bluuebunny/crossref_metadata_2025 huggingface dataset:
Summation of divergent series by order dependent mappings: Application to the anharmonic oscillator and critical exponents in field theory
Authors: Seznec R. , Zinn-Justin J.
Published: March 2003

We study numerically a method of summation of divergent series based on an order dependent mapping. We consider the example of a simple integral, of the ground-state energy of the anharmonic oscillator and of the critical exponents of φ34 field theory. In the case of the simple integral convergence can be rigorously proven, while in the other examples we can only give heuristic arguments to explain the properties of the transformed series. For the anharmonic oscillator we have compared our results to an accurate numerical solution (10−23) of the Schrödinger equation. For the critical exponents we have verified the consistency of our results with those obtained before from methods using a Borel transformation.
On the sound field due to a moving source in a superfluid
Authors: Murray J. C.
Published: March 2003

Expressions are obtained for the sound pressure and temperature fields due to the motion of a monopole point source in a superfluid. The acoustic power spectrum is also given for all the Mach number ranges associated with the problem.
The algebra generated by Hodge’s star and external differential
Authors: Plebañski Jerzy F.
Published: March 2003

The algebra A of all secondary operators generated by Hodge’s star and the external differential is investigated. It is established that the elements of A are spanned by 1, *d, *δ, Δ, *, d, δ, *Δ, where Δ:=−dδ+δd, with the coefficients being formal power series in Δ=dδ+δd. The multiplication law of A and its representations are studied.
On Blume’s integration of Schrödinger’s equation for a quantum system subject to random pulses
Authors: Gzyl Henryk
Published: March 2003

In this note we dispose of Blume’s objections to a recent article by Szyl. We show that he is forgetting about causality and that he makes obvious mistakes taking limits.
Scattering of a beam of particles by a potential
Authors: Dollard John D. , Friedman Charles N.
Published: March 2003

We discuss the potential scattering into a cone C in position space of a beam of particles with localized momenta distributed over a set K, and the derivation from time-dependent scattering theory of the formula ∫Kdk̃∫CdΩ σk̃(Ω) [where σk̃(Ω) is the scattering cross section] as a measure of the probability of this scattering. We make use in our discussion of a result of Dollard giving the probability of scattering into a cone for a single wavepacket.
A definition of asymptotically Minkowskian space–times
Authors: Persides S.
Published: March 2003

A definition of asymptotic flatness is given without the use of Einstein’s equations. For this we examine (a) the possible conditions on ℐ+ and their consequences and relationships, and (b) the coordinate transformations which preserve certain forms of the unphysical metric g̃ on a neighborhood of ℐ+. Roughly, a space–time (ℳ, g) is called asymptotically Minkowskian at future null infinity if it is weakly asymptotically simple, ℐ+ is isometric to ℐ+M (the ℐ+ of the Minkowskian space–time) and (a) Ω;μν=0, Ω−2Ω;μΩ;μ=−1, C̃λμρν=0 on ℐ+ or, equivalently, (b) Ω−2Ω;μΩ;μ=−1, Rμ ν=O (Ω2), Ω;[λRμ] ν +ΩR[λ ν;μ]=O (Ω4) on ℐ+. An equivalent definition is given based on the existence of a coordinate system in which, on a neighborhood of ℐ+, g̃ behaves as the conformal metric of Minkowski’s space–time and can be written in an explicitly given form.
A necessary and sufficient condition for York data to specify an asymptotically flat spacetime
Authors: Cantor Murray
Published: March 2003

This paper studies the conditions under which Cauchy data (ḡ,π̄,ν̄,T̄) for an asymptotically flat spacetime are determined by the freely specifiable York data (g, σ, ν, T) (τ=0), where trgσ=0, divgσ=8πν. It is shown that the space of such σ′s is infinite dimensional. Furthermore,it is shown that (g, σ, ν, T) determine conformally equivalent Cauchy data if and only if g is conformally equivalent to an asymptotically flat metric with nonnegative scalar curvature.
Local limit theorem for Gibbs random fields of particles and unbounded spins
Authors: Campanino Massimo , Del Grosso Gabriella , Tirozzi Brunello
Published: March 2003

In this paper we extend the results of 2 to Gibbsian systems of particles and unbounded spins, showing that under general conditions on the potential the local limit property is a consequence of the integral property for these systems. We give some applications of this result to the problem of the equivalence of the ensembles.
Solution of renormalization group recursion relations for a finite Ising chain
Authors: Rabinovitch A. , Sen R. N.
Published: March 2003

The recursion relations obtained by applying the renormalization group technique to a finite one-dimensional Ising chain with nearest-neighbor interaction and constant external magnetic field are decoupled and solved in closed form.
Potts models, percolation, and duality
Authors: Essam J. W.
Published: March 2003

A λ-state Potts model with multispin interactions is considered which includes models recently introduced by other workers in order to provide a Hamiltonian for site percolation. A duality transformation is obtained for this model which becomes the matching relation for site percolation when λ=1.
An application of Lax’s estimates to the determination of critical crystal thickness in nonlinear laser optics
Authors: Bassanini Piero
Published: March 2003

Lax’s estimates concerning the development of singularities of solutions of the Cauchy problem for 2×2 quasilinear hyperbolic systems are applied to the Maxwell system of nonlinear optics, which describes the propagation of a plane polarized laser wave through a uniaxial piezoelectric crystal, in a direction orthogonal to the optic axis, and neglecting absorption and dispersion. The ’’critical thickness’’ of the crystal, i.e., the distance after which (shock) singularities necessarily occur, is evaluated within an error of order less than 10−3, and is found to be proportional to the ratio of laser wavelength to peak amplitude times the nonlinear optical coefficient. The critical thickness appears to be ordinarily of the order of a few centimeters.
Transformation between the normal and antinormal expansions of boson operators
Authors: Shalitin Dan , Tikochinsky Yoel
Published: March 2003

We show that the expansion coefficients for the normal and antinormal forms of a boson operator are related by a simple transform.
A note on the Lorentz transformation
Authors: Steeb W.-H.
Published: March 2003

Using Lie theory of one-parameter transformation group, we show that the (linear) Lorentz transformation can be embedded into a class of nonlinear transformations.
The inverse problem for random sources
Authors: Devaney A. J.
Published: March 2003

The problem of deducing the statistical structure of a localized random source ρ (r) of the reduced wave equation from measurements of the field external to the source is addressed for the case when the measurements yield the autocorrelation function of the field at all pairs of points exterior to the source volume and the quantity to be determined is the source’s autocorrelation function Rρ(r1,r2) =〈ρ* (r1) ρ (r2) 〉.This problem is shown to be equivalent to that of determining Rρ from the autocorrelation function of the field’s radiation pattern and is found, in general, not to admit a unique solution due to the possible existence of nonradiating sources within the source volume. Notable exceptions are the class of delta correlated (incoherent) sources whose intensity profiles are shown to be uniquely determined from the data and the class of quasihomogeneous sources whose coherence properties can be determined if their intensity profiles are known and vice versa.
Structure and representation of correlation functions and the density matrix for a statistical wave field in optics
Authors: Sudarshan E. C. G. , Mukunda N.
Published: March 2003

A systematic structure analysis of the correlation functions of statistical quantum optics is carried out. From a suitably defined auxiliary two-point function we are able to identify the excited modes in the wave field. The relative simplicity of the higher order correlation functions emerge as a byproduct and the conditions under which these are made pure are derived. These results depend in a crucial manner on the notion of coherence indices and of unimodular coherence indices. A new class of approximate expressions for the density operator of a statistical wave field is worked out based on discrete characteristic sets. These are even more economical than the diagonal coherent state representations. An appreciation of the subtleties of quantum theory obtains. Certain implications for the physics of light beams are cited.
Electrical conductivity of polycrystalline materials
Authors: Willemse M. W. M. , Caspers W. J.
Published: March 2003

The problem of the determination of the macroscopic conductivity of statistically homogeneous and isotropic polycrystalline materials in terms of the principal values of the conductivity tensor of the constituent crystals is considered. A perturbation expansion, in terms of correlation functions with an optimal value of the zeroth-order estimate of the effective conductivity, is derived in which a separation is established into texture dependent and independent quantities. Consistence with the analogous expansion for the effective resistivity is demonstrated.
Plane symmetric static fields in Brans–Dicke theory of gravitation
Authors: Banerjee A. , Bhattacharya D.
Published: March 2003

An explicit form of the relationship between g00 and the Brans–Dicke scalar potential φ in the interior of a perfect fluid with an equation of state p=ερ as well as in the matter free space, is obtained assuming functional dependence of g00 on φ. Plane symmetric static perfect fluids in Brans–Dicke theory of gravitation are discussed. Explicit solutions are also obtained for a fluid with ε=1/3, that is, for a disordered radiation and some of its properties studied.
When does a projective system of state operators have a projective limit?
Authors: Ochs Wilhelm
Published: March 2003

In analogy to Kolmogorov’s classical extension theorem, we establish necessary and sufficient conditions under which a family {W(t1,⋅⋅⋅,tn)} of state operators, defined on the finite tensor products ℋt1⊗⋅⋅⋅⊗ℋtn of some family {ℋt∈T} of complex Hilbert spaces, extends to a state operator on the infinite tensor product ⊗t∈Tℋt.
The role of the Onsager–Machlup Lagrangian in the theory of stationary diffusion process
Authors: Yasue Kunio
Published: March 2003

The Onsager–Machlup Lagrangian is shown to have a direct relevance to a cost function for a stochastic control problem. It is found that any stationary diffusion process can be regarded as a solution to the stochastic control problem, that is, it is controlled optimally by the Onsager–Machlup Lagrangian. A deterministic limit of the stationary diffusion process is also obtained as a solution to an ordinary (nonrandom) control problem which is equivalent to the usual variational problem with respect to the Onsager–Machlup Lagrangian.
Solutions of the Rarita–Schwinger equation in the Kerr–Newman space
Authors: Einstein S. , Finkelstein R.
Published: March 2003

Solutions of the massless Rarita–Schwinger equation are found in a Kerr–Newman background. These solutions have arbitrary energy and arbitrary angular momentum about the axis of rotation, and in the eikonal limit define orbits that coincide with the principal null congruences. They are simple generalizations of corresponding solutions of the Dirac equations.
Relativistic Brownian motion and the space–time approach to quantum mechanics
Authors: Roy Sisir
Published: March 2003

An attempt has been made to extend the stochastic quantization procedures introduced by Nelson in the nonrelativistic case to the relativistic case in the four-dimensional Finsler space. The space–time in the microdomain is considered to be quantized and a more general concept of probability is needed to have a consistent and complete theory of quantum mechanics.
Generalized Stern–Gerlach experiments and the observability of arbitrary spin operators
Authors: Swift Arthur R. , Wright Ron
Published: March 2003

Under the assumption that we can create in the laboratory any electromagnetic field consistent with Maxwell’s equations, it is shown that an arbitrary Hermitian operator on a spin system can be measured using a suitable generalization of the Stern–Gerlach experiment. In particular, it is shown that every proposition about the spin-1 system is verifiable, answering the challenge of Hultgren and Shimony. The analysis also reveals complications in the standard Stern–Gerlach experiment of which many physicists are apparently not aware.
Five-term WKBJ approximation
Authors: Kesarwani R. N. , Varshni Y. P.
Published: March 2003

An expression is derived for the five-term WKBJ approximation.
Calculations of Dirac-spinor amplitudes by means of complex Lorentz-transformations and trace calculus
Authors: Eeg J. O.
Published: March 2003

A method for expressing spinor amplitudes M=? (p′σ′) ΓMu (pσ) in a formal covariant way and calculating them by trace calculations is described. By means of complex Lorentz transformations, an expression for u (pσ) ? (p′σ′) in terms of Dirac γ matrices, four vectors, and the complex Lorentz transformation coefficients is obtained. M can then be written as a trace of γ matrices similar to the expression for 𝒥pol‖M‖2. The method is easily extended to cases when higher spin spinors and matrices are involved.
On the stable analytic continuation with rational functions
Authors: Stefanescu I. Sabba
Published: March 2003

We discuss the use of rational approximants in the performance of stable analytic extrapolation from interior points of the analyticity domain to other interior points. We show that the instability of analytic extrapolation and the presence of noise sets an upper bound to the number of parameters that can be used in the solution. We generalize this result to other classes of functions which are used to fit experimental data and present a number of practical examples in form factor analysis.
Spherical integral representations for finite velocity conduction of an abruptly activated current through a crystal
Authors: Chee-Seng Lim
Published: March 2003

A source current is abruptly switched on within a crystalline medium with unaligned sets of permittivity and permeability principal axes. The current then propagates with finite velocity along an arbitrarily oriented conductor. The problem incorporates a partial zero condition and is tackled by Fourier analysis. The general solution for a scalar field is derived as a combination of four spherical integrals over the unit sphere. Two of these are time dependent and could represent the switch-on effect. Their time independent versions relative to the traveling current edge constitute both remaining spherical integrals. These must therefore participate in any eventual steady state and possibly contribute to ?erenkov radiation; their combination is expressible as a single spherical integral directly associated with a basic differential operator. A steady state is found to develop inside an expanding ellipsoid which retreats from the current edge.
Explicit evaluation of the representation functions of ISO(n)
Authors: Wong M. K. F. , Yeh Hsin-Yang
Published: March 2003

All representation functions of ISO(n) have been found in explicitly closed form. They can all be expressed in terms of Bessel functions and Clebsch–Gordan coefficients of SO(n) involving the most degenerate representation [k,0].
Asymptotic regularizations as an alternative to distributions for the study of singular hypersurfaces
Authors: Gravel P.
Published: March 2003

A technique designed to give shock wave surface and propagation equations of quasilinear differential systems is given which can be used when the distribution method does not lead to any practicable results. The technique, called ’’asymptotic regularizations,’’ uses a smoothing process of the discontinuous functions which becomes negligible as a parameter ω is made arbitrarily large, thus revealing the behavior of the discontinuities on the singular hypersurface. This paper is also, in a way, the answer to a conjecture formulated by Lichnérowicz to the effect that there should be a theorem relating distribution theory to asymptotic expansions on manifolds (as defined by Choquet-Bruhat) which could explain the formal similarity of their respective results when they are applied to the differential systems of some relativistic fluids.
Construction of doubly orthogonal functions
Authors: Jarem John M.
Published: March 2003

It is shown that the extremal functions associated with a general functional form a set of biorthogonal and doubly orthogonal functions. The theory is applied to antenna theory to find the doubly orthogonal functions of the E and H plane strip source antennas.
On electromagnetic multipole fields in a finite, spherically symmetric region
Authors: Steiger Arno D.
Published: March 2003

The electromagnetic eigenfields for the region bounded by two concentric spheres are discussed and compared with the corresponding eigenfields of a spherical cavity. These characteristic fields are the solenoidal and irrotational multipole solutions of the vector Helmholtz equation that satisfy the source-free boundary conditions. They constitute a complete set for the expansion of an arbitrary, square-integrable electromagnetic field, which may be generated by surface and volume sources. The frequencies of the solenoidal and irrotational eigenfields for the annular region are analyzed as functions of the radius ratio, α=r1/r2 (r1<r2 =constant), of the two concentric spheres. The results are illustrated by graphs and tables. Two relations obtained by applying the implicit function theorem to the transcendental eigenfrequency equations are also derived by calculating the work performed against the radiation pressure as the electromagnetic field is compressed adiabatically. The multipole fields are expressed in terms of vector spherical harmonics and vector spherical multipoles. Two formulas for the reduction of vector products of multipole fields to sums of vector spherical harmonics are derived.
Einstein spaces and homothetic motions. II
Authors: Halford W. D.
Published: March 2003

Algebraically special, nonflat vacuum Einstein spaces with an expanding and/or twisting geodesic principal null congruence are considered. These spaces are assumed to possess locally a homothetic symmetry as well as an isometry (one Killing vector). Nine metrics are obtained, six of which are twisting Petrov type II.
The virial series of the ideal Bose gas
Authors: Ziff Robert M. , Kincaid John M.
Published: March 2003

The radius of convergence ρR of the virial series of the d-dimensional ideal Bose gas is estimated by the method of Padé approximants, using at least thirty virial coefficients, which were numerically determined. A finite ρR is found for d=1 and 2, even though no phase transition occurs for these d. For d=3, ρR is consistent with Fuchs’ analytical bounds, and for d=4, 5, and 6, ρR is equal to the critical density ρc. These results are supported by some analytic results for the equation of state.
Space-times with geodesic, shearfree, twistfree, nonexpanding rays
Authors: Ludwig Garry
Published: March 2003

The Kundt class of metrics containing geodesic rays with vanishing divergence, shear and curl is obtained for more general Ricci tensors using the standard Newman–Penrose formalism. These solutions are then rederived using Penrose’s conformal technique, thereby clarifying their asymptotic behavior.
Lattice Green’s functions for cubic lattices
Authors: Rashid M. A.
Published: March 2003

The Green’s functions for a cubic lattice given by G(E)=1/π3 ∫0π∫0π∫0π (dx dydz)/[E−ω  (x,y,z)], where (i) ω(x,y,z)=(a1cosx+a2cosy)(1+cosz)+a3cosz, (ii) ω(x,y,z)=a1cosx(1+cosy+cosz+cosycosz) +a2cosy+a3cosz+a23cosycosz are evaluated exactly and expressed as products of two 2F1’s each of which represents a complete elliptic integral of the first kind. The expressions for the Green’s functions manifest the expected symmetries.
Covariant objects and invariant equations on fiber bundles
Authors: Kerner Richard
Published: March 2003

Let P(M4,G) be a principal fiber bundle over the Minkowskian space–time M4 with the structural group G. The group G is supposed to be a compact and semisimple Lie group. Let A be a connection form on P(M4,G) and F=DA its curvature form. Let gG be the Cartan–Killing metric on G, and gM4 the Minkowskian metric on M4. Let us define dπ : TP→TM4, the differential of the canonical projection from P onto M4. Then we can define a scalar product for any two vectors from P(M4,G): gP(X,Y)=gG(A(X),A(Y))+gM4Q (dπ(X),dπ(Y)). In this metric the horizontal and vertical subspaces of the connection A are orthogonal to each other. Next, we construct the Clifford algebra corresponding to the metric gP. The metric gP can be always diagonalized locally to give diag((3+N)+,1−), where N is the dimension of G. The lowest faithful representation of this algebra, which we call C(3+N,1) is of the dimension K=2[(N+5)/2]. This K-dimensional vector space is called the space of spinors over P(M4,G). We study the decomposition of these spinors into multiplets of Lorentz spinors. We also define the generalized Dirac equation for such a spinor, construct an explicit representation in the case of G=SU(2), and give the formulae for the mass splitting. Finally, the invariant interaction with vector fields over P(M4,G) and scalar multiplets is discussed, together with the physical implications of the coupled equations.
S–matrix for interacting A–fields
Authors: Palev Tchavdar D.
Published: March 2003

In the framework of the Lagrangian field theory a new statistics for charged tensor fields is considered. An interaction Lagrangian is constructed such that the S–matrix is unitary, covariant and causal.
Unitarity of supergravity and Z2 or Z2×Z2 or Z2×Z2×Z2 gradings of gauge and ghost fields
Authors: van Nieuwenhuizen P.
Published: March 2003

Unitarity can be proven from the usual Z2 grading of gauge and ghost fields, or from a Z2×Z2 grading, geometrically derived by Ne’eman and Thierry-Mieg, or from a Z2×Z2×Z2 grading derived here. The claim that only the Z2×Z2 grading leads to unitarity is incorrect. The opposite is shown to hold: signs due to different gradings are physically unobservable. We show how the Z2×Z2 grading follows from the Z2 grading by taking a product space.
Topological solution of ordinary and partial finite difference equations
Authors: Antippa Adel F. , Toan Nguyen Ky
Published: March 2003

Using the discrete path formalism, we obtain a topological solution for ordinary, as well as partial, linear inhomogeneous finite difference equations with variable coefficients and arbitrarily specified boundary conditions. The solution is homomorphic to a set of discrete paths constructed from a set of vectors determined by the level differences of the equation.
Equivalence of induced representations
Authors: van den Broek P. M. , Dirl R.
Published: March 2003

Equivalence of induced representations for finite groups is considered in order to determine those equivalence classes of space group representations which are linked by complex conjugation.
Factorization of operators I. Miura transformations
Authors: Fordy Allan P. , Gibbons John
Published: March 2003

The method of factorization of operators, which has been used to derive the Miura transformation of the KdV equation, is here extended to some third-order scattering operators, and transformations between several fifth-order nonlinear evolution equations are derived. Further applications are discussed.
Localized nonuniform patterns in a diffusion-reaction model with autocatalysis and the Langmuir–Hinshelwood saturation law
Authors: Bonilla L. L. , Velarde M. G.
Published: March 2003

The WKB method is used to predict the onset of localized dissipative structures in a one-dimensional reactor where a diffusion-reaction process with autocatalysis and the Langmuir–Hinshelwood (Michaelis–Menten, Holling) saturation law takes place.
Resonance of nonaxial symmetric modes in circular microstrip disk antenna
Authors: Chew W. C. , Kong J. A.
Published: March 2003

Resonant frequencies of the nonaxial symmetric modes in a microstrip disk are computed using two approaches: Galerkin’s method and a perturbative approach. The perturbative approach is good when the substrate of the microstrip disk is thin compared to its radius and when the dielectric constant of the substrate is high. Galerkin’s method can be used to compute the resonant frequency to high accuracy but the perturbative approach is more efficient for thin substrate and large dielectric constant. In applying Galerkin’s method, the problem is first cast into a vector dual integral equation using vector Hankel transform (VHT). Using VHT, it is also shown that the magnetic-wall model is only good when the substrate is of zero thickness. Using zero-order current distribution on the disk, we also derive the radiation field and radiation pattern. Also, by taking into account the radiation loss, the resonant frequencies are complex. We find discrepancies when we compare our results for the resonant frequency shifts with that obtained by quasistatic approach.
Nonlinear internal symmetry
Authors: Cahill Kevin
Published: March 2003

A theory of n scalar fields is outlined in which the equations of motion are invariant under all nonsingular global transformations of the fields amongst themselves, whether linear or nonlinear.
U(N) integral for the generating functional in lattice gauge theory
Authors: Bars I.
Published: March 2003

The one link integral or equivalently the generating functional of U(N) integrals in the lattice gauge theory is explicitly evaluated in terms of a character expansion.
Poincaré wave equations as Fourier transforms of Galilei wave equations
Authors: Gomis J. , Poch A. , Pons J. M.
Published: March 2003

The relationship between the Poincaré and Galilei groups allows us to write the Poincaré wave equations for arbitrary spin as a Fourier transform of the Galilean ones. The relation between the Lagrangian formulation for both cases is also studied.
A solution of an inverse-source problem in coherence theory
Authors: McGuire D.
Published: March 2003

An explicit solution is presented for a special case of the problem of determining the cross spectral density of a radiation source from its far-field intensity pattern. The case considered is that of a flat, circular source radiating into a half-space, where the source coherence properties exhibit statistical homogeneity and isotropy. The solution is in the form of a uniformly convergent series of hypergeometric functions that are straightforwardly related to Legendre polynomials.
Homothetic motions and the Hauser metric
Authors: Collinson C. D.
Published: March 2003

The Hauser metric is found in the canonical form obtained by Halford for a vacuum metric of Petrov type N admitting a two parameter group of homothetic motions. A result concerning the symmetries of vacuum metrics of Petrov type N possessing twisting geodesic rays is corrected.
Lateral boundary conditions for quasisteady atmospheric flows
Authors: Gordon Paul
Published: March 2003

The quasisteady model, derived by the author in an earlier paper, is extended to include lateral boundary conditions. The approach is to first specify a complete time-dependent problem, including boundary conditions; it is stressed that to each boundary condition there should be associated a precise physical assumption. Assuming the time-dependent problem is well-posed, it is then shown that the quasisteady assumption can be applied consistently to both the partial differential equations and the boundary conditions, thereby obtaining a well-posed mathematical model with time scales suitable for large scale atmospheric flows. Three types of conditions are considered at the lateral boundaries: (1) outflow, (2) inflow (driven)—velocity is specified and is essentially independent of the internal flow, (3) inflow (passive)—inflow is created primarily by the internal flow configuration. The upper boundary conditions include the two derived by the author in the earlier paper, the continuous and discontinuous boundary conditions, and a third condition, which is designed to allow the flow to propagate independently of the height of the region. Numerical solutions are obtained for various test cases, and convergence of the calculations is demonstrated. One sees that the calculations are reasonable, both from a mathematical and physical standpoint.
Time evolution operator for N interacting quantum harmonic oscillators
Authors: Kumar Sunil , Mehta C. L.
Published: March 2003

We discuss time evolution operator for N interacting quantum harmonic oscillators and determine certain conditions under which an explicit closed-form expression can be found for this time-ordered operator. The special case of N=2 is discussed, as an example.
Shift operator techniques for the classification of multipole-phonon states. VII. Self-consistent single step algorithm for R(5) O
l eigenstate and eigenvalue determination
Authors: De Meyer H. E. , Berghe G. Vanden
Published: March 2003

A previously derived set of quadratic relations in the R(5) shift operators Okl (‖k‖?3), is shown to be in such a way complete, that any O0l eigenvector and corresponding eigenvalue can be unambiguously obtained in a step by step calculation which starts at the highest angular momentum state. Such a calculation strictly follows the pattern of an algorithm, which unlike the tree generating mechanism, has unlimited applicability. Previous knowledge of the existence and of the degeneracy of a state not being required the algorithm itself accounts for the l multiplicity of states and is therefore called self-consistent.
On a connection between radial Schrödinger equations for different power-law potentials
Authors: Johnson Bruce R.
Published: March 2003

A general correspondence is given between the radial Schrödinger equations (in arbitrary dimensions) for confining- and inverse-power law potentials. The wave functions and Green’s functions of the two types of potentials are shown to differ by little more than a change of variable (a special case being the well-known equivalence of the harmonic oscillator and Coulomb problems). This gives rise to relationships between the discrete state eigenvalues and matrix elements. Following the lines of a recent paper by Gazeau, the relevance of this correspondence to Sturmian representations for power law potentials is examined. Generalizations are considered for potentials containing a linear combination of powers of r.
On the uniqueness of the equilibrium configurations of slowy rotating relativistic fluids
Authors: Künzle H. P. , Savage J. R.
Published: March 2003

We consider the equations of a general relativistic space-time that is stationary, asymptotically Euclidean, diffeomorphic to R4 and consists of an exterior vacuum solution and an interior perfect fluid in rigid motion. If one requires further that the solution be close to the static spherically symmetric ones (in the sense of a suitable topology on the set of stationary space–time metrics) it is shown that for a given equation of state ρ( p) and given total mass m and (small) angular momentum J there are no smooth curves of physically distinct global axially symmetric solutions. In view of a recent result of Lindblom that all such space-times are axisymmetric this result is quite general. The method is a generalization of the one used to prove (in a ’’local’’ sense) the uniqueness of the spherical solution in the static case.
Properties of the noise-induced ‘‘spurious’’ drift. I.
Authors: Ryter D. , Deker U.
Published: March 2003

The coefficients of Fokker–Planck equations associated to Langevin equations (LE) may be interrelated, since both the diffusion matrix D and the noise-induced drift a are derived from the same coefficients of the LE. If D is regular and if furthermore its dimension M equals the number of independent noise sources (conditions to be dropped in the subsequent paper II), a is uniquely determined by D if M=1 and independent of D if M?3. For M=2, a splits into a nontensor part which is uniquely determined by D and a vector field with given divergence. The result for M?3 means that to any LE with noise terms specified by their covariance matrix only, there exists another stochastically equivalent LE with a fully arbitrary deterministic part. As a byproduct it is shown that any given a can be removed by a nonlinear change of the state variables.
Lie groups, spin equations, and the geometrical interpretation of solitons
Authors: Reiter George
Published: March 2003

The integrable evolution equations imbeddable in SU (2) are shown to have two gauge equivalent forms; the AKNS form, and a spin form for which the field is a three-dimensional vector of unit length. These equations are the compatibility conditions for the existence of a bilocal Lie group in two distinct frames of reference. These frames are associated with moving bases on surfaces formed by the motion of the strings introduced by Lamb. Both forms of the evolution equation are derivable from a locality assumption for the generators of the bilocal Lie group. The assumption is sufficient to distinguish between integrable and nonintegrable systems imbedded in SU (2).
Group actions on principal bundles and invariance conditions for gauge fields
Authors: Harnad J. , Shnider S. , Vinet Luc
Published: March 2003

Invariance conditions for gauge fields under smooth group actions are interpreted in terms of invariant connections on principal bundles. A classification of group actions on bundles as automorphisms projecting to an action on a base manifold with a sufficiently regular orbit structure is given in terms of group homorphisms and a generalization of Wang’s theorem classifying invariant connections is derived. Illustrative examples on compactified Minkowski space are given.
A matrix representation of the translation operator with respect to a basis set of exponentially declining functions
Authors: Filter Eckhard , Steinborn E. Otto
Published: March 2003

The matrix elements of the translation operator with respect to a complete orthonormal basis set of the Hilbert space L2(R3) are given in closed form as functions of the displacement vector. The basis functions are composed of an exponential, a Laguerre polynomial, and a regular solid spherical harmonic. With this formalism, a function which is defined with respect to a certain origin, can be ’’shifted’’, i.e., expressed in terms of given functions which are defined with respect to another origin. In this paper we also demonstrate the feasibility of this method by applying it to problems that are of special interest in the theory of the electronic structure of molecules and solids. We present new one-center expansions for some exponential-type functions (ETF’s), and a closed-form expression for a multicenter integral over ETF’s is given and numerically tested.
Infinities of polynomial conserved densities for nonlinear evolution equations
Authors: McGuinness Mark J.
Published: March 2003

The infinities of polynomial conserved densities for several nonlinear evolutiopn equations are investigated using Noether’s theorem, and are identified as energy or momentum densities of higher-order enveloping equations. A recursive operator formula is derived for the densities.
The nonabelian Toda lattice: Discrete analogue of the matrix Schrödinger spectral problem
Authors: Bruschi M. , Manakov S. V. , Ragnisco O. , Levi D.
Published: March 2003

We investigate the discrete analog of the matrix Schrödinger spectral problem and derive the simplest nonlinear differential-difference equation associated to such problem solvable by the inverse spectral transform. We also display the one and two soliton solution for this equation and tersely discuss their main features.
An addition theorem for vector Helmholtz harmonics
Authors: Borghese F. , Denti P. , Toscano G. , Sindoni O. I.
Published: March 2003

An addition theorem for the vector solutions of Helmholtz equations under translation of the coordinate axes is proposed and its results compared with those of a previous addition theorem for Hansen’s M and N vectors. The resulting comparisons are also separated into their radial and transverse components.
K-surfaces in the Schwarzschild space-time and the construction of lattice cosmologies
Authors: Brill Dieter R. , Cavallo John M. , Isenberg James A.
Published: March 2003

We investigate spacelike spherically symmetric hypersurfaces of constant mean curvature K (which we call K-surfaces) in spherically symmetric static spacetimes. We obtain the differential equation satisfied by these surfaces from a variational principle. The spacetime Killing vector leads to a first integral in the form of a conservation of energy for a particle moving in an effective potential. An embedding of the K-surfaces’ intrinsic geometry in flat space likewise follows from an effective potential motion. We apply the formalism to the Schwarzschild solution, and display results of numerical integrations for a variety of K-surfaces and their flat space embeddings. We use these to construct ’’lattice’’ cosmological models, and obtain a foliation of K-surfaces of such models with large scale behavior of both the open and closed Friedmann type.
Static gravitational and Maxwell fields in the general scalar tensor theory
Authors: Banerjee A. , Duttachoudhury S. B.
Published: March 2003

The expression for g00 as a function of the scalar field Ψ is obtained in the general scalar tensor theory of gravitation proposed by Nordtvedt and later discussed by Barker, assuming that there exists a functional relationship between them. Exact solutions for a plane symmetric static gravitational field are also obtained in this theory. Further the calculations are extended for the static electrovac with the assumption that here both g00 and the scalar field Ψ are functions of the electrostatic potential φ, and the results are different from those previously obtained in the corresponding situation of Brans–Dicke theory.
Dynamical symmetry breaking in the Lewis–Riesenfeld oscillator
Authors: Günther Neil J.
Published: March 2003

Dynamical realization is given to the generator responsible for breaking the usual SU(3) invariance symmetry in the case of the Lewis–Riesenfeld time-dependent oscillator: H (t) = 1/2 𝒥3i[pipi+w2(t) qiqi]. This is achieved by finding a simple expression for the time-dependent Hamiltonian in the interaction picture: H=Ho+gH1. The breaking interaction is shown to transform as (6⊕6̄) of SU(3). Time-dependent dilations relate the broken Hamiltonian to the Lewis–Riesenfeld form. This scaling generates the algebra of the Weyl group and its role in oscillator noninvariance symmetries is considered.
The physical optics method in electromagnetic scattering
Authors: Asvestas John S.
Published: March 2003

The purpose of this work is to analyze the physical optics method as applied to electromagnetic scattering theory and to point out its physical and mathematical drawbacks. The main conclusions are (1) that the boundary values assumed by physical optics lead to electromagnetic fields that do not satisfy the finiteness of energy condition and, as a consequence, that integral representations of these fields cannot be obtained via the divergence theorem; (2) that the commonly accepted representations are not solutions of the physical optics problem because they fail to reproduce the assumed discontinuities of the fields on the scatterer. Despite the above conclusions, the present work should not be construed as an attempt to discredit the method but rather as an effort toward a better understanding of it. As it is well known, there have been a number of occasions in which physical optics has yielded quite satisfactory results.
On the infrared problem in nonrelativistic quantum electrodynamics
Authors: Wreszinski W. F.
Published: March 2003

Following a suggestion of Hepp and Lieb, it is shown rigorously that the infrared divergences which occur in the problem of thermodynamic stability of a system of atoms (with a finite number of levels) interacting with an ultraviolet-cutoff quantized radiation field are entirely removed upon inclusion of the term in A2 in the Hamiltonian, in the special case where the atoms are placed at the points of a regular lattice.
A study of the completeness properties of resonant states
Authors: Romo W. J.
Published: March 2003

The completeness properties of the discrete set of bound state, virtual states, and resonant states of a Hamiltonian H is investigated, where H describes a system in which a single nonrelativistic-spinless particle moves in a central cutoff potential. A limited form of completeness is obtained. It is shown that the convergence of the resulting ’’completeness series’’ is very sensitive to the detailed mathematical structure of the potential.
Equilibrium of slowly rotating relativistic fluids
Authors: Künzle H. P. , Savage J.R.
Published: March 2003

The equilibrium conditions of a relativistic fluid with nonzero viscosity and heat conduction coefficients are known to reduce to Einstein’s equations for a barotropic perfect fluid in rigid motion. We consider here the linearization of these equations on a static spherically symmetric background and show that the solution space is three-dimensional (parametrized by the angular velocity vector, for example), provided the exterior vacuum region is asymptotically Euclidean and the equation of state ρ=ρ (p) (satisfying ρ⩾p⩾0 and dp/dρ≳0) is fixed, as well as the central values of the pressure and the gravitational potential. In the exterior region this solution agrees with the Kerr solution, linearized on the Schwarzschild background. This result is the first step towards proving a certain uniqueness of the possible equilibrium configurations of slowly rotating relativistic fluids. It is obtained using invariantly defined global conditions, without assuming the existence of particular coordinate systems.
Equilibrium states for mean field models
Authors: Fannes M. , Spohn H. , Verbeure A.
Published: March 2003

We rigorously characterize the KMS and the limiting Gibbs states for mean field models. As an application we prove the convergence of the Gibbs states for the Dicke Maser model in the infinite volume limit.
The dominant partition method
Authors: Dixon Robert M. , Redish Edward F.
Published: March 2003

Employing the L’Huillier, Redish, and Tandy (LRT) wave function formalism we develop a partially connected method for obtaining few-body reductions of the many-body problem in the LRT and Bencze, Redish, and Sloan (BRS) formalisms. This method for systematically constructing fewer body models for the N-body LRT and BRS equations is termed the dominant partition method (DPM). The DPM maps the many-body problem to a fewer-body one using the criterion that the truncated formalism must be such that consistency with the full Schrödinger equation is preserved. The DPM is based on a class of new forms for the irreducible cluster potential, introduced in the LRT formalism. Connectivity is maintained with respect to all partitions containing a given partition which is referred to as the dominant partition. Degrees of freedom corresponding to the breakup of one or more of the clusters of the dominant partition are treated in a disconnected manner. This approach for simplifying the complicated BRS equations is appropriate for physical problems where a few-body reaction mechanism prevails. We also show that the dominant-partition-truncated form of the BRS equations may be obtained by distributing the residual interaction in the exit channel in a manner consistent with the dominant partition truncations of the irreducible cluster potential.
Initial value problem for two oscillators interacting with electromagnetic field
Authors: Rza̧żewski K. , Żakowicz W.
Published: March 2003

We solve exactly equations of motion for two charged harmonic oscillators interacting with electromagnetic field. Detailed analyses of the system’s behavior for small times is presented. We go beyond the one pole approximation. A simple model for the so-called soft mode instability is given. The scattering cross section is derived from time dependent solutions.
Finite subgroups of the generalized Lorentz groups O(p,q)
Authors: Patera J. , Saint-Aubin Y. , Zassenhaus H.
Published: March 2003

An algorithm is developed which permits us to construct all the finite subgroups of the generalized Lorentz groups O(p,q) up to an O(p,q) conjugation. The application of this algorithm to the Lorentz group O(3,1) is outlined, and the full list of finite subgroups compiled.
All solutions to a nonlinear system of complex potential equations
Authors: Collins C. B.
Published: March 2003

This work employs the powerful geometric methods previously developed in order to determine all solutions of the nonlinear system (∇γ)2≡∇γ⋅∇γ=f (γ), (∇2γ)2−(1/2)(N+2) f′ (γ) ∇2γ+(1/4)(N+1)[f′ (γ)]2 −(1/2) Nf (γ) f\ (γ) =−N∇γ⋅∇ (∇2γ), where f (γ) is an arbitrarily assigned function and N is an arbitrary constant. The circumstances are determined under which compatible solutions exist, not only when γ is real, but also when γ is complex, and all of the corresponding solutions are found. This is done by referring the system of equations to a set of coordinates based on the (real or complex) equipotential surfaces of constant γ. The relationship between the solutions and the geometry of the equipotential surfaces is examined, and a close association is discovered between the set of allowable equipotential surfaces and the class of surfaces of constant total (Gaussian) curvature. These results are analogous to those in Collins, Math. Proc. Camb. Phil. Soc. 80, 165–87 (1976), where the system under study was associated with equipotentials of constant radii of principal normal curvature. The geometrical method used throughout is remarkable in that it yields a knowledge of all solutions of the given system. It thereby offers the possibility of application to a wide variety of fields in physics where similar systems of equations are encountered.
Complex potential equations, special relativity, and complexified Minkowski space–time
Authors: Collins C. B.
Published: March 2003

We obtain a number of results on null geodesic congruences in Minkowski space–time M. It is first shown that the only time-invariant hypersurface-orthogonal shear-free null geodesic congruences in M are those that generate either null hyperplanes or null cones. This result is derived in two interesting and quite distinct ways. One method of proof uses Kerr’s theorem. The other method proceeds by showing that the equations specifying the class of congruences can be written in the form (∇γ)2≡∇γ⋅∇γ=1, and (∇2γ)2=−2∇γ⋅∇ (∇2γ), where γ is a potential and the operators ∇ and ∇2 refer to 3-dimensional Euclidean space. The complexified version of this system of equations has been studied previously by the author [preceding paper, J. Math. Phys. 21, 240 (1980)]. Hypersurface-orthogonal shear-free null geodesic congruences in complexified Minkowski space–time are then investigated, and a close association is discovered between the set of such congruences and the set of (generally, non-hypersurface-orthogonal) shear-free null geodesic congruences in M.
Bäcklund transformations and the symmetries of the Yang equations
Authors: Morris Hedley C.
Published: March 2003

Using the terminology of Jet bundles, we determine generalized symmetries of the Yin equations f (fyȳ+fzz̄)−fyfȳ −fzfz̄−eygȳ−εzgz̄ =0, f (eyȳ+ezz̄)−2eyfȳ −2ezfz̄=0, f (gyȳ+gzz̄)−2gȳ−2gȳfy −2gz̄fz=0, which are equivalent to the self-dual Yang–Mills equations in a particular gauge. The Bäcklund transformations of Corrigan et al. are derived and discussed as generalized symmetries.