bluuebunny/crossref_metadata_2025 huggingface dataset:
Integrability and the Painlevé property for low-dimensional systems
Authors: Ramani A. , Dorizzi B. , Grammaticos B. , Bountis T.
Published: March 2003

We examine a system described by two first-order nonlinear differential equations from the point of view of integrability. The singularity analysis in the complex-time plane is used to investigate the Painlevé property, which according to the Ablowitz–Ramani–Segur conjecture is a prerequisite for integrability for infinite-dimensional systems. We show that for such low-dimensional systems, the Painlevé analysis is still a most useful guide, but integrable cases also exist which do not possess the Painlevé property.
Higher-order symmetries of the compressible one-dimensional isentropic fluid equations
Authors: Verosky John
Published: March 2003

The equations of compressible one-dimensional isentropic flow are shown to have infinitely many higher-order symmetries by means of recursion operators. Furthermore, a new first-order conserved functional is found to be associated with a third-order symmetry via Noether’s theorem.
A Galerkin method to cylindrical KdV equations
Authors: Chen Fengsu
Published: March 2003

The variational method has been used to obtain approximate solutions of the nonlinear Klein–Gordon equation and KdV equation by Hsieh, and the numerical solitary wave solutions of cylindrical nonlinear KdV equations by Chwang and Wu. The author has already used the Galerkin method to obtain approximate solutions of some highly nonlinear KdV equations and Schrödinger equations. In the present paper, we shall employ the Galerkin method to obtain approximate solutions of cylindrical nonlinear equations.
On a Bäcklund transformation and scattering problem for the modified intermediate long wave equation
Authors: Satsuma Junkichi , Taha Thiab R. , Ablowitz M. J.
Published: March 2003

In this paper, we give a Bäcklund transformation, an associated linear scattering problem, and a method for finding the conservation laws for the so-called modified intermediate long wave equation. This equation reduces to the modified Korteweg–deVries equation in the shallow water limit.
Geometry of the dynamical systems with time-dependent constraints and time-dependent Hamiltonian: An approach towards quantization
Authors: Hamoui Adnan , Lichnerowicz André
Published: March 2003

The quantization of a dynamical system with time-dependent constraints or time-dependent Hamiltonians presents particular difficulties not only from a technical, but also from a theoretical point of view. We give here an approach to the evolution of such a quantum system in terms of star products on symplectic or canonical manifolds. These star products are particular deformations of the usual product of functions, deformations that start with the Poisson bracket. The introduction of the star products corresponds to a generalization of the Weyl–Wigner quantization on a flat phase space. This approach leads to the introduction of ‘‘two times’’ denoted t and τ, playing different roles; the time t plays the role of a geometrical time corresponding to the control, while the other, τ, which parametrizes the evolution, plays the role of a dynamical time. The classical as well as the quantum results point out the role played by the variable (t+τ). This reflects the coherence of the formalism.
Eigenvalues of anharmonic oscillators from a variational functional method
Authors: Arteca Gustavo A. , Fernández Francisco M. , Castro Eduardo A.
Published: March 2003

Analytic expressions for the eigenvalues of anharmonic oscillators are obtained from a simple variational method. Numerical results show striking accuracy in the whole range of the characteristic anharmonic oscillator parameters. The procedure also allows one to classify the set of states in three classes and yields a way of defining clearly the anharmonic and harmonic regime
A vector wave equation for neutrinos
Authors: Reifler Frank
Published: March 2003

The Cartan map gives an isomorphism between spinors and isotropic vectors. Isotropic vectors F=E+iH satisfy the condition F ⋅ F=0. We show that via the Cartan map, the particle current for neutrinos is given by j0=‖E‖, j=E×H/‖E‖, and the neutrino wave equation becomes D0F=iD×F−(DF) ⋅ v, where v=j/j0=E×H/E2=velocity field, D0=i(h/2)(∂/∂t)−V0,D=−i (h/2)∇−V, where h=Planck’s constant and V=(V0,V)=external potential. This wave equation preserves the isotropic condition, and like the equivalent Dirac equation, causes j to be the conserved current. We show that the isotropic restriction on the vector field F accounts for the observable properties of a neutrino in an external field, in particular, for the observed spectrum of the energy, momentum, angular momentum, spin, velocity, and position operators.
The Hamilton–Jacobi theory of De Donder and Weyl applied to some relativistic field theories
Authors: von Rieth J.
Published: March 2003

The Hamilton–Jacobi (HJ) theory for fields initiated by De Donder and Weyl is applied to Klein–Gordon, Dirac, and gauge fields. Conserved HJ currents are derived for each parameter on which a solution of the field equations depends, and the concept of a ‘‘complete’’ integral of the De Donder–Weyl HJ equation is discussed from which solutions of the field equations may be constructed.
Causal transformations of Wightman localizations
Authors: Castrigiano D. P. L.
Published: March 2003

Causal transformations of Wightman localizations are studied without assuming further symmetries (e.g., Galilean or Lorentz invariance). They are characterized completely by a condition which imposes analyticity and restricted growth on the matrix elements and implies a close connection between the helicity components. This condition is applied to obtain causal time evolutions. Spin-0 and spin- 1/2 systems and, generally, all simple ystems of definite spin are considered in detail. The factorizing causal time evolutions are determined completely.
The reduced Dirac Green function for the Coulomb potential
Authors: Hylton D. J.
Published: March 2003

The radial reduced Dirac Green function for the Coulomb potential is calculated for all bound states. The result is written in a form suitable for numerical calculations. The nonrelativistic limit agrees with the known radial reduced Schrödinger Green function for the Coulomb potential. Also obtained are the derivatives with respect to the energy of the relativistic and nonrelativistic radial solutions evaluated at any eigenvalue.
The eigenvalue problem for ‘‘arrow’’ matrices
Authors: Walter O. , Cederbaum L. S. , Schirmer J.
Published: March 2003

The eigenvalue problem for a particular class of ‘‘arrow’’ matrices Z=(ABB†γC), where A is a Hermitian N×N matrix, C a real diagonal M×M matrix, B an arbitrary complex N×M matrix, and γ a real number, is investigated by means of a partitioning technique. Both Hermitian (γ=1) and non-Hermitian (γ≠1) arrow matrices Z are studied. The one-dimensional case (dimension N of A equal to 1) is briefly reviewed and a detailed treatment of the multidimensional case (N>1) is presented. For Hermitian arrow matrices, the analysis leads to a new algorithm for computing the eigenvalues and eigenvectors of Z which is particularly efficient if M≫N.
Infinitesimal operators and structure of the most degenerate representations of the groups Sp( p+q) and Sp( p, q) in an Sp( p)×Sp(q) basis
Authors: Klimyk A. U. , Gruber Bruno
Published: March 2003

Explicit expressions are derived for the infinitesimal operators of the representations πλ of the most degenerate series of the group Sp( p, q) and for the irreducible unitary representations of the group Sp( p+q) with highest weight (m, m, 0, ...,0) with respect to an Sp( p)×Sp(q) basis. The Sp( p)×Sp(q) basis can be chosen arbitrarily. The irreducibility conditions for the representations πλ and the structure of the reducible representations πλ are discussed. All the unitary irreducible representations of the most degenerate series of Sp( p, q) are obtained. It is shown that there are four series of unitary representations (principal, supplementary, discrete, and ladder).
Realizations of F4 in SO(3)⊗SO(3) bases and structural zeros of the 6 j-symbol
Authors: De Meyer H. , Vanden Berghe G. , Van der Jeugt J.
Published: March 2003

The decompositon of F4 irreps in the group chains F4⊇SO(3)⊗G2⊇SO(3)⊗SO(3) and F4⊇SO(3)⊗Sp(6)⊇SO(3)⊗SO(3) is considered. In both cases a realization of the F4 Lie algebra in terms of SO(3)⊗SO(3) tensor operators is established. From these, the nontrivial vanishing of certain 6 j-coefficients is explained.
Positivity of the Bondi energy
Authors: Reula O. , Tod K. P.
Published: March 2003

We give a new proof that the Bondi momentum is time-like and future directed. This is done by extending a theorem showing the existence of solutions of Witten’s equation on a complete, asymptotically flat surface, to the case where the surface is asyptotically hyperbolic and spans a cut Ŝ of ℐ+. By choosing appropriate boundary conditions the positivity of the Bondi energy is also shown for the case where the surface is no longer free of inner boundaries but is internally bounded by the union of a finite number of marginally trapped surfaces. This argument also applies to the case of asymptotically flat surfaces.
Hamiltonian formulation of gravitating perfect fluids and the Newtonian limit
Authors: Künzle H. P. , Nester J. M.
Published: March 2003

The canonical formalism is applied to self-gravitating perfect fluids with particular emphasis on recovering the correct nonrelativistic limit also in (quasi-) Hamiltonian form. We use essentially Lagrangian coordinates by considering the fluid defined by a map from space-time into a three-dimensional material manifold which is equipped with a volume element representing physically the matter (baryon number) density. By eliminating the coordinate freedom in this material space the usual matter conservation and (relativistic) Euler equations are recovered in a (3+1)-dimensional formalism which makes it very easy to compare them to their nonrelativistic limits. By splitting the 3-metric and its canonical momenta into a conformal part and the determinant we arrive at a system of evolution and constraint equations for the gravitational field that also has a well-defined Newtonian limit provided the geometric version of the Newtonian theory is also cast into an analogous (3+1)-dimensional form. Some of the evolution equations of the relativistic theory, however, become additional constraints in the limit which represents the freezing of the gravitational (or radiation) degrees of freedom. We then use this formalism to rederive the first-order post-Newtonian approximation and obtain the standard results in a flexible geometrical form since no gauge or coordinate conditions need be imposed in advance.
Separation of variables and symmetry operators for the neutrino and Dirac equations in the space-times admitting a two-parameter abelian orthogonally transitive isometry group and a pair of shearfree geodesic null congruences
Authors: Kamran N. , McLenaghan R. G.
Published: March 2003

We show that there exist a coordinate system and null tetrad for the space-times admitting a two-parameter abelian orthogonally transitive isometry group and a pair of shearfree geodesic null congruences in which the neutrino equation is solvable by separation of variables if and only if the Weyl tensor is Petrov type D. The massive Dirac equation is separable if in addition the conformal factor satisfies a certain functional equation. As a corollary, we deduce that the neutrino equation is separable in a canonical system of coordinates and tetrad for the solution of Einstein’s type D vacuum or electrovac field equations with cosmological constant admitting a nonsingular aligned Maxwell field and that the Dirac equation is separable only in the subclass of Carter’s [Ã] solutions and the Debever–McLenaghan null orbit solution A0. We also compute the symmetry operators which arise from the above separability properties.
The multipole expansion of stationary Einstein–Maxwell fields
Authors: Simon Walter
Published: March 2003

The stationary Einstein–Maxwell equations are rewritten in a form which permits the introduction of (Geroch-) multipole moments for asymptotically flat solutions. Some known theorems on the moments in the stationary case are generalized to include Einstein–Maxwell fields.
Material sources in the nonsymmetric Kaluza–Klein theory
Authors: Kalinowski M. W.
Published: March 2003

In this paper, we deal with material sources in the nonsymmetric Kaluza–Klein theory. We consider phenomenological sources with nonzero fermion current, nonzero electric current, and nonzero spin–density tensor. From the Palatini variational principle we find equations for the gravitational and electromagnetic fields. We also consider the geodesic equation in the theory and the equation of motion for charged test particles.
Dynamical properties of non-Markovian stochastic differential equations
Authors: Hernández-Machado A. , San Miguel M.
Published: March 2003

We study nonstationary non-Markovian processes defined by Langevin-type stochastic differential equations with an Ornstein–Uhlenbeck driving force. We concentrate on the long time limit of the dynamical evolution. We derive an approximate equation for the correlation function of a nonlinear nonstationary non-Markovian process, and we discuss its consequences. Non-Markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the Markovian limit. Several examples are discussed in which the relaxation time increases with respect to the Markovian limit. For a Brownian harmonic oscillator with fluctuating frequency, the non-Markovicity of the process decreases the domain of stability of the system, and it can change an infradamped evolution into an overdamped one.
Exact solution for the discrete end-to-end intrachain memory function of a reptating polymer chain
Authors: Bernard Douglas A. , Noolandi Jaan
Published: March 2003

This article considers the dynamics of polymer chains which are subject to entanglement constraints. We give the exact solution for the end-to-end intrachain memory function of a finite, N-link bead-rod chain which diffuses in configuration space according to the reptation model described by the stochastic earthworm equations of Doi and Edwards. Defining the appropriate two-point spatial correlation function, we develop a recursion expression for its Fourier transform, the equal-time structure factor, and evaluate this expression using a generating function method. The nonuniversal, N-dependent form of the resulting memory function is illustrated and compared with the universal form achieved in the continuum limit for N→∞.
Sum rule for products of Bessel functions: Comments on a paper by Newberger
Authors: Bakker M. , Temme N. M.
Published: March 2003

Recently, Newberger considered a series of Bessel functions with as a special case the form ∑(njJ2n(z))/(n+μ). The interesting point is that he obtained new explicit expressions for the sum of the series. In this note we point out that some results of Newberger are not correct, especially the results obtained by the principle of analytic continuation. Our remarks include a correction for his important result for the series ∑Jn(z)Jn−m(z)/(n+μ).
Projection operator techniques in physics
Authors: Brittin Wesley E. , Sakakura Arthur Y.
Published: March 2003

A systematic account of projection operators (projectors) and orthogonalization techniques together with applications to selected areas of physics is presented. This unified approach is shown to have advantages over other approaches in that the mathematical statements are more precise. The mathematical level, however, is aimed at the practicing physicist and lies between rigorous mathematics and current use in physics. Further, the techniques presented have practical applications as is demonstrated by examples in the quantum theory of measurement, in the relationship between second quantization and configuration space techniques, and in an account of generalized Wannier and Bloch functions. Attention is paid to the problem of construction of orthogonal projection operators (orthogonal projectors). The construction of orthogonal projectors even in approximate form would allow the solution of many practical problems ranging from the eigenvalue spectrum problem to the construction of states for many-body systems. One can almost say that any problem in quantum mechanics can be formulated as a problem involving the construction of projectors.
Mean curvature and radiation field in SO(2) electrodynamics
Authors: Fauth D. , Sorg M.
Published: March 2003

The trivial bundle of orthonormal frames over flat space-time is decomposed into two subbundles with structure groups SO(1,1) and SO(2), respectively. The curvature in the SO(2) bundle is identified with the electromagnetic field. It is shown that on certain conditions imposed upon the bundle decomposition the exterior derivative of the mean curvature 1-form in the SO(2) bundle is equal to the curvature 2-form in the SO(1,1) bundle. These conditions are (i) the Frobenius integrability of certain distributions generated by the splitting of the associated tangent bundle, and (ii) the vanishing of the mean curvature in the SO(1,1) bundle. For a single point charge the curvature in the SO(1,1) subbundle is identical to the radiation part of the Liénard–Wiechert field.
Equivalent random force and time-series model in systems far from equilibrium
Authors: Kishida Kuniharu
Published: March 2003

Under the condition that observed time-series data is given, a stochastic Markovian equation for a physical system can be transformed into an observable non-Markovian equation used in the time-series analysis. The physical random force satisfying the fluctuation dissipation theorem is also transformed into a stochastically equivalent random force in the derivation of the time-series model of observable variables. Statistical quantities, i.e., correlation and power spectral density functions for observable variables, can be expressed not only by the physical random force, but also by the equivalent random force. A relation between the variance of physical random force and that of equivalent random force is also found.
A bounded convergence theorem for the Feynman integral
Authors: Johnson G. W.
Published: March 2003

We give a bounded convergence theorem for the Feynman integral for the class of bounded, measurable potentials.
On a class of nonintegrable equations in 1+1 dimensions with factorized associated linear operators
Authors: Cornille Henri
Published: March 2003

We consider a class of nonintegrable nonlinear equations with powerlike nonlinearities KN, ∂xKN (K being the solutions and N≥2, N integer) building explicitly their exponential type bisolitons. The denominators of the bisolitons have no soliton couplings, and the linear differential operators of the linear part of the equations are factorized operators. We extend our study to a larger class of nonlinearities: polynomial nonlinearities which are linear combinations of powerlike nonlinearities. We study the two extreme possibilities. Either the bisoliton is specific of a mixed nonlinearity, not being a solution of any component nonlinearity, or the bisoliton is common to all components. Different properties occur depending whether the components are KN or ∂xKN. For KN nonlinearities, in order to understand the origin of the factorization of the linear operators, we give a criterion which is easily checked at an almost entirely linear level of constraints. We conjecture that all possible bisolitons are of the type studied here. Finally for KN and ∂xKN we enlarge the class of bisolitons found in previous works.
On some partitions of hypergraphs and cumulants having applications in statistical mechanics
Authors: Royer Antoine
Published: March 2003

A hypergraph H={E1,E2,...,En} is a set of sets; the sets Ei are called the edges, and the elements of V(H)≡Uni=1Ei the vertices of H(if each edge contains only two vertices, we have an ordinary graph). Hypergraphs and cumulants over hypergraphs occur in various statistical mechanical problems. A cumulant over H involves a sum over partitions of the set H, whence the motivation for studying partitions of hypergraphs and related notions. Writing Ei - - - -k-(v) Ej if there exist at least k∈N vertex-disjoint paths between the edges Ei and Ej, we show that - - - -k-(v) is an equivalence relation on H, and denote by P̂kH the partition of H into its (- - - -k-(v)) equivalence classes. H is said to be k-(v) connected if every pair of edges is in the relation - - - -k-(v); we show that there exists a coarsest partition of H into k-(v) connected blocks, and denote it by P̂′kH. Given a partition P(H)={H1,H2,...,Hp} of H, we denote, for any real number κ, σκ[P(H)]≡∑pj=1(‖V(Hj)‖ −κ), σκ[P(H)] ≡∑pj=1(‖V(Hj)‖ −κmkP̂1Hj‖), where ‖V(Hj)‖ is the number of vertices and ‖P̂1Hj‖ the number of connected components of Hj. We introduce ‘‘subcumulants’’ over H, which involve only partitions of H for which σ′κ has the same value. The subcumulants corresponding to minimum values of σκ, κ∈R, are of practical interest (especially the cases κ=0 and 1). We accordingly study the set π′0κ(H) of partitions which minimize σκ; this is simply related to the set π0κ(H) of partitions which minimize σκ. We show that P(H)≤P̂′kH ≤P̂kH for all P(H)∈π0k(H) (where ≤ signifies ‘‘is a subpartition of’’), that P≤P′ for every P∈π0k(H) and P′∈π0κ−ε(H), ε>0, and that π0κ(H) is a sublattice of the (≤) lattice of all partitions of H. The sets π0κ(H) and π0κ(H), and the corresponding minimal values of σκ and σ′κ, are explicitly determined, for any hypergraph if κ≤1, and for some special types of hypergraphs if κ>1. We introduce a new notion of connectedness for hypergraphs, the σ connectivity Σ(H)≡Max{κ,{H}∈π0κ(H)}, and relate it to the vertex connectivity kv(H)≡Max{k, H is k-(v)connected}; we have, in particular, Σ(H)≤kv(H) (Σ=kv if kv=0 or 1).
Determination of point group harmonics for arbitrary j by a projection method. II. Icosahedral group, quantization along an axis of order 5
Authors: Raynal Jacques
Published: March 2003

The method described in the previous paper to obtain cubic harmonics is applied to the similar problem for the icosahedral group. The projection operators are expressed in terms of rotation matrix elements of R(π,φ,0) and R(0,π−φ,π) φ=arctan 2, acting on subspaces invariant under D5.
On a class of spinor representations of SO(7)
Authors: De Wilde P. , De Meyer H. , Van der Jeugt J. , Vanden Berghe G.
Published: March 2003

The reduction of the irreducible representations [v,0,...,0,1] of SO(2n+1) with respect to SU(2)⊗SU(2)⊗SO(2n−3) is considered. For the n=3 case all the reduced matrix elements of the SO(7) generators in the [SU(2)]2⊗SO(3) basis are calculated with the use of recursion relations.
Multispinor basis for representations of SO(N)
Authors: Nikam R. S. , Sarma C. R.
Published: March 2003

The generators of the rotation groups SO(N) (N=2n, 2n+1) have been realized using a restriction of the unitary group U(2n) defined on the 2n -dimensional fundamental representation space of spinors. These generators have been used to subduce multispinor representations of SO(N) from those of U(2n). The procedure has been illustrated for the two-spinor vector representations 〈10〉 and 〈1000〉 of SO(5) and SO(8), respectively.
Group representations in indefinite metric spaces
Authors: van den Broek P. M.
Published: March 2003

A group G of symmetry transformations of the rays of an indefinite metric space V with metric operator η leads to a projective representation U of G in V in terms of η-unitary, η-antiunitary, η-pseudounitary, and η-pseudoantiunitary operators. We investigate the restrictions which are put on the irreducible components of U by the metric, and examine to what extent it is possible to decompose V into a direct sum of indefinite metric spaces, each carrying a projective representation of G. Attention is restricted to the cases where the subgroup of G which is represented by η-unitary operators is of index 1 or 2.
The semisimple subalgebras of Lie algebras
Authors: Feldman G. , Fulton T. , Matthews P. T.
Published: March 2003

Techniques for obtaining generators of nonregular maximal subalgebras of Lie algebras, alternative to those of Dynkin, are developed. They exploit the use of orthogonal bases in weight space, which are related to quark weights. The projection from an algebra G to its nonregular subalgebras g is related to an orthogonal matrix. The roots of G which project onto roots of g can be simply specified in the orthogonal bases. The phases of the expansion coefficients of generators of g in terms of generators of G are specified in such a manner that, for a given G, the entire set { g} of maximal subalgebras have consistent phases. The condition e−β =e°β is satisfied for all generators of g. The generators of all maximal nonregular subalgebras of all exceptional algebras are exhibited.
Lee Hwa Chung theorem for presymplectic manifolds. Canonical transformations for constrained systems
Authors: Gomis J. , Llosa J. , Román N.
Published: March 2003

We generalize the analogous of Lee Hwa Chung’s theorem to the case of presymplectic manifolds. As an application, we study the canonical transformations of a canonical system (M, S, Ω). The role of Dirac brackets as a test of canonicity is clarified.
On the derivation of hydrodynamics from molecular dynamics
Authors: Mürmann Michael G.
Published: March 2003

We study the transition from molecular dynamics to hydrodynamics. Convergence of subsequences and absolute continuity of the limit are proven for the local distributions of mass and momentum. The corresponding limit dynamics is discussed with regard to the foundations of hydrodynamics. A Chapman–Enskog-like procedure leads formally to local equilibrium with the parameter functions obeying the system of the Euler equations.
A series of new analytical solutions to the nonlinear equation y
t+y
x
x
x−6y2y
x+6λy
x=0. I
Authors: Fung P. C. W. , Au C.
Published: March 2003

Following the Bäcklund transformation and using the theorems proved by the same authors, previously we obtained sets of new solutions to the KdV equation and the nonlinear equation yt+yxxx−6y2yx +6λyx=0 which transforms into the modified KdV equation when λ=0. In this paper we present another new series of solutions to the above nonlinear equation. One of our analytical solutions under a certain special condition (vacuum parameter b=0 and λ=0) is found to be identical to the one-soliton solution obtained via the inverse scattering method.
Multifrequency inverse problem for the reduced wave equation with sparse data
Authors: Weston V. H.
Published: March 2003

The inverse problem for the reduced wave equation Δu+k2n2(x)u=0 is considered where the quantity to be determined is the value of n(x) in a compact domain D in R3. The data consists of a finite set of measurements of the scattered field produced by different incident fields. The measurements are made at various points exterior to D and at possibly different frequencies. The mathematical problem involves solving a system of nonlinear functional equations. Conditions are developed which indicate when the measured body is close to a particular comparison body (a linearized perturbation is valid). A new higher order nonlinear iterative procedure is developed for the full nonlinear problem, which reduces to the usual solution in the linearized region. The method is illustrated by computational results for the one-dimensional case.
Linear response theory revisited. IV. Applications
Authors: Vasilopoulos Pagiotis , Van Vliet Carolyn M.
Published: March 2003

The one-body linear response expressions (diagonal and nondiagonal) for the dc electrical conductivity, obtained in a previous paper, are applied to specific situations. In the case of ‘‘no collisional current’’ we evaluate the relaxation times which enter an expression (diagonal) for the longitudinal magnetoconductivity; in the case of ‘‘collisional current’’ another expression (diagonal) for the transverse magnetoconductivity is evaluated. The calculations are carried out in the framework of electron–phonon interaction in crystalline materials; various kinds of phonons are considered. The formula for ‘‘collisional current’’ is also used for an analytic evaluation of the phonon assisted hopping conductivity in crystalline and amorphous materials. The results are in harmony with those of the literature or are new. Further, the nondiagonal expression leads to a result for the oscillatory Hall effect, which, in contrast with previous results, is independent of the interaction (e.g., interaction with impurities).
Spherical charged fluid distributions in general relativity
Authors: Tikekar Ramesh
Published: March 2003

Formal features of Einstein–Maxwell equations for spherically symmetric distributions of a charged perfect fluid in equilibrium are discussed. An exact solution of the system of equations for a specified choice of matter density and fluid pressure, representing a charged perfect gas is presented.
A new class of exact pp-wave solutions in simple supergravity
Authors: Embacher Franz
Published: March 2003

A class of exact solutions of the O(1) supergravity theory is presented. It is obtained from an ansatz motivated by a previously known exact plane-wave solution together with the additional assumption that the connection forms equal their torsion-free and zero-order Grassmann part. The demonstrated solutions are nontrivial and admit a covariantly constant spinor field.
Composite gluons and scalar fields
Authors: Gutierrez W. R. , Saez L. F.
Published: March 2003

We study a model of scalar fields in four dimensions which has been introduced previously as a representation of gauge vectors in terms of scalar fields. We argue that conventional weak coupling constant perturbation theory is not renormalizable; however, strong coupling expansion based on the lattice formulation is specially well suited to the model.
SO(4) reduction of the Yang–Mills equations for the classical gauge groups
Authors: Légaré M. , Harnad J.
Published: March 2003

We show that the reduction of the SU(n), SO(n), and Sp(n) Yang–Mills equations in compactified Minkowski space by certain realizations of the SO(4) subgroup of the conformal group leads to systems of ordinary differential equations. The reduced systems are interpretable as Hamiltonian systems with symmetry constrained so that the momentum map equals zero. Explicit solutions for these systems are given.
Leading and misleading logs in perturbative QCD
Authors: Pennington M. R.
Published: March 2003

Misleading results can be obtained by applying a leading logarithm approximation where it is not valid. However obvious this fact, its neglect is shown to have led to misleading and even erroneous conclusions in several recent practical applications of perturbative QCD to the problem of summing soft gluons.
Collectivity and geometry. I. General approach
Authors: Moshinsky M.
Published: March 2003

In the last decade an extensive literature appeared in which the microscopic collective behavior of nuclei was associated with definite irreducible representations (irreps) of either the O(n) or Sp(6) groups, where n=A−1 and A is the number of nucleons. It became clear that the two approaches are equivalent, as problems with 3n degrees of freedom are characterized by a definite irrep of the group Sp(6n) and for its subgroup Sp(6)×O(n) the irrep of O(n) determines that of Sp(6) and vice versa. Thus one can consider that collective effects appear when one introduces the constraint that in the many-body system the states are restricted to a definite irrep of O(n) [and thus also of Sp(6)] and the Hamiltonians are in the enveloping algebra of Sp(6) rather than in that of Sp(6n). Once Sp(6) becomes the paramount group of collective motions, the problem is to determine the matrix elements of the generators of Sp(6) in a basis characterized by irreps of its subgroups. What subgroups to choose? Rowe and Rosensteel have taken Sp(6)⊇U(3) and Sp(6)⊇CM(3), where the latter has also been considered by Biedenharn et al. In the present series of papers we analyze the problem in the chain Sp(6)⊇Sp(2)×𝒪(3), as we show that in the boson limit, i.e., when n≫1, the Casimir operator of Sp(2) goes into the Casimir operator of U(5), i.e., the corresponding chain is U(6)⊇U(5)⊇𝒪(3). In the case Sp(6)⊇U(3)⊇𝒪(3), the boson limit is U(6)⊇U(3)⊇𝒪(3). Thus in this series of papers we look at the microscopic collective model from what could be called the vibrational rather than the rotational point of view.
Collectivity and geometry. II. The two-dimensional case
Authors: Chacón E. , Hess P. , Moshinsky M.
Published: March 2003

In a previous paper of this series we showed that nuclear collective behavior can be related to the symplectic geometry of the many-nucleon system, when we introduce in it appropriate constraints. We showed in that paper that a full discussion of collective behavior in the many-body system requires—in a space of d dimensions—the basis for the irreducible representations of the Sp(2d) group in the chain Sp(2d)⊇Sp(2)×𝒪(d), as well as the matrix elements of the generators of Sp(2d) in this basis. In the present paper we implement this program fully for d=2, both because of the mathematical interest of the chain Sp(4)⊇Sp(2)×𝒪(2) and as a stepping stone to the chain Sp(6)⊇Sp(2)×𝒪(3) which is central to the discussion of collective motions.
Fermi pseudopotential in higher dimensions
Authors: Grossmann Alexander , Wu Tai Tsun
Published: March 2003

The Fermi pseudopotential is generalized from three to five dimensions, and the case of an infinite, uniform, equidistant, linear chain of such pseudopotentials is studied in detail. Similar to the three-dimensional case, zero-width resonances are also present in five dimensions. While this generalization is natural and can be carried through formally when the strength is negative, there are basic changes in the underlying structure. These results in five dimensions also apply in four dimensions.
General nonlinear realization of chiral SU2×SU2 symmetry in curved isospin space
Authors: Ebrahim Abdul , Savci Mustafa
Published: March 2003

The geometric method for constructing the nonlinear chiral SU2×SU2 invariant Yang–Mills Lagrangian in curved isospin space given by Meetz for a particular choice of coordinates is generalized to an arbitrary system of coordinates in curved isospin space. The resulting Lagrangian coincides with the general nonlinear chiral SU2×SU2 invariant Yang–Mills Lagrangian constructed previously using the matrix method.
Exact solutions of unitarily invariant matrix models in zero dimensions
Authors: Amundsen P. A. , Damgaard P. H.
Published: March 2003

Explicit constructions of Green functions for U(N) invariant-matrix Φ4 theories are given in zero space-time dimensions. The results are expressed in terms of a new class of orthogonal polynomials, which are orthogonal on the interval [−∞,∞] with respect to the weight function exp{−m2φ2−λφ4}. An explicit construction of the coefficients of these generalized Hermite polynomials is presented. We briefly discuss the ‘‘thermodynamic’’ limit N→∞ of the corresponding one-dimensional statistical system of N classical particles with logarithmic pair interactions and subjected to an external anharmonic potential.
Gradient property of bifurcation equation for systems with rotational symmetry
Authors: Gaeta Giuseppe , Rossi Pietro
Published: March 2003

We show that any polynomial equation covariant with respect to any representation of SO(2) is a gradient equation. The same holds for the fundamental representation of SO(3). For the other representations of SO(3) we give a simple necessary and sufficient condition an equation has to satisfy in order to be a gradient one. As a side result, we obtain a formula for the decomposition of the symmetrized power of an irreducible representation of SO(3) in a sum of irreducible representations. We apply our results to symmetric bifurcation theory.
Lattice degeneracies of fermions
Authors: Raszillier H.
Published: March 2003

We present a detailed description of the minimal degeneracies of geometric (Kähler) fermions on all the lattices of maximal symmetries in n=1,...,4 dimensions. We also determine the isolated orbits of the maximal symmetry groups, which are related to the minimal numbers of ‘‘naive’’ fermions on the reciprocals of these lattices. It turns out that on the self-reciprocal lattices the minimal numbers of naive fermions are equal to the minimal numbers of degrees of freedom of geometric fermions. The description we give relies on the close connection of the maximal lattice symmetry groups with (affine) Weyl groups of root systems of (semi-) simple Lie algebras.
Orbit spaces of low-dimensional representations of simple compact connected Lie groups and extrema of a group-invariant scalar potential
Authors: Kim Jai Sam
Published: March 2003

Orbit spaces of low-dimensional representations of classical and exceptional Lie groups are constructed and tabulated. We observe that the orbit spaces of some single irreducible representations (adjoints, second-rank symmetric and antisymmetric tensors of classical Lie groups, and the defining representations of F4 and E6) are warped polyhedrons with (locally) more protrudent boundaries corresponding to higher level little groups. The orbit spaces of two irreducible representations have different shapes. We observe that dimension and concavity of different strata are not sharply distinguished. We explain that the observed orbit space structure implies that a physical system tends to retain as much symmetry as possible in a symmetry breaking process. In Appendix A, we interpret our method of minimization in the orbit space in terms of conventional language and show how to find all the extrema (in the representation space) of a general group-invariant scalar potential monotonic in the orbit space. We also present the criterion to tell whether an extremum is a local minimum or maximum or an inflection point. In Appendix B, we show that the minimization problem can always be reduced to a two-dimensional one in the case of the most general Higgs potential for a single irreducible representation and to a three-dimensional one in the case of an even degree Higgs potential for two irreducible representations. We explain that the absolute minimum condition prompts the boundary conditions enough to determine the representation vector.
On the Hankel transform of a generalized Laguerre polynomial and on the convolution involving special Bessel functions
Authors: Navelet H.
Published: March 2003

In this paper we calculate two of three simple integrals which are present neither in Bateman nor in Gradshtein and Ryzhik. These integrals are useful to treat some specific physics problems.
The occupation statistics for indistinguishable dumbbells on a rectangular lattice space. I
Authors: Phares Alain J.
Published: March 2003

The method of Hock and McQuistan used recently to solve the occupation statistics for indistinguishable dumbbells (or dimers) on a 2×2×N lattice is extended further to obtain, for the L×M×N lattice, general expressions for the normalization, expectation, and dispersion of the statistics, and their limit as N becomes very large. In particular, an explicit expression of the partition function in the thermodynamic limit Ξ(x) is obtained for any value of the absolute activity x of dimers. The developed mathematical formalism is then applied to planar lattices, 1×M×N, with M=1, 2, 3, and 4. The known results for M=1 and 2 are recovered, and some new ones are obtained. The recurrence relation for the number A(q,N) of arrangements of q dumbbells on a 1×M×N lattice which has 3 and 5 terms when M=1 and 2, respectively, is found to have 15 and 65 terms for M=3 and 4. Analysis and extrapolation of the results enable one to predict the expectation 〈θ〉1MN on a planar 1×M×N lattice to be 63.4%, in the limit as both M and N become infinite. We also find an upper bound on the quantity MN[〈θ2〉−(〈θ〉)2] in the limit as both M and N become infinite. In the thermodynamic limit (M&N→∞) the partition function Ξ(1), for the absolute activity x=1, is found to be equal to 1.95. By limiting the number M of rows of infinite extent (N→∞) to just 4, we find that the error in determining Ξ(1) for the infinite two-dimensional lattice is just 4.5%. In this paper Ξ(x) is obtained for any value of the absolute activity x for M=1 and 2. A more thorough study of Ξ(x), and its fast convergence with increasing values of M, and applications will be presented in a forthcoming article.
First-order equivalent Lagrangians and conservation laws
Authors: Hojman Sergio , Gómez Javier
Published: March 2003

We present a theorem for (first-order) Lagrangian theories which associates several conserved quantities to one (s-equivalence) symmetry transformation.
Variational principle for electromagnetic problems in a linear, static, inhomogeneous anisotropic medium
Authors: Brownstein K. R.
Published: March 2003

A variational principle δ∫∫L dV dt=0 is formulated for electromagnetic problems in the time domain for a medium which is linear, static, inhomogeneous, and anisotropic. The principle involves all four electromagnetic field vectors (E,H,D,B) and no ‘‘adjoint-type’’ fields. Both the two ‘‘curl’’ Maxwell equations as well as the two constitutive equations emerge as the four associated Euler–Lagrange equations. The problem of possible variations in the field functions at the temporal boundaries is solved by using the constitutive equations as a constraint at one of the temporal boundaries.
Lorentz transformation of Debye potentials
Authors: Monroe David K.
Published: March 2003

The Debye potential formalism is a simple and elegant method of representing and analyzing radiation fields in classical electromagnetism. Despite this, there are a number of unanswered questions about the formalism. One of these, the transformation properties of the potentials under Lorentz boosts, is dealt with in this article.
Description of the degree of nonuniqueness in inverse source problems
Authors: Ramm A. G.
Published: March 2003

For time-independent and time-dependent inverse source problems the degree of nonuniqueness of solutions is characterized.
Exact diagonalization of the Hamiltonian of a Dirac particle with anomalous moment, interacting with an external magnetic field
Authors: Roux Jean-François
Published: March 2003

A unitary transformation is performed on a Hamiltonian which is built from two independent Dirac matrices with noncommuting coefficient operators. A simple symmetric and exactly diagonalizable expression is obtained for the Hamiltonian of a Dirac particle, including the effect of an external magnetic field on an anomalous moment; a nonrelativistic approximation comes readily, which allows high magnetic fields.
Binding limit in the Hartree approximation
Authors: Ruskai Mary Beth , Stillinger Frank H.
Published: March 2003

We show that the Hartree approximation cannot predict that H− has a bound state, i.e., the Hartree energy is greater than −0.5. We also show that the Hartree approximation cannot predict binding for the Coulomb model of a two-electron atom unless the nuclear charge Z is greater than 1.03 and we compute accurate upper and lower bounds to the Hartree energy for H− and He.
A Lagrangian theory of the classical spinning electron
Authors: Nash Patrick L.
Published: March 2003

A Lagrangian is defined that governs the dynamics of a classical electron with spin, moving under the influence of electromagnetic forces. The Euler–Lagrange equations associated with this Lagrangian for space-time position xα provide a generalization of the Lorentz force law. The remaining Euler–Lagrange equations lead directly to the (generalized) Frenkel–Thomas–BMT equations.
Some remarks on the application of the QCA to the determination of the overall elastic response of a matrix/inclusion composite
Authors: Willis J. R.
Published: March 2003

A ‘‘multiple scattering’’ formulation for the elastic response of a matrix containing a random distribution of inclusions is considered. The ‘‘ordinary’’ quasicrystalline approximation (QCA) is reviewed, together with a recently proposed ‘‘self-consistent’’ QCA. It is shown that the basic ‘‘self-consistent’’ postulate can be implemented without making an extra approximation in relation to scattering from the ‘‘background’’ material and that, when this extra approximation is dispensed with, the alternative self-consistent prescription that results is capable in principle of generating the overall properties exactly. In practice, there is still the need to close a hierarchy by making some assumption about interactions between inclusions. When the QCA is adopted, the alternative self-consistent prescription yields precisely the same estimates for overall behavior as the ‘‘ordinary’’ QCA. The formulation is given explicitly for elastostatics but the conclusions depend only upon the algebraic structure of the problem and apply equally well to problems of wave propagation.
Supersymmetry and Clifford algebras
Authors: Hasiewicz Z. , Kwasniewski A. K. , Morawiec P.
Published: March 2003

A canonical derivation of extended Lie superalgebras aN(p,q) right from the metric structure of the underlying ‘‘space-time’’ E(p,q) is presented. The canonical method is that of Clifford algebras C(p,q) and their representations theory. The results are tabularized.
Classical versus quantum integrability
Authors: Hietarinta Jarmo
Published: March 2003

Classical integrability and quantum integrability are compared for two degrees of freedom Hamiltonian systems. We use c-number representatives for quantum operators and the Moyal bracket for the commutator. Three different cases are found: (i) the c-number representative of the quantum mechanical second invariant is identical to the classical second invariant, (ii) O(ℏ2) corrections are needed in the classical second invariant to obtain the quantum invariant, and (iii) also the potential must be deformed by an O(ℏ2) term. Several examples from the Henon–Heiles and Holt families of integrable potentials are included.
The quantum scattering amplitude in Rn for potentials decreasing faster than ‖x‖−(n+1)/2
Authors: Combes J. M. , Ghez J. M.
Published: March 2003

Within the framework of the two-body problem in quantum mechanics, we prove an ‘‘analytic limiting absorption principle’’ for the Schrödinger operator H=H0+V, on L2(Rn), where H0=−Δ and V is a real short-range potential, that is, decreasing like ‖x‖−1−ε, ε>0, as ‖x‖→∞. Applying it in the case where V decreases like ‖x‖−(n+1)/2(log‖x‖)−1−ε, ε>0, as ‖x‖→∞, we obtain two classes of results for the non-Born part of the scattering amplitude: finiteness, continuity and high energy properties on the positive real axis, including correction to the Born approximation of the cross section; analyticity and high energy properties in the upper half-plane for the forward amplitude.
Inverse scattering for optical couplers. Exact solution of Marchenko equations
Authors: Bava G. P. , Ghione G.
Published: March 2003

An exact solution of Marchenko equations for rational scattering data of arbitrary order is developed, with reference to the case of two coupled waves propagating in a lossless (optical) waveguide. Some numerical examples are presented for the synthesis of coupling structures having a prescribed frequency response.
On the solutions of the Gel’fand–Levitan equation
Authors: Prosser Reese T.
Published: March 2003

The solutions of the Gel’fand–Levitan equation are obtained in a closed form for general rational reflection coefficients, and as a convergent limit of closed forms for reflection coefficients sufficiently close to being rational.
Electrovac type D solutions with cosmological constant
Authors: García Díaz Alberto
Published: March 2003

All type D electrovac solutions with cosmological constant for an algebraically general electromagnetic field aligned along the Debever–Penrose directions are obtained. From a single canonical metric element both the null and the non-null orbit solutions are derived simultaneously. The explicit expressions of the obtained solutions are listed in the table.