bluuebunny/crossref_metadata_2025 huggingface dataset:
Free-particle-like formulation of Newtonian instantaneous action-at-a-distance electrodynamics
Authors: Hirondel D.
Published: February 2004

From the infinite order equations of motion of conventional electrodynamics, one can extract by order depression a subclass of second order equations of motion parametrized only by initial positions and velocities. This article presents, with a view toward possible later quantization, a canonical formulation of this electrodynamics. It happens to have the same aspect as for free particles: H=(m12+p12)1/2 +(m22+p22)1/2. The p's are constant, and the canonical variables q's describe straight lines (particle positions cannot be canonical). The extension to the many-body problem is given.
Radial charged particle trajectories in the extended Reissner-Nordstrom manifold
Authors: Finley J. D.
Published: February 2004

It is shown that the trajectory of a charged particle on the extended Reissner-Nordström manifold can be such as to carry it into regions of the manifold where the definition of energy at infinity is different from the one at its point of origin. The various types of radial trajectories are classified. In the event one considers the manifold as having been produced by a collapsed star, there exist trajectories which go through both horizons, reach a minimum value of r, and go through two more horizons to a copy of the space in which it originated (flat at r = + ∞) without colliding with the matter of the collapsed star.
A new method for the evaluation of slowly convergent series
Authors: Hautot André
Published: February 2004

A new method is presented which sums certain slowly convergent series. It is based on the use of the Hankel integral transform and Schlömilch series. This method is applied with great success to the computation of lattice sums in ionic crystals. In particular, the Madelung constant is calculated with great accuracy through rather simple calculations: The final results only involve elementary functions so that the numerical evaluation is quite easy.
The distribution of the zeroes of the Jost function: The s -wave attractive exponential potential
Authors: Lavine J. P.
Published: February 2004

We show how the zeroes of the Jost function for an s -wave attractive exponential potential are distributed. In particular, we use known results, especially some of Coulomb's, on the zeroes of Bessel functions to demonstrate that there are no zeroes for complex momentum k = k1 + ik2 (k1≠0, k2≠0).
The renormalized projection operator technique for quadratic stochastic differential equations. II
Authors: LoDato Vincent A.
Published: February 2004

An equation for the mean value of the contaminant 〈Ψ(x, t)〉 is derived for the case when ‖L0(x, t)〈Ψ(x, t)〉‖ ≫ ‖K(x, t)〈Ψ(x, t)〉:〈Ψ(x, t)〉‖. The class of projection operators which produce this inequality is dictated by the following nonlinear stochastic equation: L0(x, t)〈Ψ(x, t)〉−∇x∫∫dx′ dt′G0(x, t|x′, t′)〈δν(x, t)δν(x′, t′)〉∇x′〈Ψ(x′, t′)〉=K(x, t)〈Ψ(x, t)〉:〈Ψ(x, t)〉+K(x, t)∫∫dx′ dt′G0(x′, t′|x′,t′)∇x′〈Ψ(x′, t′)〉:×∫∫dx″ dt″G0(x′, t′|x″, t″)〈δν(x′, t′)δν(x″, t″)〉∇x″〈Ψ(x″, t″)〉+S(x, t).This is a valid approach when the reaction time is much greater than the transport time, Ttrans ≪ Treact.
Generalized static electromagnetic fields in relativity
Authors: Teixeira A. F. da F. , Wolk Idel , Som M. M.
Published: February 2004

A general class of static cylindrically symmetric solutions of the Einstein-Maxwell equations coupled with a zero-rest-mass scalar field is obtained under the assumption -r 2grr = g00gφφgzz. These solutions reduce to Marder's well-known exterior solution in the absence of electromagnetic and scalar fields.
Gauge theories and Galilean symmetry
Authors: Roman P. , Leveille J. P.
Published: February 2004

Relations between a nonrelativistic local phase symmetry and the Galilean structure of the operator algebra are studied. The latter is derived from a few simple assumptions. For interacting systems, the assumption of phase independent localization leads to a unique Hamiltonian. Superselection rules for mass, time, and charge appear in intimate interrelationships.
Proper particle mechanics
Authors: Hestenes David
Published: February 2004

Spacetime algebra is employed to formulate classical relativistic mechanics without coordinates. Observers are treated on the same footing as other physical systems. The kinematics of a rigid body are expressed in spinor form and the Thomas precession is derived.
Complete sets of commuting operators and O (3) scalars in the enveloping algebra of SU (3)
Authors: Judd B. R. , Miller W. , Patera J. , Winternitz P.
Published: February 2004

We consider the ``missing label'' problem for basis vectors of SU(3) representations in a basis corresponding to the group reduction SU(3)⊃O(3)⊃O(2). We prove that only two independent O (3) scalars exist in the enveloping algebra of S U (3), in addition to the obvious ones, namely the angular momentum L2 and the two SU(3) Casimir operators C(2) and C(3). Any one of these two operators (of third and fourth order in the generators) can be added to C(2), C(3), L2, and L3 to form a complete set of commuting operators. The eigenvalues of the third and fourth order scalars X(3) and X(4) are calculated analytically or numerically for many cases of physical interest. The methods developed in this article can be used to resolve a missing label problem for any semisimple group G, when reduced to any semisimple subgroup H.
Double spectral representations of single loop amplitudes with k vertices: k ≥ 4
Authors: Frederiksen J. S.
Published: February 2004

A method developed in several previous papers is combined with the method of induction to derive double dispersion relations, with Mandelstam boundary, for the class of single loop amplitudes with four or more vertices. The spectral functions are expressed as integral representations and restrictions on the masses and kinematic invariants for which dispersion relations are valid are found. It is also discussed how representations for the low order single loop amplitudes can be obtained for wider ranges of these variables.
Principle of compensation of dangerous diagrams for boson systems. III. Finite temperature
Authors: Kobe Donald H. , Goble Gerald W.
Published: February 2004

The principle of compensation of dangerous diagrams (PCDD) is derived at finite temperature for boson systems by minimizing the average number of Bogoliubov quasiparticles in the system. The conditions obtained state that (a) the amplitude for the creation (or annihilation) of a single quasiparticle is zero and (b) the amplitude for the creation (or annihilation) of a pair of quasiparticles is zero. These conditions are expanded in finite-temperature perturbation theory, using both the density matrix and Green's function methods. In first order the resulting equations are the Hartree-Fock-Bogoliubov equations for a homogeneous boson system at finite temperature which can also be obtained from a free energy variational principle.
Coherent pulse propagation, a dispersive, irreversible phenomenon
Authors: Ablowitz Mark J. , Kaup David J. , Newell Alan C.
Published: February 2004

The initial value problem for the propagation of a pulse through a resonant two-level optical medium is solved by the inverse scattering method. In general, an incident pulse decomposes not only into a special class of pulses to which the medium is transparent but also yields radiation which is absorbed by the medium. In this respect ``this problem'' has properties markedly different from other dispersive and reversible wave phenomena some of which are tractable by the inverse scattering method. Indeed, it is remarkable that in the present case the method still applies. In particular, we show that, while there are an infinite number of local conservation laws, the integrated densities, and in particular the energy, are only conserved for a very special class of initial conditions. The theoretical results obtained are in close agreement with all the qualitative features observed in the experiments on coherent pulse propagation. Finally, we also show that causality is preserved. Two new and novel features are introduced and briefly discussed. First, we show that if the homogeneous broadening effect is a function of position in the medium, the pulses may speed up and slow down accordingly, without losing their permanent identities. Second, we have found a new kind of solution mode corresponding to a proper eigenvalue of the scattering problem which is not a bound state.
Factorizability of resonance poles in multiparticle amplitudes
Authors: Smith J. Denmead
Published: February 2004

Using the energy-analytic representation of Green's functions and relying on certain explicitly stated properties of the off-shell scattering elements, it is shown that resonance poles in the S matrix contribute poles to the off-shell scattering amplitude, and the residues there have the same factorizable form as that associated with bound state particles.
The renormalization group and the large n limit
Authors: Ma Shang-keng
Published: February 2004

The basic concepts and formulation of the renormalization group are explained beginning at an elementary level. Discussion is in the framework of classical statistical mechanics with emphasis on applications to the theory of critical phenomena. The details are worked out in the large n limit for 2 < d < 4, where n is the number of components of the fluctuating field of interest and d is the dimension of the thermodynamical system. In the large n limit, the infinite sum of ``tree graphs'' offers an exact and analytically tractable description of the renormalization group. It illustrates many concepts including the fixed point, the critical surface in the space of coupling parameters, and critical exponents. Most important, it illustrates the origin and the limitation of the scaling hypothesis. The critical behavior of various correlation functions and the free energy is examined. Attention is paid to terms often ignored in qualitative scaling arguments. We have attempted to make this paper self-contained and of pedagogical value to a wide audience.
The plane-wave expansion method
Authors: Griffin P. , Nagel P. , Koshel R. D.
Published: February 2004

A proof of the uniform convergence of the plane-wave expansion method is given. Also, an alternative method to obtain the expansion coefficients of the plane-wave expansion is derived through the use of the Rayleigh-Ritz variational method.
The maximal solvable subgroups of SO(p,q) groups
Authors: Patera J. , Winternitz P. , Zassenhaus H.
Published: February 2004

A recursive procedure is developed that makes it possible to determine all conjugacy classes under both SO(p,q) and O(p,q) of the maximal solvable subalgebras of the Lie algebras LO(p,q) [and the continuous maximal solvable subgroups of SO(p,q)]. The cases of greatest physical interest with p ≥ q ≥ 0 and p + q ≤ 6 are considered in detail (they include the Lorentz group, de Sitter groups, and the conformal group of space-time). Formulas (in terms of Fibonacci numbers) are given for the number of O(p,q) [and SO(p,q)] equivalence classes of maximal solvable subalgebras of LO(p,q).
Invariant imbedding and Fredholm integral equations with degenerate kernels
Authors: Ueno S.
Published: February 2004

In a manner similar to that given in preceding papers by Bellman and Ueno, with the aid of the Bellman-Krein formula for the resolvent, we show how to solve Fredholm integral equations of the second kind with degenerate kernels. The standard procedure for solution is to convert it into an equivalent matrix equation, but in this paper it is transformed into a Cauchy problem which can be solved effectively by high speed digital computers.
Kinetic theory and the Lorentz gas
Authors: Weyland A.
Published: February 2004

The high density properties of the velocity autocorrelation function and the diffusion coefficient are discussed in a one- and three-dimensional Lorentz gas on the basis of kinetic theory.
Asymptotic behavior of Markoffian kinetics
Authors: Matsuno Koichiro
Published: February 2004

The ergodic state with the least mean recurrence time in an irreducible Markoffian process having countable states, between any pair of which transition probability rates are definable, is the state with the least irreversible decay rate if neither the microscopic reversibility nor the doubly stochastic property holds.
The analytic noncharacteristic Cauchy problem for nonlightlike isometries in vacuum space-times
Authors: Berezdivin R.
Published: February 2004

The analytic noncharacteristic problem for the existence of a spacelike isometry in vacuum space-time, given its existence on the hypersurfaces, on the Cauchy data, is posed and solved using the ADM equations. The timelike case is also solved. In both cases the isometry will locally exist.
Concerning a criterion for the validity of the first order smoothing approximation
Authors: Lerche I.
Published: February 2004

This paper presents some statistically exact variational principles for problems in random function theory for the purpose of obtaining a criterion which will test 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 particular mathematical instances of general mathematical points. The calculations show that when the random equation under investigation is self-adjoint, and when the quasilinear approximation to it is also self-adjoint, then the exact and approximate solutions will, almost surely, agree. When either (or both) the true equation or the quasilinear approximate equation is not self-adjoint, then the exact and approximate solutions will, almost surely, disagree.
Interaction and transformation of electromagnetic and gravitational waves in Einstein-Maxwell field
Authors: Tokuoka Tatsuo
Published: February 2004

The interaction and the transformation of the electromagnetic and gravitational waves and the variation of those amplitudes are analyzed theoretically, where the Einstein-Maxwell field is assumed. Two waves are defined such that the electromagnetic vector potentials and the gravitational tensor potentials and their first derivatives are continuous while their second derivatives are discontinuous at a wave front. It is proved that the concomitant electromagnetic and gravitational waves can interact with each other if an external electromagnetic field exists. The global behaviors of interaction and transformation of the two concomitant waves are also investigated, where a Lorentz metric space-time is assumed. The variation formulas for amplitude are derived. The amplitudes may grow or decay according to a factor depending on the mean and Gaussian curvatures of an initial wave front and to a factor depending on the external electromagnetic field. When there is no external electromagnetic field, there is no interaction between the two waves and they propagate independently, while when an external field exists, the electromagnetic wave may transform into the gravitational wave and vice versa. In a case of a weak constant external electromagnetic field, where a flat space may be assumed, the amplitude of a wave varies sinusoidally with respect to the distance measured along its ray. The length of interchangeability is defined by the length in which a wave is completely transformed into its dual wave, and it is inversely proportional to the strength of an external electromagnetic field.
Radio wave propagation in nonuniform multilayered cylindrical structures-Full wave solutions
Authors: Bahar E.
Published: February 2004

Full wave solutions to problems of propagation in irregular cylindrical structures are derived. The electromagnetic parameters and the thickness of the layers of the structure are assumed to vary along the path of propagation. Exact boundary conditions are imposed at each interface between the layers of the structure, and the solutions are shown to satisfy the reciprocity relationship in electromagnetic theory. This analysis is a generalization of an earlier solution to the problem of propagation in open cylindrical structures characterized by convex, surface impedance boundaries. It can be employed to solve more realistic models of pertinent propagation problems over a broad frequency range. These include problems of propagation in the earth's crust and in the ionosphere and over widely varying propagation paths on the surface of the earth. For the purpose of the analysis, we employ generalized field transforms that provide suitable bases for the expansion of the electromagnetic fields in nonuniform cylindrical structures.
Dimensional renormalization
Authors: de Vega H. J. , Schaposnik F. A.
Published: February 2004

The analytic structure of a Feynman amplitude as a function of the number of space-time dimension (ν) is studied. A renormalization prescription by using ν as an analytic regularization parameter is given. It is shown its equivalence with BPH treatment for any graph in quantum field theory.
Scattering theory for Schrödinger operators with L∞ potentials and distorted Bloch waves
Authors: Troianiello Giovanni M.
Published: February 2004

We prove that, if q1 ε C0(R3)∩L∞(R3) and q2 ε L1(R3)∩L2(R3) are real-valued functions, the wave operators associated with the self-adjoint operators H1=−Δ+q1 and H2=−Δ+q1+q2 in L2(R3) exist and are complete. We also prove that, if q1 is periodic and q2 is in a certain weighted L2 space X, the absolutely continuous part of H2 possesses two sets of generalized eigenfunctions which belong to the dual space X* of X and are solutions of linear equations involving the generalized eigenfunctions of H1.
Relativistic quantum mechanics and local gauge symmetry
Authors: Roman P. , Leveille J. P.
Published: February 2004

The requirement that (either Abelian or non-Abelian) local symmetry transformations be globally and unitarily implementable kinematical symmetries of relativistic systems implies the emergence of a dynamical group which has been suggested in earlier studies. The group leads to a 4-velocity operator and to the Newton-Wigner position operator. Demanding gauge invariance of localization determines a unique interaction structure. Superselection rules for the gauge charges arise.
Limits of the Tomimatsu-Sato gravitational field
Authors: Kinnersley William , Kelley Edward F.
Published: February 2004

The Tomimatsu-Sato (TS) solutions of the Einstein field equations are studied in several limiting cases. In the weak-field limit we construct two Newtonian models for the source, one consisting of a rotating disc of radius a/n, the other made up of n complex point multipoles. The ``extreme'' limit q = 1 is also examined in detail, and we find there are many distinct ways of taking this limit. We are thereby led to a new two-parameter family of exact solutions which, unlike the TS metrics, are not asymptotically flat.
Summation relation for U(N) Racah coefficients
Authors: Hecht K. T.
Published: February 2004

A summation relation is given for U(N) Racah coefficients which has the form of an orthogonality relation, or a composition of recoupling transformations, except that the summation over column indices (for fixed row indices) is over multiplicity labels only. In the recoupling matrix for [f1] × [f2] × [f3] → [f], U(N) irreducible representations [f2] and [f3] are limited to be elementary, [11…10…0]≡[1k], or totally symmetric [k], or of the form [kN−1]. Results are tabulated as functions of the axial distances in [f] for [f2]=[1N−1], [1N−2], or [2N−1]; [f3]=[1], [12], or [2]; all cases which arise in the evaluation of squares of matrix elements of one- and two-body operators averaged over irreducible representations of U(N).
Bäcklund transformations for certain nonlinear evolution equations
Authors: Lamb G. L.
Published: February 2004

Bäcklund transformations associated with the Korteweg-deVries (KdV), modified KdV, and nonlinear Schrödinger equations are derived by a method due to Clairin. Also, a Bäcklund transformation relating the KdV and modified KdV equations is obtained by the same technique.
Orthogonal polynomials from the viewpoint of scattering theory
Authors: Case K. M.
Published: February 2004

It is demonstrated that there is a close parallel between the theory of a class of orthogonal polynomials and scattering theory. In both cases a fundamental role is played by a particular solution of the basic difference (differential) equation which we call the Jost function. Under rather general conditions this function has simple analytic properties. It determines and is largely determined by either the asymptotic phases or the continuous part of the weight (spectral) function. Indeed this is more than an analogy. By appropriate limiting procedures one can pass from a result about orthogonal polynomials to one in scattering theory. Conversely, scattering theory throws considerable light on theorems about orthogonal polynomials.
Statistical theory of effective electrical, thermal, and magnetic properties of random heterogeneous materials. III. Perturbation treatment of the effective permittivity in completely random heterogeneous materials
Authors: Hori Motoo , Yonezawa Fumiko
Published: February 2004

Perturbation expansion series are derived for the effective permittivity of completely random heterogeneous materials. The formulation is performed by regarding a completely random material as a limiting case of an isotropic cell material. It is emphasized that, in order to obtain a physically reasonable and mathematically correct result, the ``exclusion effect'' must be taken into account in the averaging procedure. Prescription for evaluating the perturbation coefficient of an arbitrary order is given and explicit forms of leading terms are presented. The results bear a wide variety of applications in calculating effective physical constants such as dielectric constant, magnetic permeability, electrical and thermal conductivity, and diffusion constant. It is mentioned that the idea and formulation in this article are important for more general approximations (to be studied in the succeeding Paper IV) especially in connection with the problem of electron localization in some disordered systems.
On the explicit-time-dependent invariance properties of quantum mechanical systems
Authors: Burdet G. , Perrin M. , Sorba P.
Published: February 2004

We use the notion of split extension algebra to embody a given invariance algebra of a quantum mechanical system, a realization of which is known in terms of some variables, in a richer invariance algebra expressed in terms of the same variables. By applying this procedure to a free system of particles we show how to obtain the invariance under the Schrödinger algebra and we build a bigger invariance algebra which describes a system of noninteracting particles, for example the asymptotic states in a nonrelativistic scattering problem.
Local observations of geodesics in the extended Kerr manifold
Authors: John Richard H. St. , Finley J. D.
Published: February 2004

Geodesics along the axis of symmetry in Carter's extension of the Kerr metric are divided into two types by the sign of the constant of the motion associated with the timelike Killing vector, and it is shown that this also divides them as to their place of origin on the manifold, which contains infinitely many copies of two different spaces which are flat at r = ± ∞. It is shown that geodesics cannot cross from one space to the other, but that a trajectory with properly applied acceleration can cross over.
The general exact solution of the equation of geodesics of the general exact homogeneous plane gravitational wave
Authors: Ebner Dieter W.
Published: February 2004

The general exact solution of the equation of geodesics for the general exact plane homogeneous gravitational wave is given by solving the vacuum field equations for the line element ds2 = A (u) d x2 + B (u) d y2 + 2C (u) d x d y + dz2 − dt2, with u = (z − t)/21/2 of these waves. The subclass of the exact plane sandwich waves is given explicitly by solving exactly the flatness condition for that line element. The relative energy and momentum transfer on test particles by the sandwich wave is discussed.
Fuzzy observables in quantum mechanics
Authors: Ali S. Twareque , Emch Gérard G.
Published: February 2004

The formalism of covariant conditional expectations is described as leading to an operational definition of generalized observables in quantum mechanics, wide enough to account for the fuzziness inherent in actual measurement processes, relative to a multidimensional physical continuum. As an application, a position operator for the photon is defined and its intrinsic fuzziness is discussed.
The evaluation of lattice sums. III. Phase modulated sums
Authors: Glasser M. L.
Published: February 2004

Two-dimensional lattice sums of the form Σ′exp(ik · s)k−2n are evaluated exactly in terms of Jacobian theta functions.
The polaron without cutoffs in two space dimensions
Authors: Sloan Alan D.
Published: February 2004

Hamiltonians for the polaron of fixed total momentum are defined using momentum cutoffs. A renormalized Hamiltonian of fixed total momentum is defined in two space dimensions by proving the strong convergence of the resolvents of the cutoff Hamiltonians. The Hamiltonian for the physical polaron is defined as the direct integral of the fixed momentum Hamiltonians.
Depolarization in nonuniform multilayered structures-full wave solutions
Authors: Bahar E.
Published: February 2004

In view of the recent impetus to produce rigorous solutions to more realistic models of pertinent propagation problems over a wide range of frequencies, we present in this paper full wave solutions to the problem of radio wave propagation in nonuniform multilayered structures. The electromagnetic properties of the media, the geometry of the irregular structure, and the electromagnetic source distributions are assumed to be arbitrary three-dimensional functions of position. Generalized field transforms are employed to provide a basis for the expansion of the transverse electromagnetic fields and Maxwell's equations are reduced to a set of first-order coupled differential equations for the forward and backward, vertically and horizontally polarized wave amplitudes. For open structures the complete wave spectrum includes the radiation term, the lateral waves, and the surface waves or trapped waveguide modes. For structures bounded by impedance walls (or perfect electric or magnetic walls μ/ε → 0 and ε/μ → 0, respectively) the fields are expressed exclusively in terms of waveguide modes. Exact boundary conditions are imposed at all the interfaces of the structure and the general solutions are not limited by the (approximate) surface impedance concept. The full wave approach employed is not restricted by frequency considerations. It is applicable to very broad classes of problems in which no single constituent of the total formal solution dominates. The full wave solutions may be applied to problems such as (i) propagation of ground waves over irregular and inhomogeneous terrain, (ii) scattering by rough surfaces and objects of finite dimensions, and (iii) propagation of guided waves in nonuniform artificial waveguides as well as in irregular ducts in the earth's crust or in the ionosphere.
On inverse scattering
Authors: Weston V. H.
Published: February 2004

In a previous paper the inverse problem associated with a hyperbolic dispersive partial differential equation with smooth coefficients was considered. The inverse problem (the determination of the coefficients) was formulated in terms of a dual set of integral equations involving measurable quantities, the kernels of the transmission, and reflection operators. These equations contained an unknown parameter which occurs in a linear manner. A better approach to determine this parameter is presented here. It involves an auxiliary equation, which is used to eliminate the unknown parameter from the integral equations. It is shown that the resulting system has a unique solution for a certain class of scattering problems. These uniqueness results are then strengthened when an additional equation is employed to reduce the dual set of integral equations to a single integral equation.
Analyticity in the coupling strength
Authors: Graves-Morris P. R. , Rennison J. F.
Published: February 2004

We briefly review the methods which have been used to establish the domains of analyticity of the partial wave scattering amplitude in the presence of a Yukawa potential as a function of the coupling strength, and the methods available for proving the convergence of Padé approximants to the Neumann series of the partial wave Lippmann-Schwinger equation. We then give a complete proof, using the Banach space technique first used by Lovelace, that the scattering amplitude is meromorphic in the coupling strength, and use Pommerenke's or Beardon's theorem to deduce the domains of convergence of the Padé approximants.
Branching rules for GL(N)⊃Σm and the evaluation of inner plethysms
Authors: King R. C.
Published: February 2004

It is pointed out that the operation of inner plethysm may be defined in terms of the branching rules associated with the decomposition of an irreducible representation of the general linear group into a set of irreducible representations of the symmetric group. A variety of methods of evaluating inner plethysms are developed and a number of results tabulated. Special emphasis is placed on those results relevant to the embedding of crystallographic point groups in the rotation group in three dimensions. Symmetrized squares and cubes of some of these groups are deduced and an application to the symmetry properties of 3j symbols is given.
Some comments on a recent paper of Glasser
Authors: Hautot André
Published: February 2004

The calculations which lead to results recently established by Glasser are simplified.
New commutator identities on the Riemann tensor
Authors: Pereira C. Martin
Published: February 2004

A number of new generally covariant identities which involve second derivatives of the Riemann tensor are presented. Each of these new identities can be expressed by equating to zero either (a) a particular sum of terms each of which contains an operator of the form (▿μ▿ν − ▿ν▿μ) acting on the Riemann tensor; or (b) a particular sum of terms each of which contains an operator of the form ▿a acting either on the expression (∇μRαβτω+∇βRματω+∇αRβμτω) or on the expression (∇μRαβτω+∇βRματω+∇αRβμτω); or (c) a particular sum of algebraic terms each of which contains no derivatives of the Riemann tensor, but rather is quadratic in the Riemann tensor. Each of the new identities can be expressed in all three of the above-described forms. Furthermore, each of these new identities can be thought of as an integrability condition derived from the equations that define the Riemann tensor in terms of the Γαβω or the gμν. The requirements of Riquier's existence theorem are used to guide the derivation of the identities. The operator ▿μ denotes covariant differentiation. All the new identities assume the existence of a symmetric connection Γαβμ and one of the new identities assumes the existence of a metric. Schouten's identity and Walker's identity are also discussed.
Lowest nonnegative solution of the Yukawa Hamiltonian
Authors: Nieto Michael Martin
Published: February 2004

Two recent papers [J. Math. Phys. 13, 1825 (1972); 14, 1140 (1973)] obtained rough limits 1.68 ≥ b0 ≥ 1.67 for the quantity b0 such that an energy eigenvalue of the Yukawa Hamiltonian [−ℏ2∇2/2m−U0 exp(−μrc/ℏ)/r] must be zero or positive if b≡(m/μ) (2U0/cℏ)≤b0. We point out that (along with other aspects of the Yukawa equation) the quantity b0 has long been known to a much higher precision.
On ergodic limits of normal states in quantum statistical mechanics
Authors: Prugovečki E. , Tip A.
Published: February 2004

The asymptotic behavior for t→±∞ of S(t)=exp(−i H t)Sexp(+i H t) and its time average S̄ (t)=t−1∫0tdu S(u) is discussed. Here is S an element of the Banach space B1, constituted by the trace class of operators on the (separable or nonseparable) Hilbert space H, and H is the Hamiltonian, i.e., a bounded or unbounded self-adjoint operator on H. Necessary and sufficient conditions are given for the existence of the limits S̄(± ∞) and S(± ∞) with respect to the weak topology on B1, for the latter under the assumption that the continuous spectrum of H is absolutely continuous. In addition it is shown that if, for a normal state (density operator) ρ, ρ̄(t) has a weak limit, then the limit is again a normal state. This provides further insight in the nature of Emch's ``first ergodic paradox'' [G. G. Emch, J. Math. Phys. 7, 1413 (1966)].
An initial value method for an inverse problem in wave propagation
Authors: Kalaba R. , Zagustin E.
Published: February 2004

Kay and Balanis have reduced various inverse problems in wave propagation to the solution of Fredholm integral equations. These integral equations can be further reduced to Cauchy systems.
Some differential-difference equations containing both advance and retardation
Authors: Schulman L. S.
Published: February 2004

An explicit solution is given to the boundary value problem for certain linear differential-difference equations. The solution is well behaved even in the presence of advanced interactions. Interest in these equations arises from study of time symmetric electrodynamics.
Solutions of the steady, one-speed neutron transport equation for small mean free paths
Authors: Larsen Edward W.
Published: February 2004

The solution of the steady, one-speed neutron transport equation with isotropic scattering and small mean free path is obtained. The solution is asymptotic with respect to a small parameter ε, defined as the mean free path in terms of a unit length of the same order of magnitude as a typical dimension of the domain. The solution, the leading two terms of which are given, consists of a boundary layer solution plus an interior solution. The boundary layer solution decays exponentially with distance from the boundary, the decay rate being proportional to ε−1, and it shows the effects of boundary curvature and variations in the incoming flux along the boundary. The interior solution is a multiple of the source for subcritical domains, and depends on a diffusion equation for near critical domains. The boundary condition for the diffusion equation and an asymptotic criticality condition are derived.
Five-dimensional approach to the neutrino and electron theories
Authors: Leibowitz Elhanan
Published: February 2004

The theories of the neutrino and the electron are studies from a five-dimensional point of view. The concept of periodic 5-spinors is examined, and the formalism of five-dimensional spinor calculus is applied to the manipulations of spinor equations. It is shown that the five-dimensional approach reproduces the results of the familiar four-dimensional approach in a unified and coherent manner. Furthermore, the present approach predicts in a natural way the correct coupling to the electromagnetic field, without ad hoc assumptions.
Smoothed boundary conditions for randomly rough surfaces
Authors: Wenzel Alan R.
Published: February 2004

The problem of scalar wave propagation in the half-space bounded by a rigid, randomly rough surface which is a small perturbation of an infinite plane is considered. It is shown that, if the boundary roughness is statistically homogeneous, the coherent (or average) wave satisfies a generalized impedance boundary condition on the average boundary. This is referred to as a ``smoothed'' boundary condition. Applying it to plane waves yields an expression for the effective plane-wave reflection coefficient Ce of the boundary. For the case of isotropic roughness, approximate expressions for Ce are obtained for both long (relative to the correlation length of the boundary roughness) and short waves. These expressions show that generally |Ce| < 1, and therefore that the amplitude of the coherent wave is diminished upon reflection from the boundary. This is the result of scattering of energy out of the coherent wave by the boundary roughness. It is also shown that this type of boundary can support a surface wave. This wave propagates at near-grazing incidence with a speed slightly less than the free-space propagation speed. Its amplitude decreases with propagation distance, also as a result of scattering by the boundary roughness.
The three-particle S matrix
Authors: Newton Roger G.
Published: February 2004

It is proved that a reduced T matrix, defined by factoring out of the three-particle S matrix the product of the three two-particle S matrices, is a compact operator on the energy shell, in spite of the double-scattering singularity. As a result there exists a discrete, complete set of eigenphase shifts at every energy.
Generalized free fields and the representations of Weyl group
Authors: Lukierski J. , Sienkiewicz K.
Published: February 2004

The transformation properties of generalized free fields under the transformations of the Weyl group, and particularly under the subgroup of dilatations, are discussed. It is shown that there exists, for any complex value d of the dimensionality parameter, a generalized free field, defining by means of its one-particle states the suitable irreducible representation of the Weyl group.
Faddeev-like equations with multibody forces
Authors: Gregorio M. A. , Avalos D. R.
Published: February 2004

Equations for a system of four particles interacting through two-, three-, and four-body potentials are derived using a generalization of Faddeev's technique for the three-body problem. Two alternative approaches are condsidered and simple equations for iterative solutions are written down. The method is generalized to the N-body problem with multibody forces.
A property of asymptotically flat, static, vacuum space-times
Authors: Hallidy William
Published: February 2004

It is shown that a necessary condition for stationary, asymptotically flat, vacuum space-times to be static is that the Weyl tensor be electric type to asymptotic order r−7, where r is an affine parameter along null geodesics.
Conformal spinor fields in general relativity
Authors: Maia M. D.
Published: February 2004

A spinor field which is covariant under the group of conformal motions in general relativity is defined. These spinor fields extend the concept of isospinors to the cases where conformal motions take place and coincide with Penrose's twistors in the case of flat space-time. It is found that only certain special conformal spinor fields lead to physical entities. The example of Kruskal's conformal spinors is studied.
Iterative solution of the inverse Sturm-Liouville problem
Authors: Barcilon Victor
Published: February 2004

An iterative construction of the potential function entering in a regular Sturm-Liouville problem is discussed. The given data is in the form of two spectra associated with distinct boundary conditions at one end point.
An approach to the study of quantum systems
Authors: Hioe F. T.
Published: February 2004

A perturbation method for quantum mechanical problems is presented in which the successive terms are obtained by algebraic recurrence relations without the use of any diagrams. Two examples, one an anharmonic oscillator with quartic self-interaction, and one a spin with quadratic self-interaction, are given to illustrate the use of this recurrence relation perturbation method.
Spacelike representations of the inhomogeneous Lorentz group in a Lorentz basis
Authors: Radhakrishnan B. , Mukunda N.
Published: February 2004

The problem of introducing a Lorentz basis in a spacelike representation of the inhomogeneous Lorentz group in the spinless case, is solved by the methods of integral geometry. A new description of the representation associated with isotropic lines, which is peculiar to the spacelike case, is also given.
On the relaxation to quantum-statistical equilibrium of the Wigner-Weisskopf atom in a one-dimensional radiation field. VI. Influence of the coupling function on the dynamics
Authors: Yang Janilla Jyy-wen , Davidson Russell , Kozak John J.
Published: February 2004

An investigation is made of the effect on the dynamics of spontaneous emission of the Wigner-Weisskopf atom in an infinite-system limit of various choices of the coupling function or form factor describing the atom's interaction with the spectrum of the radiation field. This is carried out both for the exact solution to the problem of spontaneous emission, obtained in the earlier papers in the series, and for some approximate solutions, also previously considered, in particular one based on the Schrödinger equation of the problem and one based on the weak-coupling Prigogine-Résibois master equation. The details of the form factor are found, by numerical computation of the solutions, to be critical in determining the nonexponential parts of the solutions, and these parts are seen to be capable in some cases of dominating the exponential parts, which are given only by the values of the form factor near the resonance energy. The approximate solutions discussed are found to vary widely in their worth, and one, which yields the exact solution for the Wigner-Weisskopf problem, is singled out as being of probable use in the statistical-mechanical description of more complicated systems.
Regular perturbations, Brillouin-Wigner expansion, and continued fractions
Authors: Graffi S.
Published: February 2004

The least eigenvalue of an operator H = H0 + g V is considered, where H0 is a semibounded self-adjoint operator in a Hilbert space and V is symmetric. It is shown that the J-type continued fraction (i.e., the sequence of the [N-1, N] Padé approximants) to the Brillouin-Wigner perturbation expansion converges to the eigenvalue, provided V is a regular perturbation of H0. An application of this result to some quantum mechanical systems, such as the helium atom, is briefly discussed.
Nonradiative algebraically special space-times
Authors: Trim D. W. , Wainwright J.
Published: February 2004

A recently characterized class of (in general nonvacuum) algebraically special space-times with twisting rays is studied. The Weyl tensor satisfies the peeling-off property along the repeated principal null congruence, and the Ricci tensor exhibits an equally simple asymptotic behavior, which is in fact compatible (via the Einstein field equations) with the presence of a suitably restricted electromagnetic or neutrino field. If the gravitational and source fields are nonradiative, the above asymptotic behavior is restricted. In this case we explicitly solve the Einstein vacuum field equations, the Einstein-Maxwell equations and the Einstein-Weyl (combined gravitational-neutrino) equations. The solutions obtained are related to the known algebraically special solutions of these equations.
Some consequences of the strengthened interpretative rules of quantum mechanics
Authors: Benioff Paul
Published: February 2004

In this paper some consequences of the strengthened interpretative rules of quantum mechanics, which were proposed in an earlier paper, are obtained. It is also seen that, in general, the usual interpretative rules are too weak to obtain these results. For example, it is proved from the strengthened rules that if f:R → R is a Borel function which is also τ-definable, then for each observable A the procedure ``measure A and compute f(A outcome)'' is an f(A) measurement procedure. It is also shown that there exist Borel f and observables A such that the above procedure is not an f(A) measurement procedure. Two methods of measuring the sum A + B of two observables are then considered: The measurement of A and B on different systems followed by addition of the results and (if A and B commute) the simultaneous measurement of A and B on the same system followed by addition. It is proved from the strengthened rules that the first method is not a valid measurement procedure and the second is valid. Besides these, other processes such as procedures for preparing mixtures of different states, and the empirical generation of probability measures from outcome sequences are considered.
The group chain S On,1⊃S O1,1⊗S On−1, a complete solution to the ``missing label'' problem
Authors: Boyer Charles P. , Wolf Kurt Bernardo
Published: February 2004

We discuss the decomposition S On,1⊃S O1,1⊗S On−1 by constructing multiplier representations over the group manifold of S O n. Explicit orthogonal and complete bases in terms of functions diagonal with respect to the canonical (S On,1⊃S On) and noncanonical (S On,1⊃S O1,1⊗S On−1) chains are provided which give a complete solution to the ``missing label'' and multiplicity problems occuring in the latter decomposition. Moreover, an integral representation for the overlap functions between the two chains is given, for which the singularity structure can be immediately ascertained. Expressions for the cases n = 3 and 4 are given.
Expansions in Breit-Wigner amplitudes and biorthogonal functions
Authors: Klink William H.
Published: February 2004

The problem of finding the expansion coefficients for a finite superposition of Breit-Wigner amplitudes is discussed. Since such amplitudes are not mutually orthogonal, another set of functions orthogonal to the Breit-Wigner functions are computed. Advantages and disadvantages of this biorthogonal set of functions are compared with conventional orthogonal functions and, in particular, the problem of reading off expansion coefficients when the modulus squared of the amplitude is known—rather than the amplitude itself—is discussed.
Spheroidal analysis of Coulomb scattering
Authors: Li Ming Chiang
Published: February 2004

In studying the spheroidal problem of a charged particle scattered by two charged centers, we have had to deal with a differential equation. Its solution was complicated. In this paper, we study a very similar differential equation, which appears in the Coulomb problem. The solution for this equation, however, can be put in a simple form. For completeness the spheroidal analysis of the Coulomb scattering amplitude is also discussed.
A novel approach to the exact calculation of correlation functions of a one-dimensional random Ising chain
Authors: Rajagopal A. K. , Grest G. S.
Published: February 2004

An exact result for the partition function for a general one-dimensional Ising chain of N spin-1/2 particles described by the Hamiltonian HN=−∑i=1NJiσiσi+1−∑i=1NHiσi is given. For an open strand, JN = 0; for a closed chain, σN+1 = σ1, JN ≠ 0. The novelty of the trick used enables one to obtain the partition function and all the spin correlation functions for open and closed chains with equal ease. Special cases of this model have been discussed before to elucidate certain features of some biological systems. New expressions for parallel and perpendicular susceptibilities for this model are also derived. When Ji and Hi are treated as random variables, the above Hamiltonian describes a one-dimensional Ising spin glass. In this case some simple models and formal averaging procedures are discussed.
Perpendicular susceptibility of two one-dimensional Ising chains
Authors: Grest G. S. , Rajagopal A. K.
Published: February 2004

Exact, closed expressions are obtained for the perpendicular and parallel susceptibilities of the one-dimensional spin-1/2 Ising model (i) with nearest neighbor interactions in a uniform magnetic field and (ii) with next-nearest neighbor interactions but without the magnetic field, in the thermodynamic limit. Graphs of the susceptibilities as a function of temperature for various magnetic field strengths in (i), and as a function of different ratios of the interaction strengths in (ii), are discussed.