bluuebunny/crossref_metadata_2025 huggingface dataset:
On rotating plane-fronted waves and their Poincaré-invariant differential geometry
Authors: Urbantke H.
Published: March 2003

After reviewing the rotating plane-fronted wave type solutions of the scalar wave equation and Maxwell’s vacuum equations in flat space (we point out that there are Yang–Mill analogs as well), we study their Poincaré-invariant geometry by discussing their characteristic differential invariants and a noninertial curvilinear coordinate system canonically associated with them. In one of the appendices we treat the shearfree and the nondiverging null hypersurfaces in complex Minkowski space, in another one we derive the Yang–Mills version of Robinson’s theorem on null electromagnetic fields.
A model for the stochastic origins of Schrödinger’s equation
Authors: Davidson Mark
Published: March 2003

A model for the motion of a charged particle in the vacuum is presented which, although purely classical in concept, yields Schrödinger’s equation as a solution. It suggests that the origins of the peculiar and nonclassical features of quantum mechanics are actually inherent in a statistical description of the radiative reactive force.
Exact solution of a time-dependent quantal harmonic oscillator with damping and a perturbative force
Authors: Khandekar D. C. , Lawande S. V.
Published: March 2003

The problem of a quantal harmonic oscillator with damping and a time-dependent frequency acted on by a time-dependent perturbative force is exactly solved. The wavefunctions are found in Schrödinger representation using the theory of explicitly time-dependent invariants and also by an expansion of the Feynman propagator. The propagator is obtained in exactly closed form by an explicit path integration of the classical Lagrangian. It is found that the wavefunctions and the propagator depend only on the solution of classical damped oscillator through a single function ρ (t). The function ρ (t) itself may be obtained as a solution of a second order nonlinear differential equation under the appropriate set of initial conditions.
Solution of a quantum mechanical eigenvalue problem with long range potentials
Authors: Stillinger Frank H.
Published: March 2003

Wavefunctions and eigenvalues for the Schrödinger equation on the half-line x⩾0 are examined in the presence of a potential v0x−2+v1x−1+v2x−1/2. With a special choice for the constant v0 the wave equation can be solved in terms of parabolic cylinder functions. In this case the spectrum is determined by an implicit equation that arises from the boundary condition that must be imposed at x=0. Depending on v1 and v2, the spectrum can contain and infinite number of discrete values, a finite number, or none. It is pointed out that continuous variations in v1 or v2 can convert negative energy bound states into positive energy responances, or vice versa, and the threshold behavior has been investigated.
Construction of Lie algebras and Lie superalgebras from ternary algebras
Authors: Bars Itzhak , Günaydin Murat
Published: March 2003

Ternary algebras are algebras which close under suitable triple products. They have been shown to be building blocks of ordinary Lie algebras. They may acquire a deep physical meaning in fundamental theories given the important role played by Lie (super) algebras in theoretical physics. In this paper we introduce the concept of superternary algebras involving Bosers and Fermi variables. Using them as building blocks, we give a unified construction of Lie algebras and superalgebras in terms of (super) ternary algebras. We prove theorems that must be satisfied for the validity of this construction, which is a generalization of Kantor’s results. A large number of examples and explicit constructions of the Lie algebras An, Bn, Fn, Fn, F4, F6, F7, F8, and Lie superalgebras A (m,n), B (m,n), D (m,n), P (n), Q (n) are given. We speculate on possible physical applications of (super) ternary algebras.
Asymptotic approximations for modified Bessel functions
Authors: Kasperkovitz P.
Published: March 2003

The behavior of a qν(x) =Iν(x)/Iνa(x), where Iν is a modified Bessel function with integral or half-integral index ν and Iνa the leading term of its asymptotic series, is investigated for x≫1. It is shown that qν(x) may be approximated by eν(x) =exp(−ν2/2x), the difference rν(x) =qν(x)−eν(x) being of order x−1/4. Bounds for rν(x) depending only on x are derived for each of the two classes of ν’s and an application of these results in scattering theory is indicated.
Conservation laws of the Benjamin–Ono equation
Authors: Chen H. H. , Kaup D. J.
Published: March 2003

We report here an empirical algorithm to construct conservation laws of the Benjamin–Ono equation.
A note on completeness
Authors: Weber T. A. , Hammer C. L.
Published: March 2003

Completeness relationships for eigenfunctions of second order differential equations are presented in a form which employs a contour integration rather than the usual integration and summation over eigenvalues. This technique which is particularly applicable for scattering problems simplifies the usual procedures and the proper weight functions are easily obtained. Some examples are given.
Quadratic Hamiltonians: The four classes of quadratic invariants, their interrelations and symmetries
Authors: Leach P. G. L.
Published: March 2003

The quadratic invariants of the three basic quadratic Hamiltonian systems-attractive oscillator, repulsive oscillator, and free particle- are shown to be the same. These invariants are divided into two categories, useful and nonuseful. The definition of useful is in terms of contributing to the (quadratic invariant based) symmetry group of the appropriate Hamiltonian. Usefulness is not invariant under a time-dependent linear canonical transformation. Hence different classes of invariants produce the different symmetry groups for the three different types of quadratic Hamiltonian considered here. The paper concludes with a consideration of a useful transformation of arbitrary quadratic Hamiltonians.
A note on the Hénon–Heiles problem
Authors: Leach P. G. L.
Published: March 2003

The Hamiltonian for the Hénon–Heiles problem, H= (1/2)(p12+p22+q12+q22)+q12q2 −(1/3) q23, is a particular example of time-independent Hamiltonians for two-dimensional oscillator systems with third degree anharmonicity. It has been used as a model for galactic motion. There has been much discussion of the possible existence of an integral other than the Hamiltonian. In this note we show that the Hénon–Heiles Hamiltonian in particular and the class in general does not possess an invariant series which is explicitly time-independent other than the Hamiltonian itself.
Mobility of nonlinear systems
Authors: Mielnik Bogdan
Published: March 2003

Global mobility is defined and is found to be decisive for the structure of a physical system. The structure of some simple nonlinear systems is elucidated by studying their dynamical mobility. It is shown that due to an excessive mobility a nonlinear system may acquire some classical features.
A phase space approach to generalized Hamilton–Jacobi theory
Authors: Samuel J.
Published: March 2003

Generalizations of H–J theory have been discussed before in the literature. The present approach differs from others in that it employs geometrical ideas on phase space and classical transformation theory to derive the basic equations. The relation between constants of motion and symmetries of the generalized H–J equations is then clarified.
Summation of partial wave expansions in the scattering by short-range potentials
Authors: Grinstein Fernando F.
Published: March 2003

Previous theorems on the convergence of the punctual Padé approximant to the scattering amplitude are extended. The new proofs correspond to the case of potentials having a shortrange tail of the type V (r)r→∞∼Vor−ρ−1 exp[−μr], where V0 is a constant, ρ an integer and μ≳0, and are restricted to within the Lehmann ellipse, in the complex cosϑ plane, where the partial wave expansion converges. Asymptotic estimates are obtained for the error of the approximants.
Structure of the gravitational field at spatial infinity. I. Asymptotically Euclidean spaces
Authors: Persides S.
Published: March 2003

A new formulation for the study of the asymptotic structure of a gravitational field at spatial infinity is presented. First, the disadvantages of the existing formulations are identified in order to recognize the underlying causes and exclude them from the new formulation. It is concluded that neither conformal nor projective completion should be used. From a study of the Euclidean space we obtain a method of completion of a three-dimensional space (ℋ,g) with positive-definite metric g so that a two-dimensional boundary ℒ is attached to the space at infinity and a three-dimensional positive definite C∞ metric ĝ exists near and on ℒ. The whole method is based on replacing the conformal transformation of the conformal completion by the relation Ω−2gij−Ω−4gimgjnΩ ;mΩ;n=?ij−?im?jn Ω‖mΩ‖n. Thus the concept of asymptotic simplicity is defined. Then the additional conditions are determined for the space to be asymptotically Euclidean. The asymptotic symmetries and the uniqueness of the boundary are examined briefly.
Structure of the gravitational field at spatial infinity. II. Asymptotically Minkowskian space–times
Authors: Persides S.
Published: March 2003

A new formulation is established for the study of the asymptotic structure at spatial infinity of asymptotically Minkowskian space–times. First, the concept of an asymptotically simple space–time at spatial infinity is defined. This is a (physical) space–time (ℳ,g) which can be imbedded in an unphysical space–time (ℳ̂,ĝ) with a boundary 𝒮, a C∞ metric ĝ and a C∞ scalar field Ω such that Ω=0 on 𝒮, Ω≳0 on ℳ̂−𝒮, and ĝμν + ĝμλ ĝνρ Ω‖λ Ω‖ρ=Ω−2 gμν +Ω−4 gμλ gνρ Ω;λ Ω;ρ on ℳ. Then an almost asymptotically flat space–time (AAFS) is defined as an asymptotically simple space–time for which 𝒮 is isometric to the unit timelike hyperboloid and ĝμν Ω‖μ Ω‖ν =Ω−4 gμν Ω;μΩ;ν=−1 on 𝒮. Equivalent definitions are given in terms of the existence of coordinate systems in which gμν or ĝμν have simple explicitly given forms. The group of asymptotic symmetries of (ℳ,g) is studied and is found to be isomorphic to the Lorentz group. The asymptotic behavior of an AAFS is studied. It is proven that the conformal metric g̃μν=Ω2gμν gives C̃λμρν=0, Ω−1 C̃λμρν Ω;μ =0, Ω−2 Cλμρν Ω;μ Ω;ν=0 on 𝒮.
On algebraically special space–times with nontwisting rays
Authors: Ludwig Garry
Published: March 2003

With the aid of the Newman–Penrose formalism and Penrose’s conformal technique Einstein’s gravitational field equations are first solved exactly as far as is possible for arbitrary sources. It is assumed, however, that space–time is algebraically special with hypersurface-orthogonal geodesic and shear-free rays. Special cases are considered. Next, the asymptotic behavior of the components of the metric tensor, the Weyl tensor, the Ricci tensor and the spin coefficients is determined in a suitable frame. Einstein–Maxwell space–times with the above properties are treated in some detail.
N-dimensional instantons and monopoles
Authors: Tchrakian D. H.
Published: March 2003

The possibility of finding solutions of the instanton and monopole types to gauge field theories on arbitrary even and odd dimensional Euclidean manifolds respectively is investigated. Suitable boundary conditions for both types are given, and new self-duality criteria are developed, for gauge field theories on N-dimensional manifolds (N?5) which are also endowed with new Action and Lagrangian densities.
Asymptotic behavior of gravitational fields in a type II coordinate system
Authors: Ludwig Garry
Published: March 2003

With the aid of Penrose’s conformal technique the asymptotic behavior of the components of the metric tensor, the Weyl tensor, the Ricci tensor and the spin-coefficients is calculated for a large class of space-times that includes the NUT (Newman–Unti–Tamburino) solution as well as all asymptotically flat space-times. The calculations are done in a coordinate system associated not with null hypersurfaces but with an asymptotically shearfree twisting null congruence. For vacuum the results presented here reduce to those of Aronson and Newman to the order given in their paper.
Space spinors
Authors: Sommers Paul
Published: March 2003

Just as Maxwell’s electromagnetic field equations govern the evolution of electric and magnetic spatial vectors if some choice of time function has been made, so also the neutrino equation and Dirac equation may be understood as governing the evolutions of certain spatial quantities. In this space-plus-time view of the spinor field equations, it is accurate and natural to regard a two-component are written in 3-plus-1 form for both the spinor fields and the corresponding null vector fields. A spatial null vector is of the form M=E+iB, with E⋅E−B⋅B=0=E⋅B, so it is also of the correct algebraic form for describing a null electromagnetic field. The time derivative of a squared neutrino field Ma, however, is -i curl Ma+〈M〉cDaMc, compared with simply -i curl Ma for a source-free Maxwell field. Here 〈M〉c is the real spatial unit vector in the neutrino propagation direction E×B, and Da is the spatial covariant derivative.
Finite nonabelian subgroups of SU(n) with analytic expressions for the irreducible representations and the Clebsch–Gordan coefficients
Authors: Abresch U. , Bovier A. , Lechtenfeld O. , Lüling M. , Rittenberg V. , Weymans G.
Published: March 2003

We present two sequences of finite nonabelian groups which are semidirect products of three Zn groups. Although these groups are not simply reducible (in the tensor product of two irreducible representations an irreducible representation is obtained more than once) we give analytic expressions for the irreducible representations and the Clebsch–Gordan coefficients.
Spinor fields invariant under space–time transformations
Authors: Beckers J. , Harnad J. , Jasselette P.
Published: March 2003

Spinor fields invariant under the subgroups of the Poincaré group or under the maximal subgroups of the conformal group of space–time are analyzed. It is shown that only certain Poincaré subgroups, all of dimension less than or equal to six, can leave two component spinor fields invariant, with rather severe restrictions on the fields. Tables listing all such invariant fields for subgroups of dimension greater than or equal to four are given. Construction of Dirac spinors and connections between invariant spinors and tensors are discussed: In particular it is shown that from any two-component spinor invariant under a Poincaré subgroup a real skew-symmetric tensor invariant under the same group may be constructed.
Oscillators submitted to squared Gaussian processes
Authors: Soize Christian
Published: March 2003

The paper is a study of oscillators governed by equations of the type aẌ(t)+bẊ(t)+cX(t)=E(t), where a, b, c are given constants and where E(t) is for example the square of a Gaussian stationary process. A constructive and numerical method, using explicit expressions of Fourier transforms, are developed in order to compute the density of the distribution function (d.f.) of X(t) and of the joint distribution of X(t) and Ẋ(t). Hence the upcrossing rates of a given level and an approximation of the d.f. of maxt∈TX(t) can be computed. A numerical example is given.
A modified Bars–Durgut equation with polynomial eigenfunctions
Authors: Onofri E.
Published: March 2003

A singular integral equation in two degrees of freedom is defined. Its structure is similar to Bars–Durgut equation for baryons in two dimensions. It admits polynomial eigenfunctions and its spectrum can be studied exactly. A comparison with numerical data available for the baryon equation shows strong similarities. The asymptotic behavior of the eigenvalues for high quantum numbers is studied in the semiclassical approximation and it is found to be in good agreement with the exact spectrum. A peculiar feature of this model is the presence of a transition from a region of periodic classical orbits with constant frequency (straight Regge trajectories in the spectrum) to a regime of aperiodic orbits (nearly parabolic trajectories).
Dynamical symmetry and magnetic charge
Authors: Schonfeld Jonathan F.
Published: March 2003

By adding to the force between an electric and a magnetic point charge a central force arising from a specially chosen potential, one can construct a system known to have the same SO (3,1) and/or SO (4) dynamical symmetry algebra as the Kepler system. We derive projective changes of variables under which the classical orbits of any such system are put in one-to-one correspondence with SO (3,1)- and/or SO (4)-invariant sets of curves on similarly invariant surfaces. This extends results hitherto established only for the Kepler system. This is surprising in that there is a sense in which the phase space of such a magnetic system is a truncation of the Kepler phase space and so one might have expected such global properties not to generalize. Our transformations apparently do not permit transcription of the corresponding Schrödinger equation into a manifestly SO (3,1)- and/or SO (4)-symmetric form, in contrast to the pure Kepler case. Such magnetic systems play roles in the theory of quantum fields in Taub–NUT space-times, and in the theory of quantum-mechanical fluctuations about extended magnetic monopoles in supersymmetric gauge theories. In passing, we use the properties of the magnetic systems to formulate a very short and direct proof that the classical orbits of the Kepler system are conic sections.
A factorization of M4: Construction of the principal bundle of orthogonal frames over M4 from O(3,3) spinors
Authors: Nash Patrick L.
Published: March 2003

The principal bundle of orthogonal frames over M4 is explicitly constructed from certain pairs of Ō(̄3̄,̄3̄)́bar)= spinors that transform as (associated) twistors under the action of the covering group of the Poincaré group. In particular, flat space–time is constructed from these associated twistors, and is thus shown to be an object derivable from geometric structures more basic than the vectors of M4. Associated twistors describe massive elementary particles. The position in M4 of such a particle can be explicitly defined in terms of the components of these twistors. The usual momentum and angular momentum variables which coordinatize the classical phase space of this elementary relativistic system of nonzero mass and arbitrary spin may also be realized in terms of this pair of associated twistors. This realization is not equivalent to descriptions of massive particles using twistors which have previously appeared in the literature.
Parametrizations of unitary matrices and related coset spaces
Authors: Macfarlane A. J.
Published: March 2003

Explicit forms of U3 and U4 matrices as functions of a single adjoint vector are displayed. Parametrizations of the coset spaces U(N+r)/(UN×Ur) are discussed, most explicitly for r=1 and 2, and related, for N=3 and 4, to the results for U3 and U4 matrices.
Field fluctuations in a two-phase random medium
Authors: Beran Mark J.
Published: March 2003

We consider here the problem of determining the mean square fluctuations in a statistically homogeneous isotropic two-phase dielectric random medium. An expression is derived for a weighted sum of the mean square fluctuations in each phase in terms of the effective dielectric constant. From this expression bounds are derived for the mean square fluctuations in each phase. An assumption is then made to allow us to obtain exact expressions for the mean square fluctuations in a particular phase.
Quantum statistics of multimode m-photon absorption process
Authors: Zubairy M. S.
Published: March 2003

A density matrix method is used to obtain an exact solution for the reduced density matrix of the field in an arbitrary multimode m-photon absorption process. The results of some earlier specialized studies of photon statistics in multiphoton absorption process can be recovered from this solution.
Formal solutions of inverse scattering problems. III.
Authors: Prosser Reese T.
Published: March 2003

The formal solutions of certain three-dimensional inverse scattering problems presented in papers I and II of this series [J. Math. Phys. 10, 1819 (1969); 17 1175 (1976)] are obtained here as fixed points of a certain nonlinear mapping acting on a suitable Banach space of integral kernels. When the scattering data are sufficiently restricted, this mapping is shown to be a contraction, thereby establishing the existence, uniqueness, and continuous dependence on the data of these formal solutions.
Properties of the noise-induced ‘‘spurious’’ drift. II. Simplifications of Langevin equations
Authors: Deker U. , Ryter D.
Published: March 2003

In a previous paper (I) we studied the interrelations between the coefficients of Fokker–Planck equations associated to a restricted class of Langevin equations. We now discuss the general case of an arbitrary state-dependent diffusion matrix D, which, in particular, may be singular. Moreover the number of noise sources, M, is now allowed to exceed the rank L of D and even the number N of state variables. The noise-induced drift a is always found to split into a part which is determined by D alone and a contribution which must lie within the tangential subspace 𝒯∥ spanned by the noise coefficients (𝒯∥ is specified by D). This second contribution strongly depends on L: While for L=1 it vanishes, it is unrestricted (within 𝒯∥) for L?3. If L=2, a simple characterization is only found under the assumptions of I; the condition on the divergence derived therein is now proved to be sufficient. Langevin equations can often be simplified in two respects: The number of noise sources is always reducible to L (unless L=2) without change of any terms in the Fokker–Planck equation, and if either L=1 or a set of conditions holds, new variables can be introduced in such a way that only L of them are directly affected by noise. (Both reductions together lead to the form considered in I.) For L?3 any given Langevin equation can be replaced by a stochastically equivalent one, the deterministic part of which has an arbitrarily chosen component in 𝒯∥.
U(N) Integrals, 1/N, and the De Wit–’t Hooft anomalies
Authors: Samuel Stuart
Published: March 2003

Formulas for the evaluation of all U(N) integrals are derived. Tables display the results for integrands involving up to six U’s and six U°’s. The complete pole structure of De Wit–’t Hooft anomalies is unveiled. The effects of 1/N2 corrections and De Wit–’t Hooft anomalies on two-dimensional U(N) lattice gauge theories in the strong coupling 1/N expansion is discussed.
Particle trajectories in 1/r fields
Authors: Arnow M.
Published: March 2003

The trajectory of a particle subjected to an attractive 1/r force is discussed. The general mathematical solution is given. Various analytical results are derived including the representations for the trajectory function.
A concise and accurate solution for Poiseuille flow in a plane channel
Authors: Siewert C. E. , Garcia R. D. M. , Grandjean P.
Published: March 2003

The recently developed FN method of solving problems in particle transport theory is used to establish a concise and accurate solution for the flow of a rarefied gas between two parallel plates. The Bhatnagar, Gross, and Krook model is used, and numerical results are given for a wide range of the Knudsen number.
Exactly solvable eigenvalue problem with hypergeometric eigenfunctions
Authors: King Michael J. , Rohrlich Fritz
Published: March 2003

A Schrödinger equation with a momentum dependent interaction leads to exact solutions ψ∈ L2(R3,d3x) with radial parts of the wave function which are hypergeometric functions and their appropriate analytic continuations. The normalization integrals are obtained in closed form.
Gödel-like cosmological solutions
Authors: Ray Dipankar
Published: March 2003

Gödels cosmological solutions have been generalized by Novello and Reboucas [Astrophys. J. 225, 719–24 (1978)]. An attempt is made further to generalize their work. A class of solutions is obtained which are Gödel-like in the sense of Novello and Reboucas, but which have singularities at both ends of time.
Dynamics in nonglobally hyperbolic, static space-times
Authors: Wald Robert M.
Published: March 2003

Ordinary Cauchy evolution determines a solution of a partial differential equation only within the domain of dependence of the initial data surface. Hence, in a nonglobally hyperbolic space-time, one does not have fully deterministic dynamics. We show here that for the case of a Klein–Gordon scalar field propagating in an arbitrary static space-time, a physically sensible, fully deterministic dynamical evolution prescription can be given. If the cosmic censor hypothesis should be overthrown, a prescription of this sort could rescue deterministic physics.
The use of anticommuting variable integrals in statistical mechanics. II. The computation of correlation functions
Authors: Samuel Stuart
Published: March 2003

By using integrals over anticommuting variables all the correlation functions in the two-dimensional Ising model and free-fermion eight vertex model are computed. The method is quite general and applicable to other solvable systems.
The use of anticommuting variable integrals in statistical mechanics. III. Unsolved models
Authors: Samuel Stuart
Published: March 2003

The Ising model in three dimensions is fermionized by using integrals over anticommuting variables. The result is generalized to the Ising model in arbitrary dimensions and in a magnetic field. Approximation methods are developed to attack unsolved statistical mechanics models. Perturbation theory and the Hartree approximation are applied to the unsolved monomer-dimer problems. The result is a numerical solution to this unsolved class of problems. Anticommuting variables appear to be a powerful approach to unsolved problems.
Gauge symmetry and its breakdown: The example of a BCS superconductor
Authors: Bose S. K.
Published: March 2003

The mathematical structure of an infinitely extended BCS super-conductor is re-examined in the light of the theory of bundle representations. The role of the homotopy group in the BCS model is clarified. The precise characterization of the constant gauge transformation in terms of a principal fiber bundle (with discrete fiber and group) is pointed out.
An improvement of Watson’s theorem on Borel summability
Authors: Sokal Alan D.
Published: March 2003

Watson’s theorem, which gives sufficient conditions for Borel summability, is not optimal. Watson assumes analyticity and uniform asymptotic expansion in a sector ‖argz‖<π/2+ε, ‖z‖<R, with ε≳0; in fact, only the circular region Re(1/z) ≳1/R is required. In particular, one can take ε=0. This improved theorem gives a necessary and sufficient characterization of a large class of Borel-summable functions. I apply it to the perturbation expansion in the φ24 quantum field theory.
The complete symmetry group of the one-dimensional time-dependent harmonic oscillator
Authors: Leach P. G. L.
Published: March 2003

The five invariants for the time-dependent one-dimensional harmonic oscillator Hamiltonian are constructed. Using the linear transformation to the time-dependent oscillator Hamiltonian, the five invariants for the latter are obtained. The differential operators which generate the dynamical symmetry of this Hamiltonian have the same commutator relations as these of the time-independent problem. An additional three operators are obtained using the method of extended Lie groups and have the same properties as those for the time-independent problem. Thus the complete dynamical symmetry of the time-dependent problem is the eight-parameter Lie group SL(3,R).
Inverse scattering problems in higher dimensions: Yang–Mills fields and the supersymmetric sine-Gordon equation
Authors: Morris H. C.
Published: March 2003

It is shown that the notion of a prolongation structure can be extended to higher dimensions and used to determine inverse scattering problems. The relationship to generalized Lax representations is also considered. The method is illustrated on the self-dual Yang–Mills equations. A generalization to include Grassman algebra valued variables is shown to provide a scattering problem for the supersymmetric sine-Gordon equation.
Remarks on characteristic classes of four-dimensional Einstein manifolds
Authors: Xin Y. L.
Published: March 2003

Using the decomposition of the curvature tensor by means of the dual * operator, several useful expressions for characteristic classes in some kinds of Einstein manifolds are obtained. Consequently, some topological restrictions of the underlying manifolds are considered.
Approximate equilibrium states for two models of an interacting boson gas
Authors: Critchley Robert
Published: March 2003

Two models for an infinitely extended boson gas are studied. The aim is to determine approximate equilibrium states for them by minimizing the free energy density over a class of trial states. For one of the models, in which the interaction is proportional to the square of the number of particles, the equilibrium state derived from the usual thermodynamic limiting argument (the Gibbs state) is also obtained. It is seen that the set of approximate equilibrium states consists of this Gibbs state and states with the same thermodynamic properties. Using the other model, in which the particles are assumed to interact according to a delta function interaction potential, some of the problems of approximate solutions are discussed.
Geometrical gauge conditions in Yang–Mills theory: Some nonexistence results
Authors: Chodos Alan , Moncrief Vincent
Published: March 2003

We investigate the possibility of defining an ’’orthogonal’’ gauge for non-Abelian Yang–Mills theory. Such a gauge would generalize, in a geometrical way, the orthogonality features of the Coulomb gauge in electrodynamics. We show however that such a gauge does not exist (even locally) in the non-Abelian case. Specifically we prove that the tangent spaces defined at every point by orthogonality to the gauge group orbits admit no integral submanifolds. We also study the question of existence of global gauge conditions in phase space. We show that such global gauges, should they exist, would induce globally defined gauges in configuration space contradicting Singer’s result. We thus conclude (modulo certain technical points which might render Singer’s argument inapplicable to our function spaces) that global gauge conditions in phase space do not exist.
Electromagnetic scattering by an infinite inhomogeneous dielectric cylinder: New Green’s function and integral equations
Authors: Alvarez-Estrada R. F. , Calvo M. L.
Published: March 2003

The scattering of electromagnetic waves by an infinite dielectric cylinder with variable dielectric permeability presents, in general, certain mathematical difficulties regarding the construction of rigorous solutions. We give a new divergenceless tensor Green’s function, specially appropriate for cylindrical symmetry, and, in terms of it, present new scattering integral equations. We prove that the series for med by all successive iterations of those scattering integral equations converge under certain conditions. Suitable transformations lead to new integral equations with Hilbert–Schmidt kernels, which imply further rigorous results.
Reciprocal-type transformations in magnetogasdynamics
Authors: Rogers C. , Kingston J. G. , Shadwick W. F.
Published: March 2003

The equations of plane, steady nondissipative magnetogasdynamics are formulated in terms of an exterior differential system. Reciprocal-type invariant transformations are derived as symmetries of this system.
Nonperiodic oscillations of Langmuir waves
Authors: Wang P. K. C.
Published: March 2003

It is shown that the single-mode equations derived from Zakharov’s model for Langmuir turbulence in a plasma in the presence of an external spatially homogeneous electric field oscillating at the electron plasma frequency has nonperiodic chaotic solutions whose power spectra have turbulence-like features. Bounds for these chaotic solutions are derived. Typical numerical results are presented for the one-dimensional case.
A comparison of iteration schemes for Chandrasekhar H-equations in multigroup neutron transport
Authors: Kelley C. T.
Published: March 2003

An iteration scheme for the Chandrasekhar H-equations in multigroup neutron transport is shown to converge to the solution of physical interest. Moreover, the convergence is more rapid than that provided by direct iteration.
A class of dissipative evolutions with applications in thermodynamics of fermion systems
Authors: Fannes M. , Rocca F.
Published: March 2003

We construct explicitly a special class of semigroups of completely positive maps on the CAR algebra and give an application on a model of thermal contact.
Generalized back coupling rules for the Racah algebra of Gln
Authors: Sullivan John J.
Published: March 2003

Two subgroup relations for double coset matrix elements (DCME) of the symmetric group SN are derived by considering the processes of subduction and induction. The duality of outer product coupling in SN and inner product coupling in Gln identifies these as generalized back coupling rules for the Racah algebra of Gln. An iterative procedure for evaluating the DCME, once a consistent phase convention is established, is given. As an example the Racah sum formula for the Clebsch–Gordan coefficients of SU2 is derived from consideration of SN coupling only.
The KdV prolongation algebra
Authors: Shadwick W. F.
Published: March 2003

It is shown that the Wahlquist–Estabrook prolongation of the KdV equation determines a Lie algebra ℒ and that ℒ is infinite-dimensional. Finite-dimensional prolongation algebras are shown to be homomorphic images of ℒ. Two such algebras—SL(2,IR) and a five-dimensional nilpotent algebra ℋ are obtained as quotients of ℒ by ideals which are respectively maximal and maximal for a given property. ℒ determines a connection on a trivial vector bundle and the connection is flat iff the KdV equation is satisfied. The symmetries of the KdV equation are used to construct automorphisms of ℒ and it is shown that ℋ is distinguished by these automorphisms. It is demonstrated that ℋ is closely related to the three classical KdV conservation laws and that the sequential prolongation process for KdV yields only representations of ℋ.
Integration of near-resonant systems in slow-fluctuation approximation
Authors: Augusteijn Marijke F. , Breitenberger Ernst
Published: March 2003

Autonomous, conservative, nonlinear oscillatory systems of many degrees of freedom with an ’’internal resonance,’’ i.e., with the linearized (’’normal’’) frequencies tied in a near-resonant relation 𝒥giωi=−, can be completely integrated in a transparent approximation which is a variant of the ’’method of slowly variable amplitude and phase.’’ It consists in developing the nonlinear coupling into a trigonometric polynomial and dropping all terms except the most slowly varying ones on the grounds that their perturbative effects are oscillatory but essentially not cumulative. In this ’’slow-fluctuation’’ technique, the amplitudes separate off the phases; they exhibit joint extrema governed by simple conservation laws and all follow from one single quadrature. The phases also require no more than quadratures. There are various possibilities of motion with all amplitudes constant and harmonic time variation at (generally) incommensurate frequencies. The approximation does not apply if a degree of freedom which occurs to the first power in the nonlinear coupling happens to dip down towards zero amplitude; abrupt phase changes can then take place and call for a separate, accurate integration covering the critical time interval. With this sole restriction the method is entirely general. It is exact in the small-amplitude limit; at finite amplitudes it differs from the exact solution for practical purposes by no more than minor high-frequency ripples; and it yields more physical insight than any other known method for less effort.
Is the Feynman–Dyson series adequate for the aysmptotic expansion of the Green’s function of the quantum mechanical anharmonic oscillator?
Authors: Yeung Wai Bong
Published: March 2003

We discuss the asymptotic expansion of the Green’s function of the quantum mechanical anharmonic oscillator by applying the method of steepest descents in the evaluation of the corresponding Euclidean path integrals. The contributions arising from the pseudoparticle solutions are then shown to be zero.
A set of commuting operators and R(3) scalars for the complete classification of quadrupole phonon-states
Authors: De Meyer H. E. , Berghe G. Vanden
Published: March 2003

A method is developed for constructing operator forms which commute with the Casimir operators of the groups appearing in the chain U(5) ⊆SU(5) ⊆R(5) ⊆R(3) ⊆ (2), according to which the quadrupole-phonon states are usually classified. An expression for such operator is given.
Inverse scattering. I. One dimension
Authors: Newton Roger G.
Published: March 2003

This paper presents two new methods of reconstructing an underlying potential in the one-dimensional Schrödinger equation from a given S matrix. One of these methods is based on a Gel’fand–Levitan equation, the other on a Marchenko equation. A sequel of this paper will treat the three-dimensional case by similar methods.
Combinatorics, partitions, and many-body physics
Authors: Polyzou Wayne N.
Published: March 2003

Some combinatorial techniques are presented which streamline the graphical analysis used in N-body scattering theory. The basic results are derived using properties of the lattice of partitions of N particles, which naturally arises on classifying translational symmetry properties of N-body operators. Classical cumulant expansions are recovered, previously obtained results are presented from a unified point of view, and some new theorems concerning connectivity of N-body equations are presented.
Analytic properties of the critical dynamics ε expansion
Authors: Bhattacharjee Jayanta K. , Ferrell Richard A.
Published: March 2003

The ε-expansion technique for evaluating certain integrals in critical dynamics is studied in detail. The analytic properties in the complex ε plane are exploited to get improved answers at the physical value of ε. A different scheme—the ? expansion—is suggested. This has a simpler analytic structure and thus gives more reliable results.
On exact solutions of the nonlinear Heisenberg–Klein–Gordon equation in a space–time of constant spacelike curvature
Authors: Mielke Eckehard W.
Published: March 2003

A nonlinear complex scalar field theory associated with a ’’squared’’ Heisenberg–Pauli–Weyl nonlinear spinor equation is considered. In a d+1 dimensional universe of constant spatial curvature exact localized solutions for the resulting [‖φ‖2d/(d−2)−const ‖φ‖2(d−1)/(d−2)] model are constructed. For ’’soliton-like’’ solutions with quantized (nontopological) charge the field energy and the Heisenberg uncertainty principle are analyzed.
Resonance of the axial-symmetric modes in microstrip disk resonators
Authors: Chew W. C. , Kong J. A.
Published: March 2003

Three methods have been used to calculate the resonant frequencies for the axial-symmetric modes in the microstrip disk resonators which also have the application as radiating antennas. The variational Galerkin’s method provides the most accurate result for the estimation of both the real and imaginary parts of the resonant frequency shifts with judicious choices of basis functions. The iterative approach gives good results for the imaginary part of the frequency shift and very crude approximations for the real part. The perturbation formula is the most efficient in computational time and is useful for sufficiently large permittivity for the substrate material and small ratio of substrate thickness to disk radius. To illustrate the application of the circular microstrip disk as a radiating antenna, the radiation pattern for the axial-symmetric mode is also plotted.
Dynamical symmetries of rotationally invariant, three-dimensional, Schrödinger equations
Authors: Truax D. R.
Published: March 2003

All rotationally invariant, time-dependent potentials for the time-dependent, three-dimensional, Schrödinger equation are classified in terms of their dynamical symmetries. A comparison is made to their classification by kinematical algebras. The degeneracy and dynamical algebras are identified for each potential. The oscillator, constant, and Coulomb potentials are shown to be unique in the sense that their degeneracy algebras are all larger than o(3).
The linear potential wavefunctions
Authors: Maurone Philip A. , Phares Alain J.
Published: March 2003

We present an exact analytic solution to the Schrödinger equation for two particles interacting via a central linear potential of the from V (r) =V0+kr. The solution is given in terms of the generalized hypergeometric functions, and is especially useful when discussing problems where the radial parameter is small.
Lower bounds for quantum energy levels through statistical mechanics methods
Authors: Nitti L. , Pellicoro M. , Villani M.
Published: March 2003

A perturbative variational method for the calculation of lower bounds to energy eigenvalues is given for a wide class of quantum mechanical systems. The method makes use of the quantum statistical partition function and exploits the inequalities satisfied by the generalized Padè approximants. The mathematical and physical content of our approach is illustrated through a standard model.
Vertex function and crossing symmetry
Authors: Heiss W. D.
Published: March 2003

An integral equation is proposed for the vertex function occurring in the quantum-mechanical many-body problem, such that the s channel and the t channel are treated simultaneously on the same level. The equation thus provides an intricate blending of the two channels. Its solution is given in closed form, and although this is complicated, it allows the physically interesting features to be investigated numerically.
Independent subsystems in the problems of few-body interaction. Two-body scattering in force field
Authors: Komarov V. V. , Popova A. M. , Shablov V. L.
Published: March 2003

A few-body quantum mechanical system is examined. It is assumed that the scattering operator of the system is a sum of two-body potential operators. Some odd ends in the sum commute. Four-dimensional perturbation potentials and second quantized formalism is used for a solution of the problem. The scattering of two distinct particles in a force field is considered as an example. For this case, the system of the integral equations for the scattering amplitudes are obtained. These amplitudes permit us to construct channel Möller operators. It has been shown that such system has unique solution equivalent to the solution of the corresponding Schrödinger equation.
Electromagnetic test fields in the Kerr–Newman metric
Authors: Bose S.K.
Published: March 2003

The form of the electromagnetic test fields in the Kerr–Newman background, with the background metric held fixed, is closedly evaluated.
Curvatures of hypersurfaces of transitivity of Bianchi model universes
Authors: Harvey Alex
Published: March 2003

The Riemann curvatures of 2-surfaces are calculated for the spatial, 3-surfaces of transitivity of the various Bianchi models. It is found that some models are generally possessed simultaneously of both negative and positive curvature. The Bianchi V models are remarkable in that however large the degree of metric anisotropy, the curvatures are always isotropic. It is also found that Bianchi IX models, though invariably compact by virtue of the group structure, may have negative mean curvature.
A note on left-flat space–times
Authors: Newman E. T. , Tod K. P.
Published: March 2003

The theory of left-flat space–times is developed by introducing a null tetrad and imposing increasingly restrictive conditions on it. These conditions are justified from different points of view. In this way we present an elementary account of several of the different approaches to left-flat spaces.
The conformal geometry of Minkowski space: Hyperbolic world lines
Authors: Briginshaw A. J.
Published: March 2003

There is a discussion of (i) the transformation properties of hyperbolic hypersurfaces in Minkowski 4-space, (ii) the association of hyperbolic world lines in Minkowski 2-space with uniformly accelerated motion.
The Ising limit of the double-well model
Authors: Constantinescu Florin , Ströter Berthold
Published: March 2003

We prove that the pure phase correlation functions of the double-well model at small temperature in an appropriate limit case tend to the corresponding correlation functions of the classical Ising model in any dimension, extending results previously obtained by Rosen (see Introduction). We use expansion methods proposed by Glimm, Jaffe, and Spencer.
Consequences of weakening the positivity property of Wightman quantum field theories
Authors: Johnson Glenn E. , Fivel Daniel I.
Published: March 2003

A weaker form of the notion of a Wightman theory is introduced. The weakened form embodies all the requirements of a Wightman theory. However, the consequences of local commutativity are obtained without an assertion that local commutation can be stated in terms of the field operators. Models are presented that illustrate the usefulness of the weakened requirements.
Charge conservation as a concomitant of conformal motions coupled to generalized gauge transformations
Authors: Katzin Gerald H. , Levine Jack
Published: March 2003

By using a Lagrangian for an electromagnetic field with sources (in which the four-current is assumed to be specifiable without consideration of any dependence upon a fundamental charge carrying field) we have established that in any conformally flat space–time (which includes Minkowski space–time) charge conservation may be obtained as a concomitant of infinitesimal Noether symmetry mappings that are not gauge transformations of the second kind. These Noether mappings, which couple geometrical and internal symmetries, are a combination of point mappings which define conformal motions in space–time with associated generalized gauge transformations of the four-vector potential.
Invariance properties of Yang equations and applications
Authors: Brihaye Y. , Nuyts J.
Published: March 2003

Exploiting the different invariances of the Yang equations we construct an infinite sequence of solutions. These depend on a series of polynomials given by recurrence relations
Linearization of relativistic nonlinear wave equations
Authors: Flato Moshé , Simon Jacques
Published: March 2003

Some linearization theorems for relativistic nonlinear wave equations are formulated and proved. Examples are discussed and the physical meaning of such a linearization is sketched. Finally, some remarks concerning gauge theories are presented.
Operator ordering and functional integrals for Fermi systems
Authors: Suzuki T.
Published: March 2003

Operator ordering for Fermi systems is formulated generally with the aid of the Grassmann numbers. The ordering schemes are restricted to a special class called s-ordering in contrast with those for Bose systems. A relation, similar to that for Bose systems, is shown to exist between different values of the equal-time contractions in the Dyson–Wick expansions of the S matrix and different operator orderings in the interaction Hamiltonian. The S matrix is independent of the ordering scheme chosen. In the functional integral context, different orderings correspond to different discretization prescriptions for the definition of the functional integrals in terms of coherent states for Fermi operators.
The Lorentz group in the oscillator realization. II. Integral transforms and matrix elements of SO(2,1)
Authors: Basu Debabrata , Mitra D.
Published: March 2003

We use the boson realization to investigate the connection between integral transforms and matrix elements of SO(2,1) in a continuous basis for both the principal and discrete series of representations. Matrices in the SO(1,1) basis are shown to be related to an integral transform of Mellin–Barnes type.