bluuebunny/crossref_metadata_2025 huggingface dataset:
Direct use of Young tableau algebra to generate the Clebsch–Gordan coefficients of S
U (2)
Authors: Nachamkin Jack
Published: March 2003

Although it is well known that the irreducible representations of the SU (N) groups may be generated by using Young tableau algebra, this technique seems to have found little use for the derivation of closed algebraic expressions for the Clebsch–Gordan coefficients of these groups. A frontal attack on the derivation of these coefficients using tableau symmetrizers is described. As an example, the SU (2) group illustrates the fundamental ideas behind the process.
Simple expression for the linear boson transformation coefficients. II
Authors: Rashid M. A.
Published: March 2003

We obtain a simple expression for the coefficients which connect a Fock state containing an arbitrary number of quasiparticles with its transformed state under a boson Bogolubov transformation.
On the equivalence of the Einstein−Mayer and Einstein−Cartan theories for describing a spinning medium
Authors: Mahanta M. N. , Rao A. Sudhakar
Published: March 2003

It is shown that the five−dimensional formalism of the Einstein−Mayer theory of 1932 can be given a new interpretation and used to describe a continuous medium with intrinsic angular momentum. The equations of motion of a spinning particle are derived from the generalized field equations and are seen to be essentially the same as the Mathisson−Papapetrou equations. Finally the correspondence of the new approach with the theories based on Cartan’s torsion tensor
Semisimple subgroups of linear semisimple Lie groups
Authors: Cornwell J. F. , Ekins J. M.
Published: March 2003

The problem of embedding a semisimple Lie group in a linear semisimple Lie group [where one (or both) may be noncompact] is investigated in detail. The analysis is based on a previous set of papers dealing with the corresponding problem for real Lie algebras.
A variational principle in statistical mechanics for particle systems with bounded pair interactions
Authors: Gerardi A. , Ianiro N. , Maffei C. , Marchioro C.
Published: March 2003

A gas of particles interacting pairwise via bounded potential is considered in the framework of rigorous statistical mechanics. It is proved that the pressure is the supremum on a class of states of the difference between the entropy and the mean energy.
Construction of spin−orbit potentials from the phase shifts at fixed energy
Authors: Hooshyar M. A.
Published: March 2003

The nonrelativistic scattering of spin−1/2 particles by central and spin−orbit potentials is considered. The form of central and spin−orbit potentials is deduced from a knowledge of the S matrix as a function of angular momentum at a fixed energy. Similar to the case of central potentials, the problem of constructing central and spin−orbit potentials from information on the phase shifts at a fixed energy has an infinity of solutions, depending on an infinite number of parameters.
A generalized theory of multiplicative stochastic processes using cumulant techniques
Authors: Fox Ronald Forrest
Published: March 2003

The rules for the construction of the nth order cumulant for time−dependent, stochastic, matrices or operators which do not commute with themselves at unequal times are derived. The results are identical with van Kampen’s rules. In the Gaussian case, Kubo’s concept of a generalized Gaussian process is criticized. Under certain conditions Kubo’s idea becomes asymptotically valid, while the same conditions justify use of the author’s earlier delta function theory. A generalized density matrix equation is presented and its behavior during the approach to equilibrium is discussed. A finite correlation time, τc, does not necessarily invalidate a monotonic approach to equilibrium.
Wave propagation in media undergoing uniform linear acceleration
Authors: Whicker Donald , Lianis George
Published: March 2003

Wave propagation in a homogenous material undergoing uniform linear acceleration is considered. The covariant constitutive equations for a holohedral, nondispersive, dielectric material derived by Lianis are applied. Expressions are found for initially plane waves propagating in the direction of accelerated motion for the case where the material functions are constant. Expressions are also found for the radiation reflected and refracted at the surface of a half−space undergoing uniform linear acceleration. A detailed energy balance across this interface is also presented.
Nonlinear differential−difference equations
Authors: Ablowitz M. J. , Ladik J. F.
Published: March 2003

A method is presented which enables one to obtain and solve certain classes of nonlinear differential−difference equations. The introduction of a new discrete eigenvalue problem allows the exact solution of the self−dual network equations to be found by inverse scattering. The eigenvalue problem has as its singular limit the continuous eigenvalue equations of Zakharov and Shabat. Some interesting differences arise both in the scattering analysis and in the time dependence from previous work.
Ergodicity of observable and ergodic hypothesis in Markovian kinetics
Authors: Matsuno Koichiro
Published: March 2003

The time average of any observable, which evolves following an irreducible Markov process with countable states each of which is a persistent state, equals the ensemble average of the same quantity if and only if the corresponding master equation does not exhibit the accumulation of its eigenvalues around the infinitesimal neighborhood of the point with the value zero and if the steady distribution as the eigenfunction with the eigenvalue zero is uniform. The nonuniform steady distribution invalidates the ergodicity of observable. The principle of a priori equal weight is identical to the ergodicity of observable.
Effect of damping on nonlinear three−wave interaction
Authors: Fuchs V. , Beaudry G.
Published: March 2003

We examine the nonlinear evolution of three coherent positive energy waves interacting resonantly in a homogeneous lossy medium. Assuming that only the low−frequency wave is appreciably damped, we establish a necessary and sufficient condition for unidirectional energy transfer from the pump to the two other waves in terms of a critical damping factor. We then find asymptotic solutions and solutions in the weakly and strongly damped regimes. Also, we examine the pump wave depletion time as a function of the damping rate and initial pump wave intensity.
The abstract Hilbert space generalization of Feenberg’s perturbation theory—A new method of quantum field theory
Authors: Bowen Samuel P.
Published: March 2003

A rigorous generalization of Feenberg’s perturbation theory to the calculation of thermodynamic Green’s functions is outlined. This method offers an algorithm for calculating correlation functions and propagators for any Hamiltonian, bounded or unbounded, and is exact and tractable in the thermodynamic limit. The method is defined and its use is illustrated by several brief examples.
Multiple scattering of waves by the doubly periodic planar array of obstacles
Authors: Twersky Victor
Published: March 2003

We analyze the three−dimensional problem of multiple scattering by a doubly periodic planar array of bounded obstacles, and compare the results with those for the grating of parallel cylinders in two dimensions and for the periodic line in three. Plane wave integral forms of the scattered field and of the multiple scattered amplitude lead directly to the array−mode functional representation in terms of the single scattered amplitude and to simple approximations corresponding to array resonances for near−grazing evanescent modes. For the grating and for the periodic line, a grazing mode corresponds to reinforcement of the excitations an obstacle receives from the waves scattered by its neighbors; for the doubly periodic array, to reinforcement of the waves of the lattice lines perpendicular to the mode’s direction. We also derive spherical wave (and conical−cylindrical wave) representations of the solution, and exhibit the results for spherically symmetric scatterers as a special case.
Vector potentials and physical optics
Authors: Gordon William B.
Published: March 2003

The general problem considered is to obtain solutions w to the vector equation v = curl(w), where v is a given divergence−free vector field with singularities. Two methods are discussed: A special method, which applies when v is of the type which occurs in the Kirchhoff theory of diffraction, and a general method, which applies to any divergence−free vector field whatever. As an example the general method is used to obtain the Maggi−Rubinowicz representations of the Kirchhoff−Helmholtz (double) integral as a line integral. The singularities of the solutions w are known to produce important optical effects, and the nature of these singularities is largely determined by topological properties of the domain on which v is regular.
A spinor field theory on a seven−dimensional homogeneous space of the Poincaré group
Authors: Ardalan Farhad , Fleming G. N.
Published: March 2003

A field theory of half−integer spin particles is constructed on a seven−dimensional homogeneous space of the Poincaré group. The mass spectrum consists of nonparallel linear trajectories. The field theory has no spacelike or lightlike solutions. Electromagnetic form factors and structure functions of the theory are discussed.
Spacetime symmetries and linearization stability of the Einstein equations. I
Authors: Moncrief Vincent
Published: March 2003

We consider the Marsden−Fischer conditions for linearization stability applied to vacuum spacetimes with compact Cauchy hypersurfaces. We show that if a vacuum spacetime S admits a Killing vector field, then the Marsden−Fischer criterion fails to be satisfied at any Cauchy surface for S. We also show that if the Marsden−Fischer criterion fails to hold on an initial surface, then there is a Cauchy development of this intial data which admits one or more Killing vectors. The number of independent Killing fields present is shown to equal the dimension of the kernel of the linear map defined by Marsden and Fischer.
Stationary electrovacuum spacetimes with bifurcate horizons
Authors: Hájíček P.
Published: March 2003

General features of all stationary electrovacuum solutions of Einstein−Maxwell equations which contain regular bifurcate horizons are studied. A certain set of invariant quantities is found in whose values the full information about the solutions is recorded. The quantities have a simple physical meaning and generalize directly the ’’local invariants’’ defined for the axially symmetric case in the previous paper [J. Math. Phys. 15, 1554 (1974)]. A necessary condition that the solutions represent a neighborhood of a black hole in an asymptotically flat spacetime is given. The condition has the form of an inequality which places an upper bound on the magnitudes of the gravimagnetic, electric, and magnetic fields at the horizon. In the case of axial symmetry, the inequality reduces to that derived in the previous paper.
The Cauchy problem in general relativity. I. Metrics containing arbitrary functions
Authors: d’Inverno R. A.
Published: March 2003

This paper develops a Lagrangian formalism (the yA−formalism) for use in investigating the Cauchy problem in general relativity. In particular it will be used in a subsequent paper to present a Lagrangian formulation of the characteristic initial−value problem in general relativity. The formalism enables one to define ’’field equations’’ and ’’Bianchi identities’’ for metrics containing arbitrary functions in the case when the arbitrary functions are treated as the field variables.
Renormalization group solution of the one−dimensional Ising model
Authors: Nauenberg M.
Published: March 2003

A renormalization group approach is applied to the one−dimensional Ising model to obtain a rapidly convergent infinite series expansion for the free energy. This series can be summed and yields the well−known analytic solution.
A new approach to the stability of matter problem. II
Authors: Federbush Paul
Published: March 2003

The main stability of matter result of Dyson and Lenard is proven by an alternate method.
An expansion theorem for the twisted product with applications
Authors: Liu Kuang Chi
Published: March 2003

A mathematically rigorous asymptotic formula in powers of the index c is obtained for the twisted product associated with the Weyl form of CCR for n degrees of freedom. When c is identified with the Planck constant, the asymptotic formula is used to give a precise meaning to the usual notion of ’’classical limit.’’
Static electrovacuum spacetimes with bifurcate horizons
Authors: Hájíček P.
Published: March 2003

We prove a necessary and sufficient condition for a stationary electrovacuum spacetime with a bifurcate horizon to be static. The condition is expressed by means of the invariant quantities introduced in the preceding paper.
Symmetry of ensembles of maximum entropy
Authors: Lubkin Elihu
Published: March 2003

There can be only one maximally random ensemble in a given convex−closed family of ensembles, because the mixing of several ensembles increases entropy. Hence, if the family is acted on by a group which does not modify randomness (entropy), the thermodynamic ensemble is invariant. This is clear only over a finite−dimensional Hilbert space, prior to thermodynamic limits. Hence, in this situation, strictly spontaneous breakdown of symmetry is impossible.
Theory of Regge poles for 1/r2 potentials. II. An exactly solvable example at zero energy
Authors: Mastalir Robert O.
Published: March 2003

We give the exact solution of the Schrödinger equation at zero energy and derive an expression in closed form for the Regge poles for a particular 1/r2 potential with the behavior r2V (r) = −V0 at r = 0 and r2V (r) = −V2 at r = ∞. We give detailed results on the properties and distribution of the Regge poles in the λ plane and find them to be in agreement with the predictions of a previous paper in this series.
Factorization−method treatment of the perturbed Morse oscillator
Authors: Huffaker J. N. , Dwivedi P. H.
Published: March 2003

By transforming the Morse oscillator from type B to type F factorization, we obtain operators for raising and lowering the vibrational quantum number v, and a recursion relation. This permits the calculation of matrix elements needed for perturbation of the Morse oscillator to any order for perturbations of the form (eau − 1)n. Explicit calculations are presented for n = 3 and n = 4, analogous to the usual cubic and quartic anharmonicity perturbations of the harmonic oscillator.
The variational approach to the two−body density matrix
Authors: Garrod C. , Mihailović M. V. , Rosina M.
Published: March 2003

A variational method for the two−body density matrix is developed for practical calculations of the properties of many−fermion systems with two−body interactions. In this method the energy E = 𝒥Hijkl ρijkl is minimized using the two−body density matrix elements ρijkl = 〈ψ‖a+ja+iakal‖ψ〉 as variational parameters. The approximation consists in satisfying only a subset of necessary conditions—the nonnegativity of the following matrices: the two−body density matrix, the ’’two−hole matrix’’ Qijkl = 〈Ψ‖ajaia+ka+l‖Ψ〉 and the particle−hole matrix Gijkl = 〈Ψ‖ (a+iaj−ρij)+ (a+kal−ρk) ‖Ψ〉. The idea of the method was introduced earlier; here some further physical interpretation is given and a numerical procedure for calculations within a small single−particle model space is described. The method is illustrated on the ground state of Be atom using 1s, 2s, 2p orbitals.
Conserved vector densities and their curl expressions
Authors: Pavelle Richard
Published: March 2003

It has been shown that all Lagrange densities which are concomitants of sets of independent geometrical objects possess conserved vectors of the Komar type. For the general conserved vector derived from these Lagrangians we give an explicit method for rewriting the vector as the curl of a two index object.
A relativistic approach to quadrupole effects on planetary orbits
Authors: Yaakobi Daniel
Published: March 2003

The geodesic curves for a static axially symmetric metric and their first integrals of motion are calculated. The conformal mapping found by Erez and Rosen leading from the axially symmetric metric to the Schwarzschild spherically symmetric metric is applied and if a quadrupole moment is taken into account initially, a correction to the motion of a planet moving in the field of the sun in the equatorial plane is found. The results are compatible with Schwarzschild solution and motion in a classical quadrupole field. The main result is a justification of the usual procedure of simply adding relativistic and classical perturbations on planetary orbits.
On the equivalence of the Ornstein–Zernike relation and Baxter’s relations for a one-dimensional simple fluid
Authors: Chen M.
Published: March 2003

If the direct correlation function c (x) for a one-dimensional simple fluid vanishes for ‖x‖≳l, where l is finite, it can be proved that the Ornstein–Zernike relation and Baxter’s relations are equivalent provided that ⩽ (K), the Fourier transform of the total correlation function h (x), is bounded for real K.
Geodesics and Newtonian trajectories
Authors: Cohn Jack
Published: March 2003

In the framework of Riemannian geometry, the problem is considered whether there is a closest geodesic, for all possible space–time metrics, to a given Newtonian trajectory. The meaning of closeness is given precision and the question is answered—in the negative.
Long-wavelength normal mode vibrations of infinite, ionic crystal lattices
Authors: Davies John A. , Mainville Carol L.
Published: March 2003

This paper is an extension of an earlier article [J. Math. Phys. 13, 1207 (1972)] in which a study is made of the long-wavelength normal mode vibrations of infinite, ionic crystal lattices. The work is applicable to lattices of all symmetries but is restricted to the rigid ion model without retardation. This article completes the mathematical formalism introduced in the earlier article. In addition, two theorems are proved. The first states that all branches of the dispersion relations for an ionic lattice will approach definite frequencies as the propagation vector approaches zero if the point group of the space group of the lattice belongs to the regular system. The second states that, for all other lattices, at least two branches of the dispersion relations will approach frequencies which depend upon the direction of the propagation vector as the propagation vector approaches zero. A number of useful techniques are introduced for determining both the qualitative and quantitative behavior of the long-wavelength normal modes. Finally it is shown that the work in this paper is easily extended to include some but not all lattice models with
Exact results in quantum many-body systems of interacting particles in many dimensions with SU(1,2)¯ (1̄,1̄) as the dynamical group
Authors: Gambardella Pascal J.
Published: March 2003

We consider a class of system of N interacting particles in any dimension—the potential includes a quadratic pair potential and an arbitrary translation-invariant position-dependent potential that is homogeneous of degree −2. The group SU(1,2)¯ (1̄,1̄) is the dynamical group for the Hamiltonian. We illustrate the significance of the Casimir operator in relation to the separation of variables method; obtain a series of eigenfunctions that transform under the unitary irreducible representations of SU(1,2)¯ (1̄,1̄) labeled by the ground state energy; indicate the structure of arbitrary eigenfunctions; and specify when the complete energy spectrum is linear. We treat N-body examples which include two- and three-body forces. For N identical particles in one dimension interacting with a quadratic pair potential and an inverse square pair potential, we exhibit a series of eigenfunctions characterized by four quantum numbers. These eigenfunctions reduce to the complete set of eigenfunctions for five particles. We indicate how a complete set of eigenfunctions for N particles are obtained.
Cylindrically symmetric stationary beam of electromagnetic radiation
Authors: Banerjee A.
Published: March 2003

An exact solution of Einstein–Maxwell equations corresponding to an infinite stationary beam of electromagnetic radiation with the energy flux along the axial direction of a cylindrically symmetric system is obtained. Explicit forms of the electromagnetic field tensors are given. Further, the timelike and null geodesics in the region of the beam are also discussed.
Conformal invariance and Hamilton Jacobi theory for dissipative systems
Authors: Kiehn R. M.
Published: March 2003

For certain dissipative systems, a comparison can be made between the Hamilton–Jacobi theory and the conformal invariance of action theory. The two concepts are not identical, but the conformal action theory covers the Hamilton–Jacobi theory.
Weyl quantization of anharmonic oscillators
Authors: Truong T. T.
Published: March 2003

It is shown that polynomial self-interactions appearing repeatedly in the mathematical physics and chemical physics literature for the case of one degree of freedom can be treated in the formalism suggested by Weyl long ago, as was the case for the harmonic oscillator. New properties of the Schrödinger wavefunctions are derived, and appropriate schemes of approximation for the eigenvalue problem arise naturally in a nonperturbative way.
Lattice approximation of the (λφ4 − μφ)3 field theory in a finite volume
Authors: Park Yong Moon
Published: March 2003

For space–time regions with finite volumes, the lattice cutoff unnormalized Schwinger functions converge to the (unnormalized) Schwinger functions as the lattice cutoff is removed.
Linked cluster expansions in the density fluctuation formulation of the many-body problem
Authors: Campbell C. E.
Published: March 2003

A perturbation theory is developed for the logarithm of the normalization integral (or partition function) of an N-body system which is either a Bose liquid in its ground state or a classical fluid in the canonical ensemble. The perturbation in the former is an n-body factor in the ground state wavefunction and in the latter is an n-body potential. The normalization function serves as a generating function for the cumulants (or static correlation functions) of the density fluctuation operator ρk. The expansions of the perturbed partition function and correlation functions are shown to be linked cluster expansions involving the correlation functions in the unperturbed system; each term in these expansions is manifestly of the proper order in N. Several approximations involving truncations of the cumulants and/or resummation of part of the terms in the linked cluster expansions are discussed.
Discrete Coulomb gas in one dimension: Correlation functions
Authors: Mehta M. L. , Mehta G. C.
Published: March 2003

In this short note we calculate the correlation and cluster functions of the discrete Coulomb gas in one dimension considered recently by Gaudin. We consider also the discrete versions of the Gaussian ensembles previously studied extensively.
Evaluation of lattice sums. IV. A five-dimensional sum
Authors: Glasser M. L.
Published: March 2003

An approach for evaluating lattice sums is presented, which requires the use of basic hypergeometric functions. The sum 𝒥 (x1x2 + x2x3 + x3x4 + x4x1 + x2x5)−s is given as an example.
Eigenvalues of the invariant operators of the orthogonal and symplectic groups
Authors: Wong M. K. F. , Yeh Hsin-Yang
Published: March 2003

Eigenvalues of the invariant operators of the orthogonal and symplectic groups have been obtained in closed form. All semisimple Lie groups, the unitary, orthogonal, and symplectic groups, are treated in a systematic way by modifying Perelomov and Popov’s method. The eigenvalues of the invariant operators for the orthogonal and symplectic groups are then calculated with reference to the unitary group.
Petrie matrices and generalized inverses
Authors: Aronowitz S. , Eichinger B. E.
Published: March 2003

The connection between Petrie matrices and a special group of generalized inverses deriving from an incidence matrix is established. These matrices are encountered in the theory of the excluded volume effect in polymers, but have wide applicability to other problems. As an example of one such application we present a greatly simplified derivation of Lagrange’s theorem, which relates the inertial tensor of a mechanical system to the distances between all pairs of particles.
Harmonic mappings of Riemannian manifolds and stationary vacuum space–times with whole cylinder symmetry
Authors: Eriş Ahmet , Nutku Yavuz
Published: March 2003

We consider stationary, cylindrically-symmetric gravitational fields in the framework of harmonic mappings of Riemannian manifolds. In this approach the emphasis is on a correspondence between the solution of the Einstein field equations and the geodesics in an appropriate Riemannian configuration space. Using Hamilton–Jacobi techniques, we obtain the geodesics and construct the resulting space–time geometries. We find that the light cone structure of the configuration space delineates the distinct exterior fields of Lewis and van Stockum which together form the most general solution with whole cylinder symmetry.
Analytic T matrices for Coulomb plus rational separable potentials
Authors: van Haeringen H. , van Wageningen R.
Published: March 2003

The l=0 partial wave projected Coulomb off-shell T matrix Tc,l=0 in momentum representation is obtained in closed form. Problems existing in the literature concerning the half- and on-shell behavior of Tc and Tc,l are discussed and clarified by means of explicit formulas. The remaining derivations in this paper are based on Tc,l=0. We consider the class of N-term separable potentials where the form factors are rational functions of p2 (in momentum representation). We prove that the l=0 T matrix corresponding to the Coulomb potential plus any such so-called rational separable potential has a very simple form, namely, it can be written in terms of rational functions and the (simple) hypergeometric function with parameters (1, iγ; 1+iγ), where γ is the well-known Coulomb parameter. Explicit analytic formulas are derived for a number of simple members of the class, the Yamaguchi potential being one of them. In this particular case the expressions of Zachary and of Bajzer are reproduced who used a method based on the O4 symmetry.
Solution of the three-body problem with inverse square potentials
Authors: Avishai Y.
Published: March 2003

The three-body problem with two-body inverse cube forces is solved by separation of the variables into an angular and a radial one. The angular equation is an integro–differential one, which can be solved by splines, while the radial equation is Bessel’s.
Statistical methods in quantum field theory
Authors: Hańćkowiak Jerzy
Published: March 2003

We make the construction of n-point functions describing quantum field theory with the aid of classical field equation solutions defined on five-dimensional space. We also introduce the generating functional for n-point functions, fulfilling the first-order functional equation, the same for all local interactions without derivatives.
The influence of linear damping on nonlinearly coupled positive and negative energy waves
Authors: Fuchs V.
Published: March 2003

The linearly damped response to the nonlinear resonant mixing of two monochromatic coherent waves, involving modes of different energy sign, is shown to be always explosively unstable. Degeneration theory, modified to encompass explosively unstable solutions, is then applied to distinguish regions of negligible and strong damping, where the equations can be solved analytically. Effective damping, characterized by a damping rate ν, much higher than the (normalized) initial excitation U0, of the source waves, increases the explosion time by a factor of ν/U0.
Heisenberg subgroups of semisimple Lie groups
Authors: Scull Sidney C.
Published: March 2003

The restriction of a unitary representation of a semisimple Lie group to a Heisenberg subgroup Hn is shown to be quasiequivalent to the regular representation of Hn. Spectral properties of elements of the Heisenberg subgroup are described. Conditions under which an element of a semisimple Lie algebra may be embedded in a Heisenberg algebra are found.
Decompositions of gravitational perturbations
Authors: Moncrief Vincent
Published: March 2003

We consider the Brill–Deser decomposition of the perturbations of a flat spacetime with compact Cauchy hypersurfaces. We propose a generalization of the Brill–Deser splitting which may be applied to the perturbations of arbitrary vacuum spacetimes with compact Cauchy slices. We split the space of perturbations of any allowed Cauchy data set into three subspaces which, with suitable inner product, are mutually orthogonal. Two of these subspaces comprise the solution set of the perturbed constraint equations, and one of these two subspaces represents pure gauge perturbations. Some possible applications of these splittings to the study of the vacuum perturbation equations and to the linearization stability problem for the Einstein equations are briefly discussed.
One-dimensional excited state reduced Coulomb Green’s function
Authors: Hostler Levere
Published: March 2003

The nth excited state reduced Coulomb Green’s function in coordinate space for the one-dimensional Kepler problem is investigated, and a closed expression for this function is obtained.
Variational method and nonlinear oscillations and waves
Authors: Hsieh Din-Yu
Published: March 2003

A direct variational method is developed for studying the asymptotic behavior of a wide class of nonlinear oscillation and wave problems. From some judiciously chosen trial solutions with adjustable parameters, equations governing the change of amplitudes and phases are derived and solved. The method is simple in concept and straightforward in application. Different aspects of the method are illustrated by applications to various examples: the oscillation of a pendulum with changing length; the motion of a charged particle in a strong magnetic field; the linear and nonlinear Klein–Gordon equations; and the linear and nonlinear Korteweg–de Vries equations.
The conditional entropy in the microcanonical ensemble
Authors: Dietz David , Greenberg William
Published: March 2003

The existence of the configurational microcanonical conditional entropy in classical statistical mechanics is proved in the thermodynamic limit for a class of long-range multiparticle observables. This result generalizes a theorem of Lanford for finite range observables.
Regge amplitudes through solution of S-matrix equations
Authors: Frederiksen Jo/rgen S. , Johnson Porter W. , Warnock Robert L.
Published: March 2003

This work is a first step in a program for construction of meson–meson scattering amplitudes with analyticity, crossing symmetry, and unitarity. The construction is to be carried out by solving a nonlinear integral equation for the partial wave amplitude a (l,s) at complex l and physical s. The program is intended to overcome the difficulties encountered in the traditional approach based on the Mandelstam iteration of double-spectral functions. An important initial step is to analyze nonrelativistic potential scattering from this autonomous S-matrix viewpoint, in which the Schrödinger equation is replaced by a nonlinear equation for the partial wave amplitude. In the present paper, it is demonstrated that the partial-wave equation has a locally unique solution, provided the potential is of a suitably restricted Yukawa type. This result indicates the feasibility of a pure S-matrix approach to dynamics. In the present report, the potential is so restricted in strength as to preclude bound states or resonances. The extension of the method to the case of strong potentials will be pursued in a later publication.
All stationary axisymmetric rotating dust metrics
Authors: Winicour Jeffrey
Published: March 2003

The Einstein equations for stationary axisymmetric space–times with a rotating dust source are systematically reduced to quadratures. The general solution depends upon an arbitrary axisymmetric solution of the flat three-dimensional Laplace equation and upon an arbitrary function of one variable.
Correlation inequalities for two-dimensional vector spin systems
Authors: Monroe James L.
Published: March 2003

A set of correlation function inequalities including Griffiths, Kelly, Sherman type inequalities are proven for a lattice system of N sites where on each site there is a vector spin [s= (sx,sz), ‖s‖=1] whose distribution of values over the unit circle is given by f (s), where f (s) =f (−s). The spins interact through two-body, anisotropic, ferromagnetic interactions. Also an external field h, hx⩾0, and hz⩾0, is present. The proof uses Gaussian random variables.
A three-dimensional neutron transport problem
Authors: Mangiarotti Luigi
Published: March 2003

We study the stationary neutron transport Boltzmann equation as applied to a three-dimensional system D, made by a rectangular multiplying core surrounded by a finite reflector, in both the Lebesgue space L2(D) and the space C (D) (with the sup norm). As a result of this analysis, we prove some basic properties, such as the continuous dependence of the neutron flux on the parameters characterizing both the geometrical and the material properties of the system and the continuous and monotonic dependence of the average number of secondary neutrons per collision in the core on these parameters.
Generalized P-representation for bounded operators
Authors: Gautrin Henri-François
Published: March 2003

We generalize the notion of P-representation, introducing a space of generalized functions, such that every Hilbert–Schmidt operator has a P-representation. Then we extend that notion to another space of generalized function, such that every bounded operator has a P-representation.
A variational principle for the Boltzmann equation for hot electrons in a semiconductor
Authors: Schlup W. A.
Published: March 2003

It is shown that the well-known Kohler variational principle for the small electric-field solution of the Boltzmann equation can be extended to arbitrary fields, if a generalization of Hamilton’s principle proposed by Djukic and Vujanovic is used.
Gauge dependence of Green’s functions in quantum electrodynamics from parallel translation
Authors: Meetz Kurt
Published: March 2003

The classical concept of parallel translation is extended to scalar quantum electrodynamics in order to give a gauge-independent definition of differentiation. This is achieved by a suitable definition of time ordering for operator products. However, due to some essentially nonlocal commutation relations, the differential equations for the Green’s functions are still gauge-dependent. The gauge dependence of the commutators can be removed by parallelism at large. Since this is not considered to be a physically reasonable concept, the gauge dependence of the Green’s functions is discussed for general linear gauges in space–time.
Operator algebra of dual resonance models
Authors: Arik M. , Coon D. D. , Lam Yuk-ming
Published: March 2003

Properties of a set of operators introduced by Baker, Coon, and Yu are discussed. The operators involve generalizations of harmonic oscillator operators and facilitate the construction of a family of dual resonance models which includes the Veneziano model as a limiting case. Matrix representations of the operators are constructed, and it is shown that the operators have finite norm in contrast with the unboundedness of creation and annihilation operators of the Veneziano model.
Interpretation of Kato’s invariance principle in scattering theory
Authors: Dollard John D.
Published: March 2003

A simple proof is given that Kato’s invariance principle holds for a class of generalized piecewise linear (GPL) functions, under the sole assumption of existence of the Mo/ller wave operators. The invariance principle for GPL functions is viewed as an expression of our freedom to change the scale of time and shift the zero point of energy. It is remarked that whenever scattering theory can be done, it can be done with bounded Hamiltonians. The motion of a particle is studied when its Hamiltonian is replaced by a GPL function of this Hamiltonian.
On superpropagator for nonpolynomial Lagrangians with internal symmetry
Authors: Kapoor A. K.
Published: March 2003

Using the exponential shift lemma, a method to evaluate the superpropagator for scalar functions of a multiplet of fields is developed. As an application we obtain the generating function 〈T (Tr exp[λΦ (x)], Tr exp[λ′Φ (y)]) 〉0 for vacuum expectation values 〈T (TrΦN(x)TrΦN(y)) 〉0, when Φ is a 3×3 matrix, which is sufficient to get the results of Ashmore and Delbourgo on the matrix superpropagator for the chiral symmetry case.
Determination of nearest neighbor degeneracy on a one-dimensional lattice
Authors: Yan C. C.
Published: March 2003

A general method is proposed for the determination of the degeneracy of nearest neighbor pairs on a one-dimensional lattice. Explicit results are given for the special cases involving two and three kinds of molecules.
Unification of gauge and gravitation theories
Authors: Tabensky R.
Published: March 2003

A new approach to local Gauge theories is presented. The theory is developed in a curved space–time, and therefore gravitation is not neglected. Besides the Yang–Mills Aαμ vector bosons associated with a symmetry group, scalar bosons gαβ appear just as naturally. The Lagrangian describing the interaction of these fields is the Ricci scalar for an extended Riemannian geometry.
Diffraction by a half-plane perpendicular to the distinguished axis of a gyrotropic medium
Authors: Hurd R. A. , Przeździecki S.
Published: March 2003

The Wiener–Hopf–Hilbert method is used to obtain an exact solution to the problem of diffraction by a perfectly conducting half-plane in a gyrotropic medium, when the distinguished axis of the medium is perpendicular to the half-plane. The incident field is a plane wave whose direction of propagation is perpendicular to the edge of the half-plane. The problem has not previously been solved exactly. The answer is given in terms of Fourier transforms of the field components; these turn out to be simple algebraic functions. But the field quantities themselves are not, in general, expressible in terms of known functions. A few special cases are investigated and possible generalizations of the problem are mentioned.
Feynman path integrals and quantum mechanics as h/→0
Authors: Truman Aubrey
Published: March 2003

When the space of paths is a certain Hilbert space H, we show how to extend the Feynman path integral ℱ of DeWitt and Albeverio and Hoegh-Krohn. Our extension enables us to integrate a wider class of functionals on H. We establish a new representation for the wavefunction in nonrelativistic quantum mechanics—the quasiclassical representation. Using our extension of ℱ and the quasiclassical representation, we discuss the problem of obtaining classical mechanics as the limiting case of quantum mechanics when h/→0.
Quantization problem and variational principle in the phase-space formulation of quantum mechanics
Authors: Cohen Leon
Published: March 2003

The problem of quantization in the phase-space formulation of quantum mechanics is considered. An integral equation for the phase-space eigenfunctions is derived which is equivalent to the standard eigenvalue equation for a quantum mechanical operator. A differential form is also given. A variational principle is derived for quasiprobability distributions. It is shown that the expected value of the classical Hamiltonian calculated with a trial quasiprobability distribution will be greater than the ground state energy only if the distribution is chosen from a certain class of functions. The notion of ψ-representability is introduced to classify these functions. They represent distributions which correspond to possible quantum mechanical states. Also, a general relation is given between different distribution functions.
Path integrals and ordering rules
Authors: Dowker J. S.
Published: March 2003

It is shown again that path-integral quantization has no preference for any particular ordering rule for the Hamiltonian.
Space–time symmetries and linearization stability of the Einstein equations. II
Authors: Moncrief Vincent
Published: March 2003

In a previous paper we began a study of the Fischer–Marsden conditions for the linearization stability of vacuum space–times with compact, Cauchy hypersurfaces. We showed that a space–time of this class is linearization stable if and only if it admits no global Killing vector fields. In this paper we derive the general nonlinear constraints upon the perturbations which are necessary, whenever Killing symmetries occur, to exclude spurious perturbation solutions. We establish the hypersurface independence of these constraints by relating them to the conserved integrals of the perturbation equations associated with the Killing symmetries of the background. As a corollary of this result, we also establish the gauge invariance of the nonlinear constraints. We briefly discuss the noncompact case and mention a possible application of our results to the study of the Hawking process of quantum mechanical particle production by black holes.
Extended inertial frames and Lorentz transformations. II
Authors: Kerner Edward H.
Published: March 2003

It is shown that there is a unique ten-parameter group of projective (fractional-linear) transformations of space–time preserving free-particle motion and containing the inhomogeneous Lorentz group as a limiting case when a characteristic fundamental length of the projective group (whose structure comes from the group of rotations in the five-dimensional space of homogeneous space–time coordinates) is made infinite. The basic differential geometry, free-particle dynamics, and Lie group algebra going with the projectivity extended space–time structure are developed, and it is remarked that the Hamiltonian for free particles most generally will have eight branches, owing to the fundamental space–time metric being that for a Finsler space. The means to projectively extending electrodynamics are also briefly noted, and the need for characterizing electrodynamics by two intrinsic quantities (charge, and a purely electromagnetic length) are pointed out.
Complete extension of the symmetry axis of the Tomimatsu–Sato solution of the Einstein equations
Authors: Reina C.
Published: March 2003

The symmetry axis of the simplest Tomimatsu–Sato field is considered. Since this manifold is not geodesically complete for every value of the parameters occurring in the metric, a complete extension is given, and it is shown that its causal structure is very similar to that of the symmetry axis of the Kerr field.
Conservation of charge and the Einstein–Maxwell field equations
Authors: Horndeski Gregory Walter
Published: March 2003

In a space of four dimensions I determine all possible second-order vector–tensor field equations which are derivable from a variational principle, compatible with the notion of charge conservation and in agreement with Maxwell’s equations in a flat space. The general solution to this problem contains the Einstein–Maxwell field equations (with cosmological term) as a special case.
On the linear connection and curvature in Newtonian mechanics
Authors: Keskinen R. , Lehtinen M.
Published: March 2003

The trajectories of a scleronomic, holonomic particle motion in an otherwise general force field are autoparallel curves in a linear connected, symmetric, ’’almost’’ semimetric space. The Riemann–Christoffel curvature tensor and its concomitants belonging to the dynamical affinity are defined, and the physical meaning is discussed.
Solution of the multigroup transport equation in L
p spaces
Authors: Greenberg William , Sancaktar Selim
Published: March 2003

The isotropic multigroup transport equation is solved in Lp, p≳1, for both half range and full range problems, using resolvent integration techniques. The connection between these techniques and a spectral decomposition of the transport operator is indicated.
Zeros of the grand canonical partition function: Generalization of a result of Lee and Yang
Authors: Baur M. E. , Sinder R. M.
Published: March 2003

A simple sufficiency condition for the zeros of a polynomial of grand partition function form to lie entirely on the unit circle in the complex fugacity (z) plane is rigorously proven. The condition has two parts: the canonical partition function Qn(M) is symmetric, Qn(M) =QM−n(M), and is bounded above by the binomial coefficient (Mn). This represents a generalization of the condition given by Lee and Yang in the context of the Ising model and the proof is independent of theirs. Necessity of the condition is trivially proven.
Intrinsic geometry of Killing trajectories
Authors: Honig E.
Published: March 2003

We use the Frenet–Serret formalism to study the intrinsic geometry of Killing trajectories that are admitted by an arbitrary n-dimensional Riemannian space. The intrinsic quantities associated with these curves, i.e. their curvatures, are found to be constants of the motion that can be evaluated in terms of Hankel determinants. The results are then applied to curves in real quantum mechanics.
Inverse problem for complex ’’ra-analytic’’ potentials of finite range
Authors: Miodek Ilia
Published: March 2003

We present a simple solution to the inverse problem for the Schrödinger equation at fixed energy for complex ’’ra-analytic’’ potentials of finite range. This is done via an interpolation formula for the regular radial solutions as functions of complex angular momentum. The interpolation formula is derived by Frobenius techniques and Cauchy’s theorem. As an application we study an inverse problem for a spherically symmetric cold plasma perturbed by a small oscillatory electric potential of fixed (finite) frequency.
New identities on the Riemann tensor
Authors: Cheng Kuo-shung
Published: March 2003

A set of new identities which involve second covariant derivatives and quadratic forms of the Riemann tensor are proved. These new identities can be thought of as integrability conditions derived from the equations that define the Rieman tensor in terms of the affine connections.
Simple supersymmetries
Authors: Freund Peter G. O. , Kaplansky Irving
Published: March 2003

Two infinite families of simple graded Lie algebras (GLA’s) over the complex numbers are described: the special linear algebras SL(m‖n) [whose Bose sector is the direct sum of a one-dimensional algebra with the ordinary Lie algebra SL(m) ×SL(n)], and the orthosymplectic algebras OSp(2r‖s) [with Bose sector Sp(2r) ×O(s)]. The GLA’s of physics fit into these two families either directly or via Inönü–Wigner contraction. These algebras along with further exceptional GLA’s constitute all the classical GLA’s, i.e., all GLA’s with a nondegenerate metric (not necessarilly Killing) form. The existence of infinite families of hyperexceptional GLA’s, i.e., of GLA’s that are simple but not classical is pointed out.
Construction of quantum fields from Euclidean tensor fields
Authors: Yao Te Hai
Published: March 2003

We define Euclidean tensor fields over 𝒮 (R4), from which we construct quantum tensor fields satisfying all the Wightman axioms except the uniqueness of the vacuum. By a process of reduction, it is possible to obtain, from some suitably chosen Euclidean tensor field, a quantum field satisfying all the Wightman axioms except the uniqueness of the vacuum and transforming according to any arbitrarily chosen one-valued finite-dimensional irreducible representation of the restricted Lorentz group L↑+. We give a Euclidean vector field and a Euclidean tensor field of rank two as examples, leading respectively to the real Proca Wightman field and the free electromagnetic Wightman field.
Superposition of states and the structure of quantum logics
Authors: Deliyannis Platon C.
Published: March 2003

A derivation of the classical Hilbert space model of quantum theory is given (including superselection rules) based (i) on various axioms on the behavior of events and (ii) an explicit formula for the superposition of two pure states in terms of transition probabilities.