered harmonic crystal. We prove rigorously that for almost all disordered chains the transmission coefficient of a plane wave with frequency ω, tN(ω), decays exponentially in N, the length of the disordered chain, with the decay constant proportional to ω2 for small ω. The response of this system to an incident wave is related to the nature of the heat flux J(N) in a disordered chain of length N placed between heat reservoirs whose temperatures differ by ΔT>0. We clarify the relationship between the works of various authors in the heat conduction problem and establish that for all models J(N)→0 as N→∞ in a disordered system. The exact asymptotic dependence of J(N) on N eludes us, however. We also investigate the heat flow in a simple stochastic model for which Fourier's law is shown to hold. Similar results are proven for two-dimensional systems disordered in one direction.
A semi-Euclidean approach to boson-fermion model theories
Authors: Brydges David , Federbush Paul
Published: February 2004

A formulation is presented for the study of semiboundedness of coupled boson-fermion model field theories. Euclidean-boson fields and ordinary fermion fields are employed. Expansion steps used to derive estimates are presented.
The unitarity equation for scattering in the absence of spherical symmetry
Authors: Tortorella Michael
Published: February 2004

We consider the problem of determining the scattering amplitude from the differential cross section at a fixed energy by using the unitarity equation when the scattering potential does not have spherical symmetry. We indicate some of the problems peculiar to this case. We prove two existence and uniqueness theorems. We give an example of nonuniqueness.
Generating functions of the hypergeometric functions
Authors: Kyriakopoulos E.
Published: February 2004

The Lie algebra, which was introduced in a previous paper to treat the hypergeometric functions by Lie theory techniques, is used to derive generating functions of the hypergeometric functions. Several generating functions are obtained from the theory of multiplier representations. Weisner's method is also applied, giving another generating function.
Duality of observables and generators in classical and quantum mechnics
Authors: Grgin Emile , Petersen Aage
Published: February 2004

In classical and in quantum mechanics physical variables play a dual role as observables and as generators of infinitesimal transformations in the invariance groups. We show that if the Lie algebra of generators is central simple, the observable-generator duality restricts the structure of the algebra of observables to two cases: a commutative, associative algebra as in classical mechanics, or a central simple special Jordan algebra as in quantum mechanics.
Explicit O (5) Wigner coefficients
Authors: Hongoh M. , Sharp R. T. , Tilley D. E.
Published: February 2004

The O (5) van der Waerden invariant is given; with its help the general Wigner coefficient in the canonical SU(2)×SU(2) chain is calculated. Some special Wigner coefficients and Gaunt-type formulas needed for the construction of the general Wigner coefficient are also presented.
Higher order diagrams in quantum gravity and the continuous dimension method
Authors: Capper D. M. , Leibbrandt G.
Published: February 2004

The following three third-order Feynman diagrams in quantum gravity are treated in the context of dimensional regularization: (a) the pure graviton triangle diagram and (b) two massless tadpole diagrams. It is shown that the graviton vertex integral is free of ultraviolet and infrared divergences as we approach Minkowski space (ω=2). It is also shown that the ultraviolet divergences arising from two-loop massless tadpole integrals either vanish completely as ω→2, or manifest themselves as poles of Weierstrass' gamma function.
A new method for the study of Feynman perturbation series
Authors: Kershaw David S.
Published: February 2004

We have systematically studied a finite-dimensional version of Feynman perturbation series with arbitrary matrices for propagators and arbitrary tensors for interaction couplings. In this formalism we obtain many old results in an elegant new manner, and we obtain a completely new fundamental integral representation for the Green's functions of boson field theories which rigorously defines these functions in our finite-dimensional version and which we hope will enable us to calculate the Green's functions in the physically important infinite-dimensional case.
Equivalent Lagrangians and path integration for generalized mechanics
Authors: Cheng Kuo-Shung
Published: February 2004

The equivalent Lagrangians for a generalized mechanical system are defined and the effects of using different members of the class of equivalent Lagrangians in classical mechanics and quantum mechanics are discussed. The path integration method is applied to quantize the generalized mechanical system.
Hamiltonian cosmology: Death and transfiguration
Authors: Ryan Michael P.
Published: February 2004

Following work of MacCallum and Taub, we show that for Bianchi-type universes of Ellis-MacCallum class B (Bianchi types II, III, IV, V, VIh≠−1, VIIh=0) Hamiltonian cosmology breaks down. We construct a quasi-Hamiltonian theory for these models.
Causality and nonlocalizable fields
Authors: Constantinescu F. , Taylor J. G.
Published: February 2004

We give a model-independent and Lorentz invariant prescription for the manner in which a nonlocalizable quantum field extends outside the light cone, in particular specifying the order of this extension. We show how our definition applies to several examples, including the nonlocalizable free field and certain functions of the massive free field; nonlocalizable functions of the massless free field presents a difficulty which has not yet been resolved.