bluuebunny/crossref_metadata_2025 huggingface dataset:
Wave propagation in a random lattice. II
Authors: Chow Pao-Liu
Published: February 2004

Propagation of the mean waves in a simple cubic crystal with small, random mass defects is studied using the results of a previous paper. The dispersion equations for two- and three-dimensional crystals are analyzed. For uncorrelated mass defects, the effective propagation constants are obtained explicitly in the limits of low frequency and near cut-off frequency. The mean reflection and transmission coefficients are determined for a plane wave incident in a crystal formed by joining a semi-infinite perfect crystal to a semi-infinite defective crystal or by connecting two semi-infinite perfect crystals to a finite imperfect crystal. We also construct the mean Green's functions for an infinite crystal lattice containing defective masses distributed throughout it or confined to a half-space.
Entropy production in the functional random-walk model
Authors: Hosokawa I.
Published: February 2004

An information-theoretical background is presented here for the functional random-walk model of a many-particle system, which was recently proposed to simulate nonequilibrium statistical mechanics in a certain coarse-graining sense. Next, entropy productivity and the maximum-entropy state in the model dynamics are studied with the new definition of entropy, which turns out to be a natural extension of the original Boltzmann entropy.
Modified Lippmann-Schwinger equations for two-body scattering theory with long-range interactions
Authors: Prugovečki E. , Zorbas J.
Published: February 2004

Two kinds of modified Lippmann-Schwinger equations are derived for the case of long-range potentials. The equations of the first kind are homogeneous and are a direct result of the fact that the standard Lippmann-Schwinger equations do not hold when long-range forces are present. The equations of the second kind depend on the existence of an operator Z such that W± = s-lim exp (iHt)Z exp(−iH0t). A general recipe for constructing Z is given and its computation is carried through for the case of asymptotically Coulombic potentials. The resulting equations are used to compare the long-range theory with the theory with a space cutoff (i.e., screened potential) in the limit in which that cutoff is being removed.
On perturbations of a Kerr black hole
Authors: Wald Robert M.
Published: February 2004

Gravitational perturbations of a Kerr black hole are analyzed using the Newman-Penrose formalism. Teukolsky has obtained decoupled wave equations for the perturbed Weyl tensor components ψ0 and ψ4. In this paper we prove that for well-behaved perturbations ψ0 and ψ4 uniquely determine each other, i.e., ψ0 = 0 if and only if ψ4 = 0. Then we solve the Kerr perturbation equations with ψ0 = ψ4 = 0 and show that the only well-behaved solutions are the trivial perturbations to other Kerr solutions via an infinitesmal change in the mass and angular momentum parameters. These results prove that either of the quantities ψ0 or ψ4 alone uniquely specifies the nontrivial part of a gravitational perturbation of a Kerr black hole. Consequences of this result are discussed.
Some properties of matrices occuring in SL (2, C) invariant wave equations
Authors: Lorente M. , Huddleston P. L. , Roman P.
Published: February 2004

A general expression is found for the anticommutator of the Lμ matrices that occur in SL (2, C) invariant wave equations. The formula is valid for a broad class of representations which includes, besides the Dirac and the Majorana representations, many other infinite and finite dimensional representations. Several related properties of the Lμ are studied and some applications are given.
Depolarization of electromagnetic waves excited by distributions of electric and magnetic sources in inhomogeneous multilayered structures of arbitrarily varying thickness. Generalized field transforms
Authors: Bahar E.
Published: February 2004

A suitable basis for the full wave expansion of electromagnetic fields in inhomogeneous multilayered structures of arbitrarily varying thickness is presented in this paper. To this end, we formulate appropriate sets of transform pairs for the transverse electric and magnetic fields. Since arbitrary distribution of electric and magnetic sources are considered, the complete expansion must be composed of both vertically and horizontally polarized waves. Each set of generalized transforms, for the vertically and horizontally polarized waves, consists 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. For a general three-dimensional distribution of sources in any of the structure's layers, the transverse electric and magnetic fields are in general two component vector functions. Thus, the transform pairs involve vector rather than scalar functions. Exact boundary conditions are employed in the analysis rather than approximate surface impedance boundary conditions. When the boundary media of the structure are regarded as perfect electric or magnetic walls, or are characterized by surface impedances, the fields are expressed exclusively in terms of infinite sets of waveguide modes.
Generalized semidirect product in group unifications
Authors: Vujičić M. , Herbut F. , Šijački Dj.
Published: February 2004

The case of a unification E of two given groups K and H when K is invariant in E (i-unification) is investigated. Necessary and sufficient conditions for the existence of E are found. It is shown that any i-unification can be constructed as a factor group of the simplest i-unification, i.e., the semidirect product K[circled tau]H with respect to a given homomorphism τ:H → Aut(K). This construction is called the generalized semidirect product (GSP). The i-unifications are put in correspondence with the group extensions via the GSP. The significance of the GSP is illustrated in elementary particle and solid state physics.
Existence and uniqueness of solutions of the Hamiltonian constraint of general relativity on compact manifolds
Authors: O'Murchadha Niall , York James W.
Published: February 2004

The Hamiltonian constraint ``G00 = 8πT00'' of general relativity is written as a quasilinear elliptic differential equation for the conformal factor of the metric of a three-dimensional spacelike manifold. It is shown that for ``almost every'' configuration of initial data on a compact manifold, with or without boundary, a solution exists. Dirichlet boundary conditions are assumed if the boundary is not empty. The solution is unique.
Existence of generalized translation operators from the Agranovitch-Marchenko transformation (Jost solutions)
Authors: Coz Marcel , Coudray Christiane
Published: February 2004

The A and M transformation for finding an integral equation for the kernel of a generalized translation operator is adapted to the s-wave regular solution. Its extension to higher l-values is then considered for Jost solutions. The integral equations for the G.T.O. kernels are similar to the s wave one, with the difference that the Riemann function for the l-wave harmonic partial differential equation has to be introduced. As a consequence the condition ∫(x+y)/2∞sl|V(s)|ds<∞,(x+y)>0, must be satisfied for the l wave, if one wants a continuous kernel.
Application of Kraichnan's direct interaction approximation to kinematic dynamo theory. III. Solution of the Kraichnan equations under Parker's ``short-sudden'' conditions
Authors: Lerche I.
Published: February 2004

Using Parker's ``short-sudden'' conditions, we solve the Kraichnan equations exactly. We find that the normal modes of the ensemble average magnetic field have very different properties in this case than when the velocity turbulence is static, which situation was investigated in earlier papers in this series. We have done this calculation for two reasons: first because exact solutions of the Kraichnan equations are few in number, and second because the nonlinearity and singularity of the Kraichnan equations is such as to emphasize the physical difference in the properties of the normal modes of the average magnetic field under a small change in the prescription of the turbulent velocity field.
Deep inelastic scattering in a renormalized perturbative model
Authors: Mason A. L.
Published: February 2004

We sum all the leading contributions to the form factor νW2 in deep inelastic electron-proton scattering in a field theory with a neutral pseudoscalar gluon. This involves calculating ladder graphs with renormalization insertions. We find that we can express νW2 in a simple way in terms of the asymptotic behavior of the renormalization parts. For ladders with only gluon rungs we obtain a result similar to Chang and Fishbane's for the Mellin transform of νW2, namely z(lnν)(exp{(g2/16π2)[Y (lnν)/(λ+1)(λ+2)]} − 1). Y and z are (calculable) functions depending on the renormalization parts. We also calculate the rather more complicated contribution from ladders with fermion rungs. Our results do not lend any support to the notion of anomalous dimensions.
Unitary representations of the SL (2, C) group in horospheric basis
Authors: Huszár M.
Published: February 2004

The matrix elements of unitary representations of the S L (2, C) group are derived in a basis defined by two-dimensional momenta corresponding to the horospheric subgroup (1β01). A parametrization fitting the above basis well is chosen on the analogy of the rotation group by sandwiching a complex rotation about the y axis with two horospheric translations. In this way the two outer subgroups can be factored out immediately in terms of plane waves which are counterparts to the exponentials formed by the Euler angles φ and ψ occuring in the rotation group. Finally, matrix elements of complex rotations about y axis are found by solving the simultaneous eigenvalue problem of the two Casimir operators. Unitary representations obtained in this way are expressed in a rather simple form in terms of Bessel functions.
Bose-Einstein condensation in the presence of impurities
Authors: Kac M. , Luttinger J. M.
Published: February 2004

It is shown that, in three dimensions, a gas of noninteracting bosons in the presence of purely repulsive impurity centers undergoes a ``Bose-Einstein'' phase transition at sufficiently low temperature. In the course of the proof it is also shown that, as the size of the system approaches infinity, the lowest energy state approaches zero with probability one.
Coupled channel operator approach to e-H scattering
Authors: Baer Michael , Kouri Donald J.
Published: February 2004

A coupled channel T operator formalism is applied to the problem of e-H collisions. Due to the electron-electron repulsion interaction, coupled integral equations for the direct and exchange amplitude density functions are obtained in contrast to the purely algebraic equations encountered in previous studies of model systems. These integral equations may be solved in a number of ways. One procedure involves the use of the Sams-Kouri homogeneous integral solution formalism to convert the integral equations into Volterra equations of the second kind. The kernals for these equations are such that a very rapid numerical solution may be obtained. Numerical results are presented for the special case of s -wave elastic scattering.
The discrete version of the Marchenko equations in the inverse scattering problem
Authors: Case K. M. , Chiu S. C.
Published: February 2004

For s -wave and one-dimensional scattering, the discrete Marchenko equations with respect to nontrivial comparison systems have been derived. A relation with the Gel'fand-Levitan equation is obtained. The continuum versions are obtained by a limiting process.
A comparison of two transformation theories of classical mechanics
Authors: Rae J. , Davidson R.
Published: February 2004

A comparison is made of two transformation theories which can be used in classical mechanics: the averaging method as generalized by Kruskal and the superoperator transformation theory used in statistical mechanics by Prigogine et al. For the class of systems considered, a striking connection is found which, on the one hand, illustrates some of the general features of the superoperator method and, on the other, provides an interesting method for calculating invariants of nearly periodic systems. This latter method is shown to be equivalent to, but more systematic than, that developed by McNamara and Whiteman.
Time evolution of a two-dimensional model system. I. Invariant states and time correlation functions
Authors: Hardy J. , Pomeau Y. , de Pazzis O.
Published: February 2004

This paper is the first one of a series devoted to the study of a particularly simple two-dimensional system of classical particles. The model is presented and some general feautres of it are established. We prove that, among states without correlations between particles with different velocities, there is a unique time invariant state with given density and hydrodynamic velocity. This ``equilibrium state'' is studied in detail. In particular its ergodic and mixing properties are investigated. We propose an approximation in order to estimate the asymptotic part of the time correlation functions and show that the long time tail is ruled by the ``hydrodynamic'' behavior of the model, namely by the evolution of the long wavelength perturbations.
Generalizing Riemannian geometry
Authors: Hudgin Richard H.
Published: February 2004

The properties of Riemannian geometry necessary to relativity have been used as a basis to derive a more general geometry. Emphasis is placed on a natural development with the result of considerable generalization. Several examples are discussed including the Brans-Dicke field equation which are but one special case of the new manifolds. The scalar field is not introduced ad hoc but is a natural geometrical quantity.
Scattering theory in a model of quantum fields. I
Authors: Albeverio Sergio
Published: February 2004

We study a model of quantum field theory with ``Yukawa-like'' interaction λ∫Φb+(x)Φb−(x)Φa(x)d x between nucleons (b) and mesons (a). It is a version of Nelson's model with relativistic kinematics and has been renormalized by J. P. Eckmann. The infinite mass renormalization is a power series in λ2, chosen in such a way as to confer on the renormalized Hamiltonian Ĥ the correct relativistic single particle spectrum. Physical one nucleon states are given by a modified Friedrichs one-particle expansion constructed by Eckmann. The Heisenberg picture's creation-annihilation operator for dressed nucleons and mesons are studied in detail, as a preparation for the construction of the correspondent asymptotic fields, carried through, in this paper, for the mesons fields in general and for the nucleon fields on particular states (the general case is treated in the second paper of this series). Analytic properties of the interacting fields in λ are proved and commutation relations of the asymptotic fields are established. Moreover, strong asymptotic states are constructed as well as isometric wave operators. Finally some reduction formulas for the meson-nucleon scattering are derived.
Griffiths' inequalities for Ashkin-Teller model
Authors: Lee Ching Tsung
Published: February 2004

The two Griffiths' inequalities for the correlation functions of Ising ferromagnets and two others added by Kelly and Sherman and by Sherman are extended to what we call generalized Ashkin-Teller model. In this model we consider a system of N particles; each can exist in r possible states. Let a collection of pairs of particles be represented by a graph with particles as vertices and pairs of particles as edges. The ``many-body interaction'' among a cluster of particles represented by such a graph G(A) is - JA(JA ≥ 0) when the particles in each connected component of G(A) all exist in the same state; it is 0 otherwise. For the special case with r = 2 and two-body interactions only, the Ashkin-Teller model is equivalent to Ising model. Therefore, what we present in this paper can be considered as yet another way of proving the original correlation inequalities for Ising ferromagnets with two-body interactions. We have also discovered another new inequality, namely 〈δA〉 〈δABRS〉 + 〈δAB〉 〈δARS〉 - 〈δAR〉 〈δABS〉 - 〈δAS〉 〈δABR〉 ≥ 0.
Irreversible behavior of a thermally insulated system
Authors: Fernández Julio F.
Published: February 2004

The time evolution of a system coupled to a reservoir, in such a way that no energy exchange at all takes place, is examined, considering the system plus reservoir as dynamically closed. An H-theorem is proved, more precisely, it is shown quite generally that if the system and reservoir are initially uncorrelated, then the Gibbs-Jaynes entropy at time t, S(t), obeys the relation S(t) ≥ S(0). We have previously exhibited a simple model where S(t) > S(0). Some relaxation times of S(t), for an x-y model (system) interacting (no energy exchange) with an Ising model (reservoir), are obtained approximately. The values obtained seem reasonable. It is also shown, for this particular model, that if the motion of the system, but not the reservoir, is inverted at time T, then its Gibbs-Jaynes entropy τ, later SMI (τ; T), is given by SMI(τ; T) ≃ S(T + τ), i.e., the entropy keeps evolving in time as if the motion inversion had not taken place.
Gravitation and the new improved energy-momentum tensor
Authors: Ohanian Hans C.
Published: February 2004

We give precise definitions of the weak and strong principles of equivalence and show that the new gravitational theory based on the improved energy-momentum tensor of Callan, Coleman, and Jackiw [Ann. Phys. (N.Y.) 59, 42 (1970)] satisfies both of these principles. As a consequence of the equality between the 4-momentum given by the canonical energy-momentum tensor and the ``momentum'' given by the pseudotensor that is the source of gravitation, the weak principle is also shown to hold in more general Einstein theories. Investigation of the interactions of a scalar field in the new gravitational theory shows that, besides the familiar long range interaction, there exists a new short range gravitational interaction between any scalar field and other matter.
Linear integral transformations generated by the three-dimensional neutron transport kernel
Authors: Boffi V. C. , Spiga G.
Published: February 2004

Two theorems are established by which the theory of linear integral transformations in a Lebesgue space Lp(D), p ≥ 1, can be appropriately extended to solve linear integral equations with kernel of nonfinite double norm with respect to the considered Lp(D). An application of these theorems to a physical problem of three-dimensional neutron transport theory is illustrated.
Some rigorous results for the vertex model in statistical mechanics
Authors: Brascamp H. J. , Kunz H. , Wu F. Y.
Published: February 2004

It is shown that the free and periodic boundary conditions are completely equivalent for the ice-rule (six-vertex) models in zero field. With an external direct or staggered field, we establish that in an ice-rule model the free and periodic boundary conditions are equivalent, and also equal to some special boundary conditions, either at sufficiently low temperatures or with sufficiently high fields in the appropriate direction. Regions of constant direct polarization are found. We also establish the existence of the spontaneous staggered polarization in an antiferroelectric using the Peierls argument.
An exact solution of a scalar-tensor theory of gravitation
Authors: Ihrig E. , Sen D. K.
Published: February 2004

An exact, closed-form, static spherically symmetric solution to the field equations of a scalar-tensor theory is given. This is compared with the series solution given previously. Also, an analysis is made of the geodesics of the theory.
On the improper neglect of certain terms in random function theory
Authors: Lerche I. , Parker E. N.
Published: February 2004

This paper presents some exact solutions of problems in random function theory for the purpose of testing the validity of an approximate method known variously in the many different fields of its application as first order smoothing theory, first order cumulant discard, quasilinear theory, or the adiabatic approximation. The hydromagnetic dynamo equations are used here, as particularly appropriate for such an investigation. The calculations show that in one case the exact and approximate solutions agree. In the other case the approximate solution is wrong. Hence, in the absence of a general criterion for validity, a result based on first order smoothing theory is a conjecture rather than a fact. This impacts strongly on much of the recent work on hydromagnetic dynamos.
Relation between the boson calculus and Zhelobenko's method
Authors: Lohe M. A. , Hurst C. A.
Published: February 2004

A comparison is made between the method of constructing finite-dimensional representations of the classical groups using the boson calculus in its standard or modified form and the method of Zhelobenko, which uses polynomials over a homogeneous space defined by a certain triangular subgroup. It is shown that the two methods can be directly related, so that one construction can be mapped into the other.
Spinor representations of the orthogonal groups
Authors: Lohe M. A.
Published: February 2004

It is shown how to construct all spinor representations of O(n). For the low order groups, this is done in such a way as to obtain the representation space of the covering group. More generally all representations of O(n) are constructed in spaces of harmonic homogeneous polynomials. This is achieved for the spinor representations by finding realizations of the Lie algebra of O(n) which are new. Results are written out explicitly for O(3).
Phase operators and phase relations for photon states
Authors: Volkin Howard C.
Published: February 2004

For a quantized mode of the radiation field, the operator whose classical analog is the ordinary phase factor of the mode amplitudes has been shown to be nonunitary. A mathematically rigorous formulation of the phase P is given on the basis of the canonical factorization theorem. All other phase quantities are defined in terms of P and P†. Many of the seemingly complex features of phase operators are found to be simple direct consequences of the general mathematical theory. It is easily seen that P is a partial isometry but not a unitary operator. In contrast to the amplitude operator, it is found that P is not a spectral operator and the set of phase eigenstates is not complete. Mathematically precise operator relations, including the rigorous statement of commutation rules, are developed. For each of the phase operators, a complete spectral analysis is given, with the nature of the spectrum, spectral decomposition (if any), and eigenstates shown explicitly. The values of the various phase operators are compared between phase states and coherent states.
Matrices of finite Lorentz transformations in a noncompact basis. III. Completeness relation for O(2, 1)
Authors: Mukunda N.
Published: February 2004

A parametrization of the elements of the three-dimensional Lorentz group O(2, 1), suited to the use of a noncompact O(1, 1) basis in its unitary representations, is derived and used to set up the representation matrices for the entire group. The Plancherel formula for O(2, 1) is then expressed in this basis.
The mathematical problem of reflection solved by an extension of the WKB method
Authors: Chakraborty B.
Published: February 2004

Starting with two first order linear differential equations having slowly varying coefficients and mutually connected by the dependent variables, the reflection problem is solved approximately as in the cases of electromagnetic and acoustic waves. An extension of the WKB method is developed and applied to study this problem up to any higher order of accuracy one requires. The solution of the second order differential equation in normal form by the extended WKB method is used to find the characteristics of propagation at a point of discontinuity of higher order derivative of the parameter.
Anomalous dimensions in one-dimensional quantum field theory
Authors: Parisi G. , Zirilli F.
Published: February 2004

We study the short distance behavior of the Green's functions of two operators in a soluble one-dimensional model of quantum field theory with dimensionless coupling constant. Integer power behavior does not occur. The leading terms of the Wilson expansion of two operators at short distances are determined.
Nonlinear Padé approximants for Legendre series
Authors: Fleischer J.
Published: February 2004

We introduce a new kind of Padé approximants for Legendre series based on the solution of a nonlinear system of equations. These Padé approximants have many properties in common with the well-known Padé approximants for Taylor series. In the examples studied here, the poles and zeroes of the Padé approximants lie on the cut and separate each other-a property which one expects to hold in general for Padé approximants. A proof of convergence follows the same lines as for Taylor series. Moreover, it turned out that these nonlinear approximants converge more rapidly than the linear approximants introduced in an earlier work. They may become a powerful tool in the summation of Legendre series.
New forms for the representations of the three-dimensional Lorentz group
Authors: Mukunda N. , Radhakrishnan B.
Published: February 2004

We present a uniform construction of all the principal series representations of the three-dimensional Lorentz group with generators constructed in terms of oscillator operators. In all cases, the Hilbert space and a hyperbolic generator have a simple appearance, while the other two generators give rise to nonlocal transformations involving Bessel functions.
Structure of the combinatorial generalization of hypergeometric functions for SU(n) states. II
Authors: Huang Cheng-Sheng , Wu Alfred C. T.
Published: February 2004

In the construction of the general SU(5) states, the action of each individual lowering operators (raised to a power) operating on the semimaximal state leads to an operator-valued polynomial which is shown to belong to the class of generalized hypergeometric functions in the sense of Gel'fand (namely, they are Radon transform of linear forms). Three new functions are found at the SU(5) level and their content in terms of known lower-hierarchy functions are explicitly exhibited. The structure of the general SU(n) states due to the combined action of all lowering operators is quite complicated, but the action of each individual lowering operator taken one at a time may still be manageable for higher n, and, in the spirit of boson operator formalism, this may be one systematical way of producing high-hierarchy generalized hypergeometric functions.
Nonlinear stability problems for the sine-Gordon equation
Authors: Callegari Andrew J. , Reiss Edward L.
Published: February 2004

Two stability problems for the nonlinear sine-Gordon equation are studied. The stability of a class of time independent (static) solutions is studied using linear dynamic stability theory. An asymptotic approximation of the nonlinear transient response to small disturbances of an unstable static state is obtained by the two time method. Interpretations of the results are given for the continuous pendulum problem and for the Josephson tunnel junction. A proof of the validity of the asymptotic approximation is given.
Asymptotic estimation of Fourier transforms and light cone dominance
Authors: Chen T. W.
Published: February 2004

The usual method of asymptotic estimation of Fourier transforms, the phase oscillation method, is examined. It is found that the usual argument of phase oscillation can be misleading due to either locations of singularities or absolute integrability of functions. As a by-product we have found that the scaling law for the inelastic e-p scattering should also be valid as the energy change v→∞ regardless of the momentum transferred squared κ, according to the usual approach of light cone dominance.
Introduction to nonstandard analysis
Authors: Voros A.
Published: February 2004

Nonstandard analysis is a recent branch of mathematics in which usual notions about analysis and topology can be formulated in an attractive and condensed manner. The main feature of this theory is that it introduces the concept of infinitely large or small numbers and that it allows one to compute with them in exactly the same way as in ordinary analysis. We believe that in the long run this new language might be usefully applied to physics. However, we only present a few examples of a rather trivial nature, our purpose being to give a short introduction of the subject to physicists. Thus we omit most of the technical subtleties especially those of a metamathematical nature, and we concentrate our attention on the practical side of the theory.
A variational approach to the theory of multipoint Padé approximants
Authors: Epstein Saul T. , Barnsley Michael F.
Published: February 2004

The existence and bounding properties of the various multipoint Padé approximants, and their complements, with respect to functions representable by series of Stieltjes, are established by using a generalized Hylleraas variational principle. The main discussion uses the phraseology of a typical frequency dependent polarizability function, and in an appendix the results are simply generalized.
The application of Regge symmetry to the 9-j symbol
Authors: Holman Wayne J.
Published: February 2004

The Regge transposition symmetry is applied to one of the six Wigner coefficients in the defining expression for the Wigner (9-j) symbol; couplings are then performed, and an expression for the (9-j) symbol is obtained which factorizes the sums of the angular momenta in two rows and their differences into different factors.
Convergence in the mean of solutions to the neutron integral Boltzmann equation in three-dimensional systems
Authors: Boffi V. C. , Premuda F. , Spiga G.
Published: February 2004

The Neumann series solution as well as practical solutions for the stationary integral Boltzmann equation, which governs the flux distribution of monoenergetic neutrons in a three-dimensional system made by an isotropically scattering and multiplying material, are built up by extensively using the concept of double norm and the theory of bounded linear integral transformations in a Lebesgue space Lp. The convergence in the mean as well as other basic properties of the proposed solutions are studied for the cases of both distributed and isotropic deltalike sources.
Current algebras of free systems at finite temperature
Authors: Girard André
Published: February 2004

This paper is a study of the representations of the current algebra for an infinite, free, Bose or Fermi system at finite temperature. The state of the algebra is calculated for a finite system by use of the grand canonical formalism of statistical physics, and the thermodynamic limit is used to get the representation of the infinite case. An expression of the states is given in terms of determinants of one particle operators. In a second part, the usual formulas for the occupation density, the condensation temperature for bosons, etc., are recovered. It is also found that the canonical and grand canonical formalisms are equivalent when used to study Fermi systems in the thermodynamic limit, but not so for the Bose systems. It is postulated that this has something to do with the phase transition of Bose systems. Finally, the problem of the Hamiltonian is discussed in some details. The states calculated previously are used to test a method for calculating expectation values of the Hamiltonian, given the states of the algebra; it yields the correct value for the case of the free system at finite temperature.
Motion of a charged lightlike particle in an external field
Authors: Cawley Robert G.
Published: February 2004

We investigate the behavior of a charged photon in an external field, discussing the general theory and working out some examples. The mathematical basis for the equations of motion is a Stueckelberg action principle combined with a treatment which parallels that of Jacobi's principle.
Differential equations for one-loop generalized Feynman integrals
Authors: Barucchi G. , Ponzano G.
Published: February 2004

A system of (2N−1) first-order linear homogeneous differential equations in each variable is derived for the generalized (with Speer λ parameters) Feynman integrals corresponding to the one-loop graph with N external lines. This system of differential equations is shown to belong to the class studied by Lappo-Danilevsky. A connection with the matrix representation of the monodromy group in all variables is pointed out.
On the inverse problem for a hyperbolic dispersive partial differential equation. II
Authors: Weston V. H. , Krueger R. J.
Published: February 2004

In a previous paper the inverse problem for a dispersive hyperbolic partial differential equation was shown to be reducible to a system of two coupled integral equations involving the kernels of the scattering operators. Here the uniqueness question is considered. The conditions on the scattering kernel to insure uniqueness of the solution of the system of integral equations are developed.
Conformally invariant orthogonal decomposition of symmetric tensors on Riemannian manifolds and the initial-value problem of general relativity
Authors: York James W.
Published: February 2004

It is shown that an arbitrary symmetric tensor ψab (or ψab) of any weight can be covariantly decomposed on a Riemannian manifold (M,g) into a unique sum of transverse-traceless, longitudinal, and pure trace parts. The summands involve only linear operators and are mutually orthogonal in the global scalar product on (M,g). Each summand transforms separately into itself if the decomposition is carried out properly in a conformally related space (M,g). The decomposition is therefore determined by a conformal equivalence class of Riemannian manifolds. This property makes the decomposition ideally suited to the initial-value problem of general relativity, which becomes, as a result, a well-defined system of elliptic equations. Three of the four initial-value equations are linear and determine the decomposition of a symmetric tensor. The fourth equation is quasilinear and determines the conformal factor. The decomposition applied to the space of symmetric tensors on (M,g) can be written in terms of a direct sum of orthogonal linear spaces and gives a framework for treating and classifying deformations of Riemannian manifolds pertinent to the theory of gravitation and to pure geometry.
Classification of space-times in general relativity
Authors: Adler Ronald J. , Sheffield Charles
Published: February 2004

The relationship between the Petrov classification of Riemannian space-times and the Debever-Penrose principal null directions is developed in explicit algebraic terms.
Exact nonplanar solutions of the classical relativistic three-body problem
Authors: Chern De-Ching , Havas Peter
Published: February 2004

It was shown recently by Havas that for a Newtonian system of three particles there exists a class of exact solutions which is nonplanar, such that the particles revolve with constant angular velocity in circular orbits in parallel planes. Such motions are possible for central forces which are arbitrary functions of the mutual separations, provided that the forces are repulsive between one pair of particles and attractive between the two other pairs (which for Coulomb forces corresponds to two like charges and one unlike one). In this paper, it is established that such motions are possible also for relativistic three-body systems with time-symmetric electromagnetic or mesic interactions; they reduce to the Newtonian solutions in the appropriate limit. Beyond this, there also exist exact relativistic solutions with the same orbits which have no nonrelativistic counterpart. These include solutions with all electric charges of the same sign, as well as solutions with all three particles on the same side of the axis of rotation; degenerate cases include planar and nonplanar two-particle solutions and a one-particle circular solution.
The differentiable and causal structures of space-time
Authors: Woodhouse N. M. J.
Published: February 2004

An improved version is presented of Ehlers, Schild, and Pirani's axiomatization of the differentiable and causal structures of space-time. It is shown that, under certain physically reasonable axioms, the properties of freely falling particles and light signals define a causal and differentiable structure on space-time. Further, it is shown how the causal structure define a causal and differentiable structure light signals propagate along conformal null geodesics.
Theory of elastic constants of heterogeneous media
Authors: Korringa J.
Published: February 2004

The theory of elastic equilibrium of heterogeneous, macrohomogeneous bodies is cast in the form of a linear integral equation with the following properties: (1) The equation contains a constant elastic tensor which can be chosen freely to optimize any approximation method. (2) The singularity of the kernel is such that the integral must be interpreted as the principal value, thereby providing a clear separation between structure-dependent and structure-independent contributions. (3) The mean elastic tensor equals the above-mentioned constant tensor plus the space average of the dependent variable. (4) A term proportional to this average appears separately in the equation. (5) The integral equation facilitates the rederivation of several well-known approximations and opens new possibilities, of which some are discussed, in particular, a self-consistent imbedding method and an approximation based on correlation functions.
Statistical theory of effective electrical, thermal, and magnetic properties of random heterogeneous materials. I. Perturbation expansions for the effective permittivity of cell materials
Authors: Hori Motoo
Published: February 2004

A perturbation formulation is developed for the effective permittivity of random heterogeneous materials that are statistically homogeneous but not necessarily statistically isotropic. The formal perturbation solution is expressed explicitly by means of the many-point correlation functions of the permittivity field. For a broad class of random multiphase materials called cell materials, the second- and third-order perturbation effects are determined as functions of the depolarizing factor tensors of cells. In the special case where the medium is statistically isotropic, the formulas giving the effective permittivity to third order are shown to be in substantial accord with the results obtained by previous investigators.
Green's function for Markovian systems
Authors: Thomson J. J. , Benford Gregory
Published: February 2004

Many perturbation series solutions to stochastic differential equations suffer from secularity; that is, individual terms in the series behave as some power of an independent variable, and thus diverge as that variable goes to infinity. We derive a method of renormalizing the ``free'' or ``unperturbed'' Green's function by summing a certain class of terms and including them in the Green's function. The terms included in this class correspond to Markovian interaction with the stochastic field. The remainder of the perturbation series corresponds to non-Markovian corrections. We give a diagrammatic interpretation of the individual terms in the perturbation series. We may solve, under certain assumptions, the explicit form of the Markovian Green's function. We apply this method to plasma turbulence, and show that it produces Dupree's theory of turbulence. We derive the condition for validity of the perturbation expansion, which is that particles are not ``trapped'' by the turbulent waves.
Spin zero couplings in the Veneziano model
Authors: Dobson Peter N.
Published: February 2004

The problem of the positivity of the residues in the simple Veneziano model is investigated. Previous studies of this problem have concentrated on the residues of poles lying along specific daughter trajectories, and hence needed to work only with polynomials of fixed low degree. A technique is developed here which is applied to all the spin zero daughters in the model, and which therefore deals with polynomials of arbitrarily high degree. It is found that the spin zero residues are all positive if α0 ≥ 1/2, where α0 is the intercept of the leading trajectory in the model.
Relations among elements of the density matrix. I. Definiteness inequalities
Authors: Band William , Park James L.
Published: February 2004

The statistical operator of quantum theory may be determined empirically by computations based upon the measured mean values of a set of observables we have called a quorum. The requirement that a statistical operator be positive semidefinite is then used to generate a family of inequalities connecting these quorum means. Like the simpler uncertainty relations, these inequalities are universal, valid for all quantum states. In the special case of pure states, the method yields a family of equalities.
A new expansion method in the Feynman path integral formalism: Application to a one-dimensional delta-function potential
Authors: Goovaerts M. J. , Babcenco A. , Devreese J. T.
Published: February 2004

An expansion method in the path-integral formulation of quantum mechanics, as proposed in a previous paper, is extended to account for states with odd parity. The method is tested on the case of a one-dimensional attractive delta-function potential and the well-known solutions for both bound and scattering states are obtained analytically by an exact summation of the expansion series. The applicability of the method is discussed and it is shown how the energy spectrum could be determined by means of Stieltjes theory of moments.
Lattice Green's function for the simple cubic lattice in terms of a Mellin-Barnes type integral. II
Authors: Inawashiro Sakari , Katsura Shigetoshi , Abe Yoshihiko
Published: February 2004

The series representation of the lattice Green's function for the simple cubic lattice I(a)=π−3∫oπ∫oπ∫oπD−1dxdydz, where D=a-iε-cosx-cosy-cosz, around the singularity a=1 is obtained in fractional powers of a2−1 (convergent for |a2−1|<1), by the method of analytic continuation using a Mellin-Barnes type integral and also by use of the analytic continuation of 3F2 (, , ; , ; 1) as a function of the parameter. It gives leading and full expansions near the singularity a=1.
On the Green's functions for the Bethe-Salpeter equation. II
Authors: Hormozdiari Iraj , Huang Justin C. , DeFacio Brian
Published: February 2004

Considering the Bethe-Salpeter equation as a relativistic equation, we have studied the free particle Green's functions for unequal mass scalar bosons, interacting via a translationally invariant potential. The scattering Green's function found by Huang and DeFacio (HD) is presented for all possible Ω-plane contours for the unequal masses case. Only two k-plane contours are found to be physically interesting. The causal, advanced, and retarded Green's functions are listed in an appendix for unequal masses for the physical contour. The timelike Green's functions again require severe restrictions on the interaction potential as found by HD, and possible Bethe-Salpeter bound states are briefly discussed.
Generating functional for covariant time-ordered products of currents
Authors: Shtokhamer R.
Published: February 2004

Assuming that a functional of the form F(A) = T exp(iB(A)) generates covariant time-ordered products of currents, general properties under Lorentz transformations are derived for the expansion coefficients of the functional B(A). The functional B(A) is explicitly constructed for the case of simple commutations relations between currents. The Feynman conjecture is discussed.
Identity satisfied by the d-type coefficients of SU(n)
Authors: Rashid M. A. , Saifuddin
Published: February 2004

Using a very simple approach, we obtain one identity for each SU(n), satisfied by its d-type coefficients.
Conformal group in a Poincaré basis. III. Degenerate series
Authors: Macfadyen N. W.
Published: February 2004

We construct systematically all the unitary irreducible representations of the group SU(2,2) which are realized on the two manifolds Z and Z introduced in Paper I of this series; these include all the degenerate representations at present known apart from the exceptional or ladder series. This particular realization of the global theory displays the Poincaré subgroup in a simple form, and we examine the reduction products under this group. We find that the degenerate first series contain only space-like momenta and a single spin fixed by the invariants of SU(2,2); the degenerate second series on the other hand contain only spinless representations of P, while the nature of the momenta which appear depends on the particular series concerned.
Hill's functions and the one-dimensional Schrödinger equation
Authors: Casey K. F. , Weaver L.
Published: February 2004

Over a region of finite width in which the potential varies with respect to a single Cartesian coordinate, it is possible to transform the one-dimensional Schrödinger equation into Hill's equation. It is thus possible to express the connection of the wavefunction and its normal derivative across the region exactly, in terms of the Fourier expansion coefficients of the potential profile. As a consequence, the reflection and transmission amplitudes and the bound-state energies associated with such a region may be directly calculated without actually solving an equation in the interior of the region. These results are applied to the solution of several examples, including the problem of s-wave scattering by a central potential.
Mixed basis matrix elements for the subgroup reductions of SO(2,1)
Authors: Kalnins E. G.
Published: February 2004

By using the irreducible decomposition on the two-dimensional light cone, the mixed basis matrix elements for the three subgroup reductions of SO(2,1) are calculated. These matrix elements are calculated for the principal series only and can be expressed in terms of well-known special functions. As a consequence of appearing in this context, some new properties of these special functions are given.
A linked cluster evaluation of contour integrals in statistical mechanics
Authors: Horwitz Gerald
Published: February 2004

A linked cluster expansion is obtained for the logarithm of the partition function which constitutes an asymptotic expansion in 1/N for a normal system. The result is obtained by means of a new and rather general way of asymptotically evaluating a type of integral common in statistical mechanics.
Unstable particle scattering in the LSZ formalism
Authors: Liu Tsu-huei , Zimmerman Robert L.
Published: February 2004

The properties of the unstable particles are studied by investigating the Lee model and a modified form of it. We define the unstable particle to be the complex pole of the analytically continued Green's function on the unphysical Riemann sheet. The mass and lifetime of the unstable particles are determined. Different ways of calculating the renormalization constant are discussed. The Lehmann-Symanzik-Zimmermam (LSZ) formalism is extended to include the unstable particles. Decay and scattering amplitudes for the unstable particles are calculated. The formalism is exact and does not depend on the arbitrary separation of the total Hamiltonian. Comparison with results obtained by other methods is discussed.
Relations among elements of the density matrix. II. Exotic conservation laws
Authors: Park James L. , Band William
Published: February 2004

Ordinary quantal conservation laws are associated with null operators for time rate of change and are valid for causal evolution of the system through either pure or mixed states. There is, however, a larger class of quantal constants of the motion, some of which are conserved only for pure state evolution. After an analysis of the theoretical origins of these exotic conserved quantities, several illustrations are presented with empirical interpretations based on the quorum theory methods used in Paper I.
The evaluation of lattice sums. II. Number-theoretic approach
Authors: Glasser M. L.
Published: February 2004

Number theory is used to sum several series of the form Σaijk … (ai2 + bj2 + …)−s in two and three dimensions.