bluuebunny/crossref_metadata_2025 huggingface dataset:
High-Energy Fixed-Angle Potential Scattering
Authors: Johnson Porter
Published: February 2004

We continue the study of the asymptotic behavior of the scattering amplitude f(k, θ) at high-momenta k for fixed (nonforward) scattering angles θ. The considerations here are limited to the class of potentials for which the momentum-space representations V(q) decrease less rapidly than some inverse power of q as q → ∞ through positive real values. We place some additional relatively simple conditions upon V(q) for q > 0 which are sufficient to guarantee that the asymptotic limit of f for large k with fixed θ is, in fact, the first Born approximation f1(k, θ).
Almost Symmetric Spaces and Gravitational Radiation
Authors: Matzner Richard A.
Published: February 2004

A generalization of the idea of Killing fields to spaces which are not symmetric is given. The field so defined specifies coordinate lines along which the variation of the metric tensor is the slowest possible in a global sense. Thus it generalizes the Killing fields in spaces with a symmetry where the metric tensor does not change along Killing trajectories. Several examples are given, and the method is then applied to spaces containing gravitational radiation of the type considered by Issacson.

For spaces containing radiation, it is shown that a real functional λ[ξ], associated with every vector field ξ, measures some parameters associated with the radiation. In the simplest case this parameter is the ``energy density'' of the radiation, but, if a sufficient number of vector fields can be invariantly defined in the background, the average gravitational ``stress'' associated with the wave may also be measured. We conclude with some conjectures about further application of these ideas to the theory of gravitational radiation.
Exact Occupation Kinetics for One-Dimensional Arrays of Dumbbells
Authors: McQuistan R. B. , Lichtman D.
Published: February 2004

By utilizing a branch-dependent counting technique, exact relationships are developed which describe the ensemble average of the kinetics of occupation by dumbbells of finite one-dimensional arrays of compartments. It is shown that, as the number of compartments per array tends to infinity, 〈θ(t)〉, the ensemble average of the fraction of an array which is occupied, is given by 〈θ(t)〉=1−exp{−2[1−exp(−vt)]},where v is the striking frequency and t is time. By contrasting these results with the statistics of one-dimensional arrays of dumbbells, it is demonstrated that it is inappropriate to employ classical statistical-mechanical methods (e.g., the Bethe approximation) to treat the kinetic aspects of occupation where configurational correlation exists. (Here we define configurational correlation to be the situation in which the occupation of a compartment precludes the occupation of one of its nearest neighbors.)
Crossing and Unitarity in a Multichannel Static Model. I
Authors: Ehrhardt P. O. G. , Fairlie D. B.
Published: February 2004

The infinite multichannel-scattering process of the two-particle scattering of mesons of arbitrary isospin off an isospin-½ target, inelastic two-particle channels being admitted, is considered in the static limit. The restrictions on the S matrix arising from crossing under SU(2) and two-particle unitarity are expressed in terms of three equations alone in the limit of degenerate meson masses. These equations are solved by a perturbative technique, the expansion parameter being a measure of the strength of the inelastic scattering. The principal result of this paper is that the inelastic amplitudes are all related, so that if one is zero all must be zero. Comparisons are made with strong-coupling theory, which also requires an infinite number of channels.
Poincaré Group and the Invariant Relativistic Equations for Massive Particles of Any Spin
Authors: de Azcárraga José A. , Boya Luis J.
Published: February 2004

The aim of this paper is to clarify some aspects of the connection between the Poincaré group and the invariant equations for nonzero-mass particles of any spin (Bargmann-Wigner equations). With this purpose we first make some general considerations about the representations of the Poincaré group and analyze the equivalence between the realizations corresponding to a given class and a selected ``canonical'' one which was given by Wigner. For the spin-½ case the equivalence is given by the Chakrabarti transformation, and for higher spins we introduce a generalization of it; we also consider specifically the case S = 1. We give the form of the equations which provide the corresponding canonical realization; some comments about the equivalence of the theories provided by the different realizations are also made.
Retarded and Advanced Electromagnetic Fields in Friedmann Universes
Authors: Katz Amnon
Published: February 2004

Maxwell's equations of classical electrodynamics are solved in the framework of the curved space-time of the Friedmann universes. Explicit formulas are given for the retarded and advanced fields in terms of the four-current.
Modified Admittance, Perpendicular Susceptibilities, and Transformation of Correlations of the Ising Model
Authors: Kim Shoon Kyung
Published: February 2004

A modified admittance is introduced to give Kubo's admittance at nonzero frequencies and to give the isothermal static admittance at zero frequency within the scope of the Kubo linear-response theory. The method is demonstrated by exact calculations of the frequency-dependent perpendicular susceptibility at zero field and its modified susceptibility of the regular Ising model. The results appear as linear combinations of the equilibrium spin-spin correlation functions of the lattice. The results are valid for all dimensions and all frequencies and temperatures. A (q + 1) × (q + 1) matrix a(q) describes the linear combinations explicitly, where q is the coordination number of the lattice. The properties of this matrix are extensively discussed as a special case of a matrix A(q)(ξ), which satisfies a simple quadratic equation of the form [A(q)(ξ)]2 = (1 + ξ)q for arbitrary values of ξ. Fisher's algebraic transformation of the spin-spin correlation functions for the regular Ising lattice is derived from the linear relation which holds between the perpendicular susceptibility and the corresponding modified susceptibility. By means of the product rules of the matrix A(q)(ξ), the higher-order spin-spin correlation functions are expressed in terms of the lower-order ones in complete generality.
Local Operator Algebras in the Presence of Superselection Rules
Authors: Federbush Paul
Published: February 2004

An introductory study is made of the relation between the local algebra of observables associated to a region of space-time and the algebra of all operators (disregarding superselection rules) associated to the same region of space-time. With a reasonable axiomatization of the problem and assuming the local algebra of observables is a factor of type I, II∞, or III, the relation between the two algebras is specified up to unitary equivalence in terms of algebraic invariants.
Algorithm for Reducing Contracted Products of γ Matrices
Authors: Kahane Joseph
Published: February 2004

A construction algorithm is given which allows any partially contracted product of γ matrices to be reduced in one line to a simple canonical form involving only the uncontracted indices.
New Solutions of the Einstein-Maxwell Equations from Old
Authors: Harrison B. Kent
Published: February 2004

Methods are discussed with which one may derive theorems which allow one to generate new solutions of the Einstein-Maxwell equations from old ones. The old solutions used to generate new ones must admit at least one nonnull Killing vector and may be required to satisfy other conditions, depending on the theorem derived. Examples of derivable theorems are shown; these theorems are used in turn to show how generation of new solutions is accomplished. Examples of the latter are shown, such as generation of Brill or electrified NUT space from the Schwarzschild solution, generation of a new twisted Melvin universe from flat space, and generation of a new generalization of the Ozsvath-Schücking metric. Possible physical interpretations, uses, and extensions of this type of theorem are discussed.
Solution of the Equations of Radiative Transfer in a Free-Electron Atmosphere
Authors: Bowden Robert L. , Richardson Norman R.
Published: February 2004

The radiative-transfer equations are solved for an electron-scattering stellar atmosphere as formulated by Chandrasekhar. The solution employs a transformation of the integro-differential form of the transfer equations into singular integral equations for the angular intensities of the radiation field. The Milne problem is solved to illustrate the method. In addition, the relationship is found between the above method of solution and Case's normal-mode expansion method. This leads to an alternate procedure for finding the normal-mode expansion coefficients. As an example of the method, the constant distributed source problem is solved for a half-space medium.
Relativistic Stochastic Processes
Authors: Hakim Rémi
Published: February 2004

Relativistic stochastic processes in μ-space are defined and studied in a completely (and manifestly) covariant manner, without particularizing the time variable. It is shown that a number of usual definitions such as ``Gaussian process,'' etc., cannot be given a fully invariant meaning. Markovian processes are also studied. We find anew, as a particular case, results already obtained by Łopuszaǹski [Acta Phys., Polon. 12, 87 (1953)] in the case of Markovian processes in Minkowski space-time. Several suggestions are made to generalize these results.
Kinematic Singularities of Helicity and Transversity Amplitudes and Asymptotic Regge-Pole Contributions
Authors: McKerrell A.
Published: February 2004

The crossing relation for transversity amplitudes is used in a simple proof of the kinematic-singularity structure of helicity amplitudes, both in the general-mass and in various particular-mass cases. A comparison with earlier results is made. The kinematic properties of helicity and transversity amplitudes are employed in the derivation of an asymptotic expression for the contribution of Regge poles to the amplitude.
Spin-Orbit Interactions of the Configuration l
n−1l′l″
Authors: Roth Charles
Published: February 2004

Matrix elements for the spin-orbit interactions of the configuration ln−1l′l″ in L-S coupling are expressed as linear combinations of radial integrals.
Narrow Resonance Saturation of Sum Rules: A Nonuniqueness Theorem
Authors: Atkinson D.
Published: February 2004

It is shown that, if the superconvergence relations appertaining to a two-particle scattering process are saturated by an infinite tower of resonances of mass mJ, where J is the spin, then mJ must increase less quickly than J in all cases. With this observation, it is shown that the complex of all the superconvergence relations for all the processes a(J1) + a(J2) → a(J3) + a(J4), where a(J) is the spin-J member of the same tower of particles, possesses an infinity of solutions for the coupling constants. It is concluded that the superconvergence relations are incomplete, and need to be supplemented by some new physical principle, if they are to be of any practical use. A possible exception to this rule is when all but a finite number of residues are constrained to be positive, with no negative coefficient from the isospin crossing matrices. In this case, a given solution may be unique if mJ increases not more quickly than J½.
One- and Two-Dimensional Green's Functions for Electromagnetic Waves in Moving Simple Media
Authors: Compton R. T.
Published: February 2004

This paper considers the one- and two-dimensional Green's functions associated with electromagnetic radiation in a moving medium. The medium is assumed to be lossless, to have constant permittivity and permeability, and to move with constant velocity with respect to a given inertial coordinate system. For each source (line source or plane source) both the time-dependent and the harmonic Green's functions are found. The results are obtained by means of special transformations which convert the equations to be solved into standard forms. The significance of the results, in terms of one- and two-dimensional Cerenkov radiation, is discussed.
Diffusion Length and Criticality Problems in Two- and Three-Dimensional, One-Speed Neutron Transport Theory. II. Circular Cylindrical Coordinates
Authors: Williams M. M. R.
Published: February 2004

An integral equation is derived which describes the diffusion of neutrons from a plane source perpendicular to the axis of an infinite circular cylinder. The equation is solved by a Fourier transform in the axial direction and by the subsequent solution of a singular integral equation for the radial distribution; this is accomplished as a result of a certain replication property possessed by the original integral equation. We have inverted the Fourier transform to obtain the simultaneous r − z variation of the neutron density in the cylinder. In addition, a formula is given from which the angular distribution of neutrons may be obtained. By approximating the density along the axis of the prism with the asymptotic distribution, it has been possible to assess the effect of axial leakage on the cylindrical critical problem. A critical equation is derived and the appropriate extrapolated endpoints to be used in this are defined.
Strong-Coupling Limit in Potential Theory. II
Authors: Frank William M.
Published: February 2004

The analytic properties of the Jost function in the coupling constant g, derived in an earlier article for a restricted class of potentials, are rederived generally for potentials V(r), for which |V(r)| can be bounded by a monotonically decreasing potential V̄(r), such that ∫dr|V̄(r)|12<∞. In particular, potentials with nonlinear exponential tails are studied as a function of the energy and coupling constant. Earlier results of Sartori on the energy dependence of the Jost function, derived only for special cases of such potentials in the Born approximation, are demonstrated to be true generally for large classes of such potentials.
Microscopic Approach to Kinetic Theory: Inhomogeneous Systems
Authors: Chappell Willard R.
Published: February 2004

The microscopic linearized Vlasov equation is solved in terms of a generalized inverse dielectric function ε−1(r, r′; t, t′) and the initial phase-space density fluctuation. This expression is then used to calculate the density autocorrelation function and to obtain a generalized kinetic equation for plasmas and gravitational gases. It is shown that many of the results for the inhomogeneous system have a close similarity to the corresponding results for homogeneous systems. In particular, the test-particle theory is exhibited and an expression is obtained for the phase-space density of the polarization cloud associated with a test particle.
Galilean Tensor Calculus
Authors: Pinski G.
Published: February 2004

Galilean transformations are expressed as transformations in a five-dimensional space, with a subsidiary condition, and a Galilean tensor calculus with a nonsingular metric is developed. It is shown that the homogeneous Galilei group is isomorphic to a subgroup of the pseudo-orthogonal group O(4, 1), which leaves the difference of two components of a vector invariant. A set of scalar variables for a Galilean-invariant S matrix is selected. A Galilean-invariant phase space is defined and a recursion relation derived.
Inverse Wave Propagator
Authors: Lalor Éamon
Published: February 2004

In a recent publication, Wolf and Shewell gave a formal solution to the inverse diffraction problem, i.e., to finding the field distribution in the plane z = 0 from the knowledge of the field in an arbitrary plane z = z1 > 0 in the half-space into which the field is propagated. The solution involved the use of a singular kernel. In the present paper the inverse diffraction problem is treated in a rigorous manner. Our method makes use of the representation of the field as an angular spectrum of plane waves and demonstrates the usefulness of this type of representation. It is shown that by the use of a suitable truncation procedure one may avoid the use of a singular kernel or the generalized function theory.
Response of a Many-Particle System to Quasistatic Changes in Volume
Authors: Gillis N. S.
Published: February 2004

A study is made of the linear dissipative processes associated with viscous flow in a many-particle system. Central to this study is a direct examination of the linear-response properties of the system when it is influenced by a dynamical perturbation which induces a time-dependent change in the size and shape of the containing volume of the system. By examining the linear response of the pressure-tensor operator to such a perturbation, we derive correlation-function expressions for the coefficients of viscosity η and ζ and for the shear and bulk moduli G0 and K0. Essential to this discussion is the careful examination of the behavior of certain spectral functions at finite volume. It is found that in order to carry through the analysis in a consistent fashion, one must require that these spectral functions exhibit a special singular behavior. In particular, it is found that the static moduli G0 and K0 are related to the singular parts of the relevant spectral functions, whereas the viscosity coefficients are related to the nonsingular parts of these same spectral functions. The expressions obtained are compared with the familiar Kubo-Mori expressions for the coefficients of viscosity η and ζ.
Transmission and Reflection of Electromagnetic Waves at the Boundary of a Relativistic Collisionless Plasma
Authors: Özizmir Ercüment
Published: February 2004

The exact solution of the transmission and reflection problem for transverse electromagnetic waves incident on a bounded plasma has been discussed to some extent by several authors. Shure considered the special cases of perpendicular incidence on nonrelativistic half-space and slab plasmas and made use of van Kampen-Case modes to construct the solution. For both half-space and slab plasmas, we generalize his results to (i) arbitrary temperatures (relativistic) and (ii) arbitrary angles of incidence. For simplicity, we consider the special case where the incident electric field is perpendicular to the plane of incidence and assume that particles are reflected specularly at the interface. We proceed somewhat differently from Shure, and use a Laplace transformation in obtaining our solution. We also show that present solutions can be expressed as a superposition of van Kampen-Case modes appropriate to a relativistic plasma.
Proof of the Fermion Superselection Rule without the Assumption of Time-Reversal Invariance
Authors: Hegerfeldt G. C. , Kraus K. , Wigner E. P.
Published: February 2004

The superselection rule which separates states with integer angular momentum from those with half-integer angular momentum is proved using only rotational invariance.
Nonlinear Boundary-Value Problems in One- and Two-Dimensional Composite Domains
Authors: Canosa José
Published: February 2004

Some nonlinear boundary-value problems in one- and two-dimensional composite domains have been solved by a general eigenfunction-expansion method. The advantage of the method is that separable problems in more than one dimension can be solved almost as easily as one-dimensional problems. An optimum eigenfunction-expansion basis has been found that leads to accurate solutions with only a few terms in the expansion.
Variational Solutions of Nonlinear Poisson-Boltzmann Boundary-Value Problems
Authors: Anderson N. , Arthurs A. M.
Published: February 2004

Variational solutions of one-dimensional nonlinear Poisson-Boltzmann boundary-value problems in the theory of colloids and plasmas are obtained. The accuracy of the solutions is measured in terms of upper and lower bounds for the field energy which result from complementary variational principles.
Determination of the Amplitude from the Differential Cross Section by Unitarity
Authors: Newton Roger G.
Published: February 2004

Banach-space fixed-point theorems are used to prove two results: (a) If the differential scattering cross section is smooth and small enough, relative to the wavelength of the relative motion of the colliding particles, there always exists an amplitude function which satisfies elastic unitarity and whose squared modulus equals a given differential cross section. (b) Under somewhat stronger conditions this amplitude is uniquely determined (except for the sign of its real part) by the generalized optical theorem (unitarity) and it can be constructed by iterating the latter. The condition for (a) ensures a priori that the real part of the amplitude cannot vanish at any angle, and that for (b) implies that its real part cannot be smaller than twice its imaginary part. These results are then generalized to inelastic and production processes.
Interpretation of Γ[jk]i in a Huygens Model
Authors: Muraskin Murray
Published: February 2004

We describe a classical field theory based on Huygens' principle which is characterized by an additional degree of freedom which, to our knowledge, has not been discussed previously. This additional degree of freedom asserts that the forward propagation cone is different from the backward cone. The purpose of this paper is to find a function which describes this degree of freedom, and next, to understand this effect in reference to other theories. We find that this additional degree of freedom can be described by means of Γ[jk]i. The object Γ[jk]i is then related to the torsion of a preferred-frame geometric theory. The additional degree of freedom is of interest since it enables one to introduce Γ[jk]i in a framework involving characteristic equations, described by gij, and bicharacteristics described by Γ(jk)i, such that the role of Γ[jk]i can be understood. Also, the theory furnishes a generalized framework for gravitational theory. Paths with noncontinuous slopes appear also in Feynman's path-integral approach. Thus, this type of discontinuity has physical interest here also, although we do not pursue this point in this paper.
Asymptotic Fields in Some Models of Quantum Field Theory. I
Authors: Ho/egh-Krohn Raphael
Published: February 2004

A quantum field with nonlocal interaction is considered. We prove under a proper smoothness condition on the interaction that the asymptotic limits of the annihilation-creation operators exist. The asymptotic limits are then used to prove that the state space decomposes as a tensor product of an incoming (outgoing) Fock space and a zero-particle space.
Green's Functions for Electromagnetic Waves in Moving Lossy Media
Authors: Chen K. C. , Yen J. L.
Published: February 2004

The equations governing the potentials for electromagnetic waves in moving lossy media are obtained by using a covariant formulation. A versatile form of the time-dependent Green's function is derived by first transforming the wave equation to the normal form and then applying the Fourier-integral technique. The time-harmonic Green's function is also obtained.
Class of Representations of the IU(n) and IO(n) Algebras and Respective Deformations to U(n, 1), O(n, 1)
Authors: Chakrabarti A.
Published: February 2004

We define directly the matrix elements of the generators of the algebra of U(n) × I2n on a chosen basis. This construction, though naturally infinite-dimensional, has a very close formal resemblance (interpretable, if so desired, in terms of a suitably defined ``contraction'' procedure) to the Gel'fand-Zetlin (GZ) representation for U(n + 1). The representations we obtain are characterized by (n - 1) integers and one continuous parameter. We then exploit the formal analogy with the GZ pattern in order to prove the necessary commutation relations and to derive the explicit expressions for some invariants. However, direct alternative methods are indicated where they are useful. Our representation is easily enlarged to that of (U(n)⊗U(1))×I2n, which we use, together with a deformation formula to obtain a class of representations of the U(n, 1) algebra. The irreducible components are characterized by (n - 1) integers and two continuous parameters. We compare our deformation formula with that of Rosen and Roman. We indicate briefly the typical difficulties that arise for the case IU(p,q) (q ≥ 1). Parallel constructions, finally, are given for the IO(n) and O(n, 1) algebras
First-Order Phase Transitions in Quantum-Coulomb Plasmas
Authors: Carmi Gideon
Published: February 2004

A simplified model is suggested for the understanding (in principle) of the mechanism of a phase transition in a Coulomb system on a uniform neutralizing background. Quantum theory is taken into account only in so far as it provides discrete collective energy levels and, possibly, fermion statistics for the calculation of the collective modes. Other features stemming from the uncertainty relations are supposed to be irrelevant to the mechanism of the phase transition. (This is qualitatively justified in the text which goes with Fig. 1.) This procedure provides an ``effective quantum Hamiltonian'' Hqu, which incorporates the relevant quantum features and from which one can calculate the (approximate) quantum partition function using classical methods: zapproxQu=1N!hN∫⋯∫ exp (−βHqu)d3x1⋯d3pN. In the evaluation of this integral we use the same approximation in which the plasma modes are collective, viz., the RPA (random phase approximation). Because of the freezing-out of the collective degrees of freedom at the relevant temperatures, and because the number of these degrees of freedom changes with temperature and density, Hqu describes a system with variable degrees of freedom, which seems to provide the mechanism for the phase transition. Preliminary numerical evaluations indicate a phase transition at T = 0 for an electron plasma at rs = 7.6, i.e., just below the region of metallic densities. This is shown by finding a concave region in the free energy as a function of the density. The ground is then prepared for numerical evaluation of the transition at T ≠ 0. For white dwarfs we find a transition temperature of 107 ∼ K°.
Matrix Elements in Systems with Nonunitary Symmetry
Authors: Aviran A. , Zak J.
Published: February 2004

The Eckart-Wigner theorem is generalized to include nonunitary groups. The proof is based on the connection between corepresentations of a nonunitary group and the representations of its unitary part. All possible cases of the corepresentations have been considered, and general expressions for matrix elements of operators with given symmetry have been obtained. It has been shown that the antiunitary symmetry leads, in general, to additional connections between different matrix elements.
Hyperbolic Differential Equations in Two Dimensions
Authors: Kundt W. , Newman E. T.
Published: February 2004

We analyze the general two-dimensional hyperbolic differential equation of second order by means of a substitution method. Our main interest lies in the support of the solutions, i.e., in an answer to the question: under what circumstances can a signal be transmitted along null rays? It turns out that, in general, a signal spreads, i.e., fills the entire future of an event. However, reasonably large classes of differential equations do permit nonspreading (characteristic propagation) solutions. As examples it is shown that multipole solutions of the flat space-time scalar wave equation and Maxwell equations fall into the non-spreading class, whereas multipole solutions of the corresponding equations in a curved Schwarzschild background always show spreading (or continuous reflection).
Theory of the Small-Angle X-Ray Scattering from Randomly Oriented Plane Laminas
Authors: Wu Hsin-i , Schmidt Paul W.
Published: February 2004

In a calculation of the intensity of small-angle x-ray scattering from dilute suspensions of noninteracting randomly oriented particles with uniform electron density, the effect of the particle shape can often be conveniently described by a function G(M) called the intersect distribution. An intersect is defined to be a line which has both ends on the boundary of the particle and which passes through a given point in the particle. For an intersect with length M, the intersect distribution G(M) is the probability-density function, averaged over all allowed orientations of the intersect and over all points of the particle through which an intersect with length M can be drawn. Then G(M) dM represents the probability that an intersect has a length between the values M and M + dM. Since the calculation of G(M) for a three-dimensional particle appeared too complicated for the first part of an investigation of the properties of G(M), the intersect distribution has been studied for the simpler case of a randomly oriented plane lamina with a smooth convex boundary. Emphasis has been given to a determination of the properties of G(M) which affect the intensity of small-angle x-ray scattering in the outer part of the scattering curve. In this angular region the intensity is determined by the behavior of G(M) at small M and in the neighborhood of M values at which G(M) or its derivatives are discontinuous. An approximate expression for G(M) for small M has been obtained. Discontinuities of G(M) are found to be associated with some special values of the function M(t1, t2), which gives the length M of the intersect as a function of the two boundary points at which the ends of the intersect are located, with the end points being specified by the arc length ti along the boundary from a fixed reference point to the end point i. When M(t1, t2) has a maximum, a saddle point, or a double point, G(M) has been found to be discontinuous. [The function M(t1, t2) can have no minima.] For a maximum of M(t1, t2), G(M) has a finite discontinuity, while the discontinuity is logarithmic for a saddle point. For two types of double points which have been studied, G(M) has discontinuities proportional to |D − M|−⅙ and |D − M|−¼, where D is the value of M at which M(t1, t2) has the double point. For a plane lamina, the approximate expression for G(M) shows that the form of G(M) for small M has no effect on the outer parts of the scattered intensity curve. [For three-dimensional particles, the small-M behavior of G(M) does affect this part of the scattering curve.] The effect of the discontinuities in G(M) on the outer portion of the scattering curve has been calculated. An expression is developed for G(M) and the scattered intensity for an elliptical lamina, and the results of this calculation verify the properties of G(M) for a plane lamina with an arbitrary smooth convex boundary.
Transmission Properties of an Isotopically Disordered One-Dimensional Harmonic Crystal
Authors: Rubin Robert J.
Published: February 2004

The amplitude SN(ω) of a wave of frequency ω which is transmitted by a disordered array of N isotopic defects in a one-dimensional crystal has been investigated in the limit in which N → ∞ while the over-all concentration of the defects in the array remains fixed. The transmitted amplitude SN(ω) is proportional to the reciprocal of the magnitude of an Nth-order determinant whose elements depend explicitly upon the spacings between defects, the incident frequency ω, and the relative mass difference Q = (M − m)/m between the defect particles and the particles of the host crystal. SN(ω) is represented as exp [−NαN(ω, Q, C)], where C is the over-all fractional concentration of defects; two types of estimates of αN(ω, Q, C) are obtained. First, assuming that the spacings between nearest-neighbor pairs of defects are independent random variables, upper and lower bounds are obtained on αN(ω, Q, C) which are independent of N. Provided that C is sufficiently small, the lower bound is positive. Second, Monte Carlo estimates of αN(ω, Q, C) are obtained in the cases Q = 1, C = 0.1 and Q = 1, C = 0.5, for arrays of 3 × 104 defects. These Monte Carlo estimates are compared with the previously obtained bounds. It is also shown that at the special frequencies of Matsuda and for Q ≥ Qcrit, the limiting value of αN(ω, Q, C) is positive in the entire concentration range 0 < C < 1. Explicit upper and lower bounds are obtained on α(sin (π/4), 1, C).
Electro-Optical Effects. III
Authors: Carroll M. M. , Rivlin R. S.
Published: February 2004

The theory of electro-optical effects developed in previous papers is applied to the study of the reflection-refraction of an electromagnetic wave at the interface between two isotropic centrosymmetric materials to which a static electric field is applied. The theory is developed initially for an arbitrary angle of incidence and arbitrary direction of the static field. Detailed implications are obtained in the case when the static field is normal to the interface and when it is parallel to the interface and in the plane formed by the normal to the interface and the direction of propagation.
Representations and Classes in Groups of Finite Order
Authors: Gamba A.
Published: February 2004

There are two main results in this paper. First, it is shown that we can develop a theory of classes in close analogy to the usual theory of representations. We can introduce concepts, such as reducible and irreducible classes, sum and product of classes, reduction of a class when going from a group to a subgroup, etc. Second, it is shown that it is possible to associate a ``magic square'' to each group. It is related to the numbers of pairs of commuting elements between classes and it can be used immediately to find the structure of the ``tensor operators'' of the group.
Note on the WKB Method
Authors: Nesbet R. K.
Published: February 2004

In the phase integral WKB method, a solution u1(z) of a second-order linear differential equation is represented in terms of its logarithmic derivative iy(z) which satisfies a simple nonlinear first-order equation. This representation does not in general lead directly to an independent second solution of the original equation. However, if y(z) is expressed in the form q(z) + iq′(z)/2q(z), where q(z) satisfies a nonlinear second-order equation, then q(z) can be used to determine a second solution to the original equation. These two solutions remain linearly independent throughout their domain of definition. It is shown that q(z) is given by the sum of alternate terms in the well-known asymptotic expansion of y(z). Any two linearly independent solutions of the original equation, normalized so that the Wronskian is −2i, give q(z) in the form (u1u2)−1.
Particle Motion and Interaction in Nonlinear Field Theories
Authors: Derrick G. H. , Kay-Kong Wan
Published: February 2004

A variational method is given for determining the motion and interaction of particles associated with fields governed by nonlinear differential equations. For field equations derived from Lagrangian densities of the type gικ(∂θ/∂xι) (∂θ/∂xκ) + f(θ), one obtains an attractive inverse-square law of force between like particles, provided f(θ) vanishes more rapidly than (constant) θ4 for θ → 0.
Infinite-Spin Ising Model in One Dimension
Authors: Thompson Colin J.
Published: February 2004

The partition function z, the pair correlation function ρ, and the zero-field susceptibility χ for the one-dimensional Ising model with infinite spin, are expressed in terms of the eigenvalues and eigenfunctions of an integral equation. The eigenfunctions of the integral equation are shown to be the oblate spheroidal wavefunctions, and, from known asymptotic expansions, high- and low-temperature expansions are given for z, ρ, and χ. It is shown that the low-temperature behavior of z, ρ, and χ differs qualitatively from the corresponding behavior for all finite spin.
High-Energy Scattering for Yukawa Potentials
Authors: Müller H. J. W. , Schilcher K.
Published: February 2004

A reexamination is made of nonrelativistic scattering by a superposition of Yukawa potentials in the frame of a high-energy perturbation method developed previously by one of the authors. It is found that for Yukawa potentials expandable in ascending powers of r, the S matrix may be written in a remarkably simple form. A high-energy asymptotic expansion is obtained for the phase shift. The residue function at the Regge poles is found to have the same general form as for a Coulomb potential and is formally independent of any high-energy approximation.
Analytic Functionals in Quantum Field Theory and the Regularization of Ultraviolet Divergences
Authors: Thiess Frank B.
Published: February 2004

The commutator and propagator distributions associated with free-particle fields are represented as boundary values of analytic kernels in complex space-time. A distribution product of such quantities is then defined as a boundary value of the product of the analytic kernels of its various factors, with the proviso that the product kernel be understood in the sense of Hadamard's ``finite part'' in those cases when it would otherwise be nonintegrable. For the case of quantum electrodynamics, the momentum-space representation of the products of causal propagators are derived. It is demonstrated by explicit calculation that the second-order scattering matrix elements thus obtained are identical to those usually obtained by means of Pauli-Villars regularization and renormalization.
Coherent Soft-Photon States and Infrared Divergences. I. Classical Currents
Authors: Kibble T. W. B.
Published: February 2004

As a first step toward a treatment of soft-photon processes which is free of infrared divergences and avoids the necessity of introducing a fictitious photon mass, the specification of asymptotic photon states belonging to non-Fock representations is discussed. As in the work of Chung, a basis consisting of generalized coherent states is used, but in contrast to his work, these states are rigorously defined in terms of von Neumann's infinite tensor product. It is shown that the states must be given an additional label which serves to distinguish various ``weakly equivalent'' vectors, and which corresponds formally to an infinite phase factor. A nonseparable Hilbert space HIR is defined (as a subspace of the infinite tensor-product space) which may be regarded as the space of all possible asymptotic photon states. The interaction of the electromagnetic field with a prescribed classical current distribution is discussed, and it is shown that a unitary S operator, all of whose matrix elements are finite, may be defined on HIR.
Evolution of the Probability Distributions and of the Correlation Functions in a Bogoliubov Plasma
Authors: Kritz Arnold H. , Radin S. , Sandri G.
Published: February 2004

Recently we developed a matrix formulation of nonequilibrium statistical mechanics which we applied to dilute gases (nr03≪1) and to small momentum transfer interactions (φ0/kT ≪ 1). We now show that the matrix formulation of the nonequilibrium equations can be extended to the Bogoliubov gas (φ0/kT=1/nr03≪1). The asymptotic behavior is calculated for times long compared with the plasma frequency for: (i) the probability distribution functions, and (ii) the Mayer correlation functions. The collision integrals that determine the higher-order kinetic equations for the Bogoliubov gas are thereby constructed. The calculations performed directly with the nonlinearly coupled Mayer functions are shown to be equivalent to those performed with the linearly coupled probability distribution functions. In lowest order our theory coincides with a result obtained previously by Bogoliubov.
Another Interpretation of the Optical Scalars
Authors: Kantowski R.
Published: February 2004

In this paper an interpretation of the optical scalars θ and σ (the expansion and shear of an irrotational null congruence) is given in terms of the principal curvatures of a two-dimensional subspace of the instantaneous rest frame of an arbitrary observer. The two space is defined as the intersection of the observer's rest frame and the particular null hypersurface the observer is intersecting.
Minimum Uncertainty Product, Number-Phase Uncertainty Product, and Coherent States
Authors: Jackiw Roman
Published: February 2004

The number-phase uncertainty products proposed by Carruthers and Nieto are studied to determine whether they are minimized by coherent states. It is found that coherent states do not minimize these products. States that do minimize some of the uncertainty products are constructed. Variational techniques for the study of arbitrary uncertainty products are developed.
Transmission of Electromagnetic Waves through a Conducting Slab. I. The Two-Sided Wiener-Hopf Solution
Authors: Baraff G. A.
Published: February 2004

This is the first of a series of papers dealing with propagation of electromagnetic waves through a metallic slab of finite thickness. In this first paper, we present a method for solving the integrodifferential equation governing the electric field in the interior of the metal when the electrons in the interior of the metal suffer diffuse reflection at each surface. The method is potentially of use in a wide class of problems, namely, the finite-slab generalization of all those semi-infinite-medium problems which are conventionally studied by the Wiener-Hopf technique. The solution given here is an iterative one with successive terms converging as e−L/l, where L is the thickness of the slab and l is the range of the kernel of the integral term in the equation.
Relationships among the Wigner 9j Symbols
Authors: Jang S.
Published: February 2004

Several identities satisfied by the 9j symbols or by the product of 6j and 9j symbols are derived by means of the symmetry properties of the Möbius strip type 15j symbol; in particular, the identity {adgbehcfi}{ajmbknclp}=  ∑ xyz (2x+1)(2y+1)(2z+1){adgxjm}{behykn}{cfizlp}{xdmyenzfp}{xjgykhzli}. The resulting recursion relations for the 9j symbols are also considered.
Structure of the Dirac Bracket in Classical Mechanics
Authors: Mukunda N. , Sudarshan E. C. G.
Published: February 2004

We discuss the structure of the Dirac bracket in classical mechanics. We consider a generalization of the usual Poisson bracket and show the close connection of this generalization to the Lagrange brackets of classical mechanics. We show how the Dirac bracket appears as a particular case of the generalized Poisson bracket, thus giving a simple reason why the Jacobi identity holds for the Dirac bracket. We also discuss the nature of the transformations generated via the Dirac bracket and the relation of these to canonical transformations.
Unitary Representations of the Lorentz Groups: Reduction of the Supplementary Series under a Noncompact Subgroup
Authors: Mukunda N.
Published: February 2004

Unitary representations of O(2, 1) belonging to the exceptional class are reduced with respect to the noncompact subgroup O(1, 1). We recover the result that the spectrum of the generator of this subgroup covers the real line twice. Unitary representations of O(3, 1) belonging to the supplementary series are reduced with respect to the noncompact subgroup O(2, 1). These representations of O(3, 1) may be labeled by a parameter ρ in the range 0 < ρ < 1. Representations corresponding to 0 < ρ ≤ ½ yield upon reduction only those representations of O(2, 1) that belong to the continuous nonexceptional class; each of these appears twice. A representation corresponding to ½ < ρ < 1, however, yields upon reduction a single representation of O(2, 1) of the exceptational class (with parameter σ = ρ − ½) and, in addition, all the representations of O(2, 1) of the nonexceptional continuous class. The exceptional representation appears only once, while the nonexceptional ones appear twice each.
Numerical Solution of a Singular Integral Equation Encountered in Polymer Physics
Authors: Schlitt D. W.
Published: February 2004

A numerical method for the solution of an integral equation of the type encountered in the Kirkwood-Riseman theory of intrinsic viscosities of flexible macromolecules is investigated. The absolute accuracy and rate of convergence of the method are evaluated for a special case and the results of this method are compared with another recently proposed method of solution.
Scattering of Scalar Waves by a Convex Transparent Object with Statistical Surface Irregularities
Authors: Chen Yung Ming
Published: February 2004

The scattering of time-harmonic spherical scalar waves by a large, convex, transparent, dense, and three-dimensional object with statistically corrugated surface is considered. The maximum deviation of the corrugated surface from the smooth one is assumed to be small, and hence the boundary-perturbation technique is utilized in this study. First, the scattering of scalar waves by a large, transparent, and dense sphere with statistical surface irregularities is treated as a canonical problem in the general discussion. After the perturbation solution is expanded asymptotically for large ka, it is found that the higher-order solutions can be obtained from the zeroth-order solution in a simple and straightforward manner. Then this relationship is generalized to scattering by a large, convex, transparent, and dense object with statistical surface irregularities; a general recipe is given. Finally, the asymptotic expressions of mean values of the scattered wavefunction and the scattered intensity are given for the general problem.
Local Characterization of Singularities in General Relativity
Authors: Geroch Robert
Published: February 2004

We formulate a new approach to singularities: their local description. Given any incomplete space-time M, we define a topological space, the ``g boundary,'' whose points consist of equivalence classes of incomplete geodesics of M. The points of the g boundary may be thought of as the ``singular points'' of M. Local properties of the singularity may now be described in a well-defined way in terms of local properties of the g boundary. For example, the notions: ``dimensionality of a singularity,'' ``past and future of a singular point,'' ``neighborhood of a singular point,'' ``spacelike or timelike character of a singularity,'' and ``metric structure of a singularity'' may all be expressed as properties of the g boundary. Two applications of the g boundary outside of the realm of singularities are discussed: (1) In the case in which the space-time M is extendable (for example, Taub space), the g boundary is shown to be that regular 3-surface across which M may be extended [in this case, the Misner boundary between Taub and Newman-Unti-Tamburino (NUT) space]. (2) With a slight modification of the definitions, the g boundary of an asymptotically simple space-time is shown to be Penrose's surface at ``conformal infinity.'' The application of the g boundary technique to singularities is illustrated with a number of examples. The g-boundary structure of one particular example leads to our consideration of non-Hausdorff space-times.
General Griffiths' Inequalities on Correlations in Ising Ferromagnets
Authors: Kelly D. G. , Sherman S.
Published: February 2004

Let N = (1, 2, ⋯, n). For each subset A of N, let JA ≥ 0. For eachi∈N, let σi ± 1. For each subset A of N, define σA=∏i∈A σi. Let the Hamiltonian be − ΣACN JA σA. Then for each A, B⊂N, 〈σA〉≥0 and 〈σAσB〉−〈σA〉〈σB〉≥0. This weakens the hypothesis and widens the conclusion of a result due to Griffiths.
Renormalization and Composite Effects in the Lee Model
Authors: Broido Michael M.
Published: February 2004

We consider the version of the Lee model with relativistic kinematics. The mass renormalization of the V particle, described in purely field-theoretic terms, is a nonlocal effect. We discuss the composite limit of the model. The natural choice of composite field is nonlocal in the elementary constituents. In the composite limit, Z1 does not vanish. The Hilbert-space formalism of the composite theory is not equivalent to that of an N-θ theory with a four-particle interaction. All these results are cutoff independent.