bluuebunny/crossref_metadata_2025 huggingface dataset:
Lattices of effectively nonintegral dimensionality
Authors: Dhar Deepak
Published: March 2003

We construct a class of lattice systems that have effectively nonintegral dimensionality. A reasonable definition of effective dimensionality applicable to lattice systems is proposed and the effective dimensionalities of these lattices are determined. The renormalization procedure is used to determine the critical behavior of the classical XY model and the Fortuin–Kasteleyn cluster model on the truncated tetrahedron lattice which is shown to have the effective dimensionality 2 log3 /log5. It is found that no phase transition occurs at any finite temperature.
A C*-algebra formulation of the quantization of the electromagnetic field
Authors: Carey A. L. , Gaffney J. M. , Hurst C. A.
Published: March 2003

A presentation of the Fermi, Gupta–Bleuler, and radiation gauge methods for quantizing the free electromagnetic field is given in the Weyl algebra formalism for quantum field theory first introduced by Segal. The abstract Weyl algebra of the vector potential is defined using the formalism of Manuceau. Then the Fermi and Gupta–Bleuler methods are given as schemes for constructing representations of the algebra. The algebra of the physical photons is shown to be a factor algebra of a certain subalgebra of the original algebra of the vector potential. In this formalism, the application of the supplementary condition in the Fermi method, and the supplementary condition and indefinite metric in the Gupta–Bleuler method, can be interpreted as the means by which a representation of this factor algebra is obtained. The Weyl algebra of the physical photons is the Weyl algebra associated with the radiation gauge method. It is also shown that in the Fock representation of the Weyl algebra given by the Fermi method, automorphisms of the algebra corresponding to Lorentz transformations cannot always be implemented by unitary transformations. This leads us to construct a new representation of the Weyl algebra which provides a covariant representation for the vector potential.
Gauge equivalence of the electrodynamics of charged bosons
Authors: Sohn R. , Haller K.
Published: March 2003

The quantum electrodynamics of charged scalar and vector bosons is formulated in the Lorentz gauge, and the effect of the charged particle–photon interaction on the subsidiary condition is explicitly taken into account. The results are extensions of earlier work on spinor quantum electrodynamics, but the presence of seagull vertices and anomalous current commutators in the case of the charged bosons make the extensions nontrivial. An operator gauge transformation that encompasses equations of motion as well as the commutator algebra of the field operators is developed; it is used to transform the theory from the Lorentz gauge to the Coulomb gauge.
A simple derivation of a closed formula for Bogoliubov boson transformations
Authors: Raduta A. A. , Badea M. , Badralexe E.
Published: March 2003

Considering the states with an arbitrary number of bosons and their transformed states under Bogoliubov transformations as wavefunctions of an oscillator type, a very simple derivation for the matrix elements of the Bogoliubov transformations is given.
A class of solutions of the Dirac equation in the Kerr–Newman space
Authors: Einstein S. , Finkelstein R.
Published: March 2003

In a region of spacetime that may be described by the Kerr–Schild metric, the gravitational field equations define a field of O(3) matrices. By examining the spin representations of these rotations it is first shown how the gravitational field equations define a spinor field, and it is then shown how this spinor field is related to special solutions of the massless Dirac equation in the Kerr–Newman space. These special solutions have arbitrary angular momentum about the axis of rotation and in the classical limit correspond to orbits that coincide with the principal null congruences.
Characterization of the Szekeres inhomogeneous cosmologies as algebraically special spacetimes
Authors: Wainwright J.
Published: March 2003

The Szekeres inhomogeneous cosmological models are invariantly characterized as a subclass of the algebraically special type {22} solutions of the Einstein field equations for irrotational dust, and their relationship to the locally rotationally symmetric dust solutions is clarified.
Acoustic emission and the plate Green’s function
Authors: Pardee W. J.
Published: March 2003

The stress at an arbitrary point in an elastic medium due to an acoustic emission is written in a stress Green’s function formalism. This formalism separates the mathematical description of acoustic radiation into separate factors describing the source and the medium response, which, it is hoped, will facilitate identification of source characteristics from remote observations. The description of the medium response is shown to be equivalent to a well posed elliptic boundary value problem for a 36 component Green’s function. This (frequency analyzed) Green’s function is calculated for the infinite isotropic elastic medium and for a similar plate. The latter example includes a complete description of dispersion, mode conversion, and the normal modes of the slab, although the latter need not be explicitly identified.
Ergodic state with least mean recurrence time in Markovian kinetics
Authors: Matsuno Koichiro
Published: March 2003

We present a proof of the theorem that the ergodic state with the least mean recurrence time in an irreducible Markov process having countable states is identical, with probability unity, to the state with the least irreversible decay rate if neither microscopic reversibility nor the doubly stochastic property holds.
General relativistic magnetofluids
Authors: Esposito F. Paul , Glass E. N.
Published: March 2003

General relativistic hydromagnetic systems are studied in the infinite conductivity limit. It is shown that when the frozen-in magnetic field lies in surfaces of constant pressure, the fluid acceleration and magnetic field are orthogonal. The theorem is proved that a shear-free infinite conductivity magnetofluid is irrotational if and only if the Weyl tensor is pure electric type. A restricted steady state is formulated and discussed, and within that state it is shown that an infinite conductivity magnetofluid cannot be electrically neutral.
Path integration of a one-dimensional three-body problem with three-body forces
Authors: Khandekar D. C. , Lawande S. V.
Published: March 2003

A one-dimensional three-body problem with three-body forces is treated by the path integral approach of Feynman. This involves essentially the path integration of a Lagrangian in plane polar coordinates with a potential energy term depending on both the radial and angular coordinates. An exact expression for the propagator is obtained.
Generalized method of a resolvent operator expansion
Authors: Znojil M.
Published: March 2003

The method of inversion of a quasitridiagonal matrix is suggested. The more general interpretation of the resulting expansion of the resolvent operator on a vector is given that does not use the concept of matrix elements nor inner product in a vector space. From this point of view, the linear operator Ĥ is employed recursively to define the basis starting with M initial vectors. The expansion of the action of the resolvent operator R̂ (E) = (E−Ĥ)−1 on any basis vector is given in the same basis with simply calculated coefficients, thus generalizing the usual power series expansion.
Charged particles in external fields. I. Classical theory
Authors: Ruijsenaars S. N. M.
Published: March 2003

A general perturbation theory is presented which can be used to study the interaction of relativistic charged particles with external fields. The theory is applied to the classical Dirac and Klein–Gordon equations. For external fields which are test functions on space–time retarded and advanced fundamental solutions are shown to exist, and their relation with the evolution operator is established. The S operator is shown to be Lorentz covariant and causal. The implementability in Fock space of the evolution is considered. It is shown that electric fields give rise to an implementable evolution while other kinds of fields in general do not.
Reciprocity relations and forward amplitude theorems for elastic waves
Authors: Varatharajulu V.
Published: March 2003

Relations are derived between the amplitudes of scattered elastic waves from obstacles of arbitrary shape when the direction of observation and incidence are reversed and interchanged, similar to the reciprocity theorem for the scalar wave equation. For waves which undergo a polarization change on scattering (longitudinal to shear and vice versa), a new type of reciprocity relation is derived which is peculiar to elastic waves. Expressions for the scattering cross section are obtained for shear and longitudinal incident waves, and it is shown to be proportional to the amplitude of the scattered wave in the forward direction alone. Incident waves are restricted to plane, monochromatic waves.
Positive solutions and subcriticality of energy dependent transport systems in slab geometry
Authors: Pao C. V.
Published: March 2003

The energy dependent transport system in an anisotropic medium in slab geometry subjecting to internal source and incoming fluxes is investigated. The investigation is based on a corresponding integral equation of the boundary value problem from which a recursion formula for the determination of the solution is obtained. It is shown by using the notion of an upper solution that the convergence or divergence of the sequence of iterations depends solely on the existence or nonexistence of an upper solution. Through the construction of a suitable upper solution one can obtain an explicit estimate for the value of c, which represents the average number of secondary neutrons per collision, in terms of the (optical) slab length 2a so that the system is either critical or subcritical. It is shown in particular that if c<[1−E2(a)]−1, where E2(a) is the exponential integral of order two, then the integral equation has exactly one nonnegative solution for any nonnegative source and incoming fluxes. This result insures the subcriticality of the system as well as a constructive recursion formula for the determination of the solution. Estimates for a more general system and the energy independent system are also obtained.
A Lagrangian formulation for noninteracting high-spin fields
Authors: Doria Francisco Antonio
Published: March 2003

We develop here some properties of Clifford algebras and of ’’algebraic’’ or Sauter spinors that lead to a very simple classification scheme for the Lorentz group representations. We apply our results to a Dirac-like Lagrangian and get a general formulation for noninteracting high-spin fields; the equations for spin 1/2, 0 and 1, 3/2 and 2 are explicitly calculated; the first three are seen to reproduce some previous results by Teitler.
Identification of the velocity operator for an irreducible unitary representation of the Poincaré group
Authors: Jordan Thomas F.
Published: March 2003

For a particle described by an irreducible unitary representation of the Poincaré group, for either positive mass or zero mass and discrete helicity, it is shown that the velocity operator can be identified by its transformations under the Poincaré group together with the assumption that it is a Hermitian operator whose different components commute with each other.
Ashkin–Teller model as a vertex problem
Authors: Wu F. Y.
Published: March 2003

It is shown that the Ashkin–Teller model on any planar lattice is equivalent to an eight-vertex model on a related lattice. The exact equivalence is given for finite lattices with a boundary. We show, in particular, that the AT model on the triangular or honeycomb lattice is related to an eight-vertex model on a Kagomé lattice. The occurrence of two phase transitions in the AT model in general is also discussed.
An infinite number of conservation laws for coupled nonlinear evolution equations
Authors: Haberman Richard
Published: March 2003

The n-dimensional Zakharov-Shabat eigenvalue problem and the corresponding time dependencey of the vector eigenfuncions are considered. It is known that certain coupled systems of nonlinear partial differential equatons are equivalent to the time invariance of the spectrum. Here, for any such coupled system, and infinite sequence of conservation laws is explicitly derived. As an example, this result is applied to the equaions describing three resonantly interacting nonlinear wave envelopes.
On a family of interior solutions for relativistic fluid spheres with possible applications to highly collapsed stellar objects
Authors: Whitman Patrick G.
Published: March 2003

A one-parameter family of interor solutions of Einstein’s field equations for a static spherical fluid is given. It is shwon that for various values of the parameter and choices of the constants in ingegration, several previously known solutions for static fluids are contained therein. This family of solutions can be joined continuously to the Schwarzchild exterior solution, and as such may be applicable to be investigation of stellar interior where high central densities and and pressures are of interest.
Lorentz transformations as space-time reflections
Authors: Krause Jorge
Published: March 2003

A rank-two tensor is built out of the 4-velocities of two inertial observers, which corresponds precisely to the most general Lorentz matrix connecting the two Cartesian frames of the observers. The Lorentz tensor is then factorized as the product of two ’’complementary’’ space-time reflections. It is shown that the first tensorial factor performs the very essential tasks (i.e., FitzGerald contraction and time dilation) of the corresponding Lorentz transformation, while the second factor is just an internal reflection performed in one and the same intertial frame. Thus, in its essential features, a Lorentz transformation between two different inertial frames obtains upon performing just one space-time reflection. It is also shown that the (same) Lorentz tensor of the two inertial observers can be factorized into ’’complementary’’ reflections either by two hyperplanes with spacelike normals, or else by tow hyperplanes with timelike normals, which geometric meaning is rather simple. An application of the presented formalism to Dirac’s 4-spinor transformation law is also briefly discussed.
Construction of the Yukawa2 field theory with a large external field
Authors: Rosen Lon
Published: March 2003

We consider the Yukawa2 model with (relativistic) interaction density λψ̄Γψφ+μφ, where Γ=1 or γ5. For sufficiently large μ, we apply the Glimm–Jaffe–Spencer cluster expansion to construct the infinite volume theory satisfying the Wightman and Osterwalder–Schrader axioms including a positive mass gap.
Heavens and their integral manifolds
Authors: Boyer Charles P. , Plebañski Jerzy F.
Published: March 2003

By using the apparatus of exterior forms, a new spinorial notation and Cartan’s theory of integral manifolds, some new results concerning complex strong heavenly metrics are established. In particular, the study of a subfamily of two-variable heavens (type G-[−], D-[−], and N-[−]) is reduced to linear equations, a prolongation process related to first and second heavenly equaions is studied leading to a (presumably) infinite heirarchy of 1−forms, and finally, the symmetries of the studied structure are investigated from the point of view of its description by Pfafian forms, elucidating in this way previous results concerning Killing vectors.
On self-reciprocal functions under a class of integral transforms
Authors: Wolf Kurt Bernardo
Published: March 2003

We use the fact that a rather general class of integral transforms—are equivalent to hyperdifferential operators, to formulate the problem of self-reciprocal functions under these transforms as an eigenvalue problem for (second-order) differential operators. We thus find the solution for Fourier, Hankel, bilateral Lapace, Bargmann, Weierstrass-Gauss and Barut-Girardello transforms. These involve the Schrödinger attractive and repulsive harmonic oscillator and/or centrifugal potentials wavefunctions. A general concept of ’’self-reproducing’’ functions is introduced which includes all of the above plus linear potential wavefunctions. In particular, two new generalized bases for Bargmann’s Hilbert space of analytic functions are found.
Rederivation of the Jin–Martin lower bound
Authors: Naito Seichi
Published: March 2003

With the help of the Phragmén-Lindelöf theorem, we can rederive the full Jin-Martin’s results on the total cross section lower bound.
T matrix and effective range function for Coulomb plus rational separable potentials especially for I=1
Authors: van Haeringen H.
Published: March 2003

The off-shell l=1 T matrix in the momentum representation for the pure Coulomb potential and for the Coulomb plus a rational plus a rational separable potential of the Yamaguchi type is obtained in closed form. The amplitude, the effective range function, and the effective range parameters are derived from the T matrix and are given in closed form. For a large number of rational separable potentials we prove thar the effective range function is real analytic at zero energy. We give, however, an axample of potential for which this effective range function has a pole at the orign. From t hese effective range functions a certain function W is extracted which does not depend either or l or on the particular potential. This function W is studied in detail. We indicate howe the result s of this paper can be generalized to arbitrary values of l and to all Coulomb plus rational separable potentials.
The number of bound states of the Coulomb plus Yamaguchi potential
Authors: van Haeringen H. , van der Mee C. V. M. , van Wageningen R.
Published: March 2003

It is shown that certain assertions on the number of bound states of a Coulomb plus Yamaguchi potential which Zachary [J. Math. Phys. 12, 1379 (1971); 14, 2018 (1973)] claims to have proved are incorrect. We prove that there are always infinitely many bound states if the Coulomb part of the potential is attractive and that, in case the Coulomb part of the potential is repulsive, there is one bound state only if the Yamaguchi potential is sufficiently attractive.
Regge trajectories for a velocity dependent potential
Authors: Ferreira Erasmo M. , Merí Ricardo , Sesma Javier
Published: March 2003

We study the distribution of the singularities in the complex angular momentum plane of the S matrix for a velocity-dependent potential, and note some deviations with respect to the general behavior established for static potentials. We analyze the physical implications of our results concerning the existence of bound states and resonances.
Nonstandard vector connections given by nonstandard spinor connections
Authors: Luehr C. P. , Rosenbaum M. , Ryan M. P. , Shepley L. C.
Published: March 2003

A unique two-component spinor connection, which we call the standard connection, is determined by the requirement that it be compatible with the spinor inner product and that it give rise to the standard 4-vector connection. Here we take the most general spinor connection, presuming that the conjugate spinor connection is uniquely determined by it, and examine which 4-vector connections are thereby determined. We classify such nonstandard spinor connections and the resulting 4-vector connections and show that the most general torsion tensor can be so generated. However, it is not possible to generate in this way the most general tensor describing incompatibility of the 4-vector connection with the 4-vector inner product. These results illuminate the relationship which must exist between nonstandard theories for spinors and for vectors.
Matrix superpropagators with derivatives
Authors: Kapoor A. K.
Published: March 2003

An earlier method of evaluation of matrix superpropagators without derivatives is extended to cover all such cases of interest. Matrix superpropagators with derivatives are reduced to superpropagators without derivatives by a straightforward application of Wick’s theorem for tiem ordered products. A simple connection is found between the superpropagators involving the fiels with derivatives at one of the points opnly and superpropagators obtained by replacing fiels with derivatives by fields without derivatives. The results of the present paper are sufficient to allow evaluation of all superpropagators, with and without derivatives, encountered in the second order for nonlinear chiral Lagrangians.
Existence, uniqueness and properties of the solutions of the Boltzmann kinetic equation for a weakly ionized gas. I.
Authors: Molinet Frédéric A.
Published: March 2003

The Boltzmann kinetic equation for a weakly ionized gas in the presence of a time dependent exterior electric field and a static exterior magnetic field has been transformed into an integral equation. Existence and uniqueness theorems have been proved for inverse power-law potentials of the form A/rs with s≳3 and for a large class of initial distribution functions. For soft potentials (3<s⩽5), these theorems have been derived from the general properries of the integral operator. For hard potentials, 5<s⩽+∞, where no generla properties of the integral operator can be directly proved, an iteration procedure which constitutes the main part of the present work has been developed. In each case, some important properties of the solution have been established.
Conditional expectations in generalized probability theory
Authors: Cycon H. , Hellwig K.-E.
Published: March 2003

Expectations have been considered as dual objects of instruments in several papers on generalized probability theory and quantum theory. Here, we relate a generalized conditional (GC) expectation to a given instrument and a given state by two requirements, which are analogous to the axioms by which the classical conditional expectation is related to a given sub-σ-algebra and a given probability measure. In examples we illustrate the close similarity of GC expectations with classical conditional expectations. Eventually, we introduce a rich class of quantum stochastic processes, which are Markovian.
Highest weights of semisimple Lie algebras
Authors: Laskar W.
Published: March 2003

The nine well-known semisimple Lie algebras are partitioned in two classes: Wlpc=1 (all roots have the same length) and Wlzc≠1 (the roots have two different lengths of ratio equal to c1/2). For each of these two classes a general expression is given for few elements of interest as the highest weight vector (h.w.v.) L and its power δ (L), the eigenvalues of the second order Casimir operator, the width of a weight diagram, the dimensions and the matrix elements of irreducible representations of the algebras. In the Appendix are given two examples of application of this paper.
On a topological problem arising in physics
Authors: Lafon J.-P. J.
Published: March 2003

The investigation of a large class of problems in physics requires the determination of the ranges of some parameters ξ, E, ⋅⋅⋅ for which equations of the form F (r; ξ, E,⋅⋅⋅) =0 have some or no roots in a given bounded or unbounded interval of r. The solution of this problem is given under the form of three general theorems. Examples of utilization in physics are also discussed.
Composite next nearest neighbor degeneracy
Authors: McQuistan Richmond B.
Published: March 2003

Expressions are derived which yield, exactly, the composite degeneracy of those arrangements of simple, indistinguishable particles on a one-dimensional lattice space, which are characterized by the number of nearest and next nearest neighbor pairs.
Killing inequalities for relativistically rotating fluids. II
Authors: Hansen R. O. , Winicour Jeffrey
Published: March 2003

Theorems that the angular momentum density and the angular velocity of locally nonrotating observers are postive are established for general relativistic fluids which rotate differentially with positive angular velocity. The results apply to the pseudostationary case in which the system possesses an ergoregion. An application to the stability of ergoregions is discussed.
Inequivalent sets of commuting missing label operators for SU(4) ⊆SU(2) ×SU(2)
Authors: Quesne C.
Published: March 2003

We exhibit one possible choice for the four functionally independent label operators available. We prove that they can be separated into two inequivalent, i.e., functionally independent, sets of commuting label operators, namely the set of operators Ω and Φ first considered by Moshinsky and Nagel, and the set of operators C(202) and C(022).
Evolution equations possessing infinitely many symmetries
Authors: Olver Peter J.
Published: March 2003

A general method for finding evolution equations having infinitely many symmetries or flows which preserve them is described. This is applied to the Korteweg–de Vries, modified Korteweg–de Vries, Burgers’, and sine–Gordon equations.
Axiomatic basis for spaces with noninteger dimension
Authors: Stillinger Frank H.
Published: March 2003

Five structural axioms are proposed which generate a space 𝒮D with ’’dimension’’ D that is not restricted to the positive integers. Four of the axioms are topological; the fifth specifies an integration measure. When D is a positive integer, 𝒮D behaves like a conventional Euclidean vector space, but nonvector character otherwise occurs. These 𝒮D conform to informal usage of continuously variable D in several recent physical contexts, but surprisingly the number of mutually perpendicular lines in 𝒮D can exceed D. Integration rules for some classes of functions on 𝒮D are derived, and a generalized Laplacian operator is introduced. Rudiments are outlined for extension of Schrödinger wave mechanics and classical statistical mechanics to noninteger D. Finally, experimental measurement of D for the real world is discussed.
Invariants for the time-dependent harmonic oscillator
Authors: Macki Jack W.
Published: March 2003

Lewis showed that in the case p (t) ≡1, h=1, I (t) = (1/2) {p2(t)[ρ (t) y′ (t) −y (t) ρ′ (t)]2+h2y2(t)/ρ2(t) } is constant in time if y (t) solves (p (t) y′) ′+q (t) y =0, and ρ (t) solves p (t) ρ3(t) L[ρ]=h2 (h constant). Recently, Eliezer and Gray showed that I (t) =const is just the conservation of angular momentum in an appropriate physical interpretation. We show, using a change of variable technique, that I (t) =const reduces to sin2ϑ+cos2ϑ=1. We discuss uniqueness and extendability of solutions to the above equation in ρ.
Localized solutions of a nonlinear electromagnetic field
Authors: Vazquez Luis
Published: March 2003

The electronlike localized solutions, for a nonlinear electromagnetic field obtained from the Born–Infeld Lagrangian, are studied.
Time-dependent dynamical symmetries and constants of motion. III. Time-dependent harmonic oscillator
Authors: Katzin Gerald H. , Levine Jack
Published: March 2003

This paper is a continuation of previous Papers I and II [J. Math. Phys. 17, 1345 (1976); 18, 424 (1977)]. In the present paper we apply the theory (based upon Lagrangian dynamics) developed in I and II to obtain the dynamical symmetries and concomitant constants of motion admitted by the time-dependent n-dimensional oscillator (a) Ei≡χ̈i +2ω (t) xi=0. The dynamical symmetries are based upon infinitesimal transformations of the form (b) χ̄i=xi+δxi, δxi≡ξi(x,t) δa; t̄=t+δt, δt≡ξ0(x,t) δa which satisfy the condition (c) δEi=0, whenever Ei=0. It is shown that such symmetries of the oscillator (a) will be time-dependent projective collineations. For such symmetries which satisfy the R1 restriction (defined in I) it is shown there exist concomitant constants of motion C1 of the oscillator, which for n=1 are time-dependent cubic polynomials in the χ̇ variable, and for n⩾2 are time-dependent quadratic polynomials in the χ̇i variables. It is shown that those symmetries which satisfy the R2 restriction (Noether symmetry condition discussed in I) are time-dependent homothetic mappings consisting of time-dependent scale changes, time-dependent translations, and rotations. The concomitant Noether constants of motion C2 are time-dependent quadratic polynomials in the χ̇i variables for all n. The Noether constant of motion C2 [referred to as C2(B)] for which the associated underlying symmetry mapping is the time-dependent scale change is shown to include as a special case when n=1 a class of invariants formulated by Lewis [Phys. Rev. Lett. 18, 510 1967)] (by means of a phase space analysis which applies Kruskal’s theory in closed form). For the case of general n it is shown that the time-dependent symmetric tensor constant of motion Iij constructed by Günther and Leach [J. Math. Phys. 18, 572 (1977)] is included as a special case of a time-dependent symmetric tensor constant of motion Kij, where Kij is obtained by use of a time-dependent related integral theorem by means of the symmetry deformation of the constant of motion C2(B) with respect to the affine collineations; such collineations are a subset of the projective collineation symmetries mentioned above. The symmetries and their concomitant constants of motion of the oscillator (a) with ω (t) of the form ω (t) =a+bect are obtained.
−Δ plus a bad potential
Authors: McKean H. P.
Published: March 2003

The purpose of this paper is to associate with −Δ+V (x) a self-adjoint operator in case V is nonnegative. This has been done in many ways by previous authors under a variety of conditions. The point of the present work is to do this under conditions applying to, e.g., any many-body potential, the only requirements being that V:R3n→[0,∞] be continuous and that V−1(∞) be not too large in the sense of volume and/or capacity; especially, no conditions of growth are imposed upon V. The method of proof is probabilistic, being based upon familiar properties of the Brownian motion.
Broken linear transformations
Authors: Gervois A. , Mehta M. L.
Published: March 2003

The properties of mixing and complete mixing are studied for the baker’s transformation and some generalizations with the usual measure dμ (x) =dx. When each linear portion maps on the whole segment, mixing is true. When some linear portions do not map on the whole segment, mixing can hold or not, depending on the transformation even with a more general measure.
Bounds for ladder graph scattering amplitudes on the boundary of their cut
Authors: Wanders G. , Morenzoni E.
Published: March 2003

The physical s channel of a ladder graph amplitude contains the cut of this analytic function. Exact bounds for the modulus of the sum of the ladder graph amplitudes of the scalar gφ3 theory are obtained in this channel. The derivation of these bounds is based on an analytic continuation of the Fourier transforms of the ladder graph amplitudes. The results are compatible with a smooth asymptotic Regge behavior, up to a logarithmic factor.
D (1,0) Killing structures and ℰ potentials
Authors: Hacyan S. , Plebański J. F.
Published: March 2003

Type D metrics in vacuum or with a special electromagnetic field are studied using the fact that they admit a D (1,0) Killing spinor. It is shown that the ℰ and Φ potentials of Ernst can be obtained in a straightforward way for these types of metrics.
Stationary axially-symmetric solutions of Einstein–Maxwell-massless scalar field equations
Authors: Eriş A. , Gürses M.
Published: March 2003

A procedure is presented which enables one to construct solutions to the stationary axially-symmetric gravitational field coupled to massless scalar and Maxwell fields.
Fluid space–times including electromagnetic fields admitting symmetry mappings belonging to the family of contracted Ricci collineations
Authors: Norris L. K. , Green L. H. , Davis W. R.
Published: March 2003

This paper investigates certain symmetry mappings belonging to the family of contracted Ricci collineations (FCRC) (satisfying gijℒRij=0) admitted by the general fluid space–times, including electromagnetic fields, that were classified and studied earlier by Stewart and Ellis (1967). Many of the results obtained are applicable to the perfect fluid models treated by Wainwright (1970) and Krasiński (1974,1975). A major part of this paper represents an extension of previous investigations (1976) of the Robertson–Walker metrics and more general perfect fluid space–times that admit FCRC symmetry mappings and concomitant conservation expressions. More specifically, these results provide a number of theorems relating to the more general fluid space–times that admit FCRC symmetry mappings (including both timelike and spacelike symmetry vectors) that lead to conservation expressions and specific conditions on the metric tensors for the given particular cases of these space–times. Also the form of the symmetry mappings induced on the electromagnetic fields (when they are present) is investigated in the case where specific symmetry mappings on the metric tensor are admitted. In particular, the results of Wainwright and Yaremovicz (1976) relating to homothetic motions admitted by given space–times, corresponding to perfect fluids including electromagnetic fields, are largely embraced by the more general results obtained in this paper.
On the macroscopic equivalence of descriptions of fluctuations for chemical reactions
Authors: Keizer Joel
Published: March 2003

Three descriptions of spontaneous fluctuations in macroscopic systems have been proposed: One uses generalized Fokker–Planck equations and treats fluctuations as a stochastic diffusion process; another uses a connection between fluctuations and dissipation and generalizes the Langevin method; the third is the master equation theory which treats fluctuations as arising from a birth and death process. For a variety of systems it is known that the master equation theory is identical to the fluctuation–dissipation theory in the macroscopic limit. For chemical reactions it is shown here that the appropriate diffusion process also becomes identical with the fluctuation–dissipation theory in the macroscopic limit.
Quantum system subject to random pulses
Authors: Gzyl Henryk
Published: March 2003

We ’’solve’’ the Schrödinger equation for a system subject to random pulses, and show how to compute ensemble averages of observables or their Laplace transforms.
Approximate symmetry groups of inhomogeneous metrics
Authors: Spero Alan , Baierlein Ralph
Published: March 2003

A useful step toward understanding inhomogeneous space–times would be to classify them, perhaps in a fashion analogous to that used for spatially homogeneous space–times. To that end, a technique for determining an approximate simply-transitive three-parameter symmetry group of a three-dimensional positive-definite Riemannian metric is developed. The technique employs a variational principle to find a set of three orthonormal vectors whose commutation coefficients are as close as possible to a set of structure constants. The Bianchi classification of the structure constants of three-parameter groups is then used to classify these inhomogeneous metrics. Application of this technique to perturbed homogeneous metrics is discussed in detail. We find that only four types of symmetry groups can be considered generic in the space of all perturbed homogeneous metrics.
Localized solutions of a nonlinear scalar field with a scalar potential
Authors: Vazquez Luis
Published: March 2003

The exact localized solutions for a nonlinear scalar field with a scalar potential are studied. In particular, we compare the stability of the above solutions and those obtained by Rosen in absence of the scalar potential.
Stationary localized solutions in nonlinear classical fields
Authors: Vazquez Luis
Published: March 2003

The existence of stationary localized solutions for the Dirac field interacting with Maxwell and pseudoscalar fields is studied.
Equivalence transformations for nonlinear evolution equations
Authors: Magri Franco
Published: March 2003

A systematic approach to the study of nonlinear evolution equations based on the theory of the equivalence transformations is suggested. In this paper it is applied to the Burgers and to the Korteweg–de Vries equations. The main result is that the Hopf–Cole transformation for the Burgers equation and the Miura, Bäcklund, and Hirota transformations for the Korteweg–de Vries equation (together with the linear equations of the inverse scattering theory) are all deduced from a single general equivalence condition.
Subalgebras of real three- and four-dimensional Lie algebras
Authors: Patera J. , Winternitz P.
Published: March 2003

The Lie subalgebras of all real Lie algebras of dimension d?4 are classified into equivalence classes under their groups of inner automorphisms. Tables of representatives of each conjugacy class are given.
New algorithms for the Molien function
Authors: Jarić Marko V. , Birman Joseph L.
Published: March 2003

Two new forms are given for the Molien (generating) function for multiplicity cn1 of the identity representation in the symmetrized nth power of representation Γ of finite group G. These are M (Γ,G;z) =Σncn1zn=1/‖G‖Σg exp [Σlzlχ (gl)/l] =1/‖G‖ΣgΠj[1−zγj(g)]−δ j, where g is an element in G γj(g) an irreducible character in the Abelian subgroup A generated by g, δj the subduction coefficient of Γ of G↓γj of A; we usually take Γ irreducible. These forms have the merit of only requiring characters. In the following paper these algorithms are used to compute the Molien function for space group irreducible representation.
Calculation of the Molien generating function for invariants of space groups
Authors: Jarić Marko V. , Birman Joseph L.
Published: March 2003

The new algorithms for computing the Molien generating function for a representation of a finite group obtained in the preceding paper are applied to obtain an expression which can be used for irreducible representation (*kn) of any crystallographic space group G. It proves convenient to express M (Γ,G;z) as a sum: M (Γ,G;z) =1/‖P‖Σkckm̄ (Γ,gk;z), where the partial Molien function m̄ (Γ;gk;z) is labelled by a coset representative gk carrying the class index k of the point group P=G/T, T being the translation group, the sum is over classes k, and ck is the order of class Ck(P). The resulting form was used to compute M (Γ,G;z) for irreducible representations *Γn, *Xn, *Rn of nonsymmorphic space group A-15 or O3h-Pm3n in which many high temperature superconducting crystals occur. Certain of these representations (matrix groups) are identified as generalized Coxeter groups, i.e., unitary groups generated by reflections. The Molien function for these groups as the required form given by Shephard and Todd: M (Γ,G;z) =[Πi(1−zdi)]−1. The di satisfy dimensionality theorems.
On approximating the resolvent of a rotated Hamiltonian in the scattering region
Authors: Singh S. R.
Published: March 2003

We show that, with certain restrictions on the potentials, the Bubnov–Galerkin method enables one to approximate the resolvent of a two-body rotated Hamiltonian in the strong sense. In the general N-body case we find that one might encounter some spurious singularities. However, we suggest a slight modification in the method that enables one to construct a sequence that converges strongly to the exact resolvent. This provides a procedure to approximate the scattering amplitudes for all N-body collisions.
On the theory of time-dependent linear canonical transformations as applied to Hamiltonians of the harmonic oscillator type
Authors: Leach P. G. L.
Published: March 2003

Writing the canonical variables (qT, pT) as (ωT), we develop a method for transforming the time-dependent Hamiltonian H=Aμν(t) ωμων+Bμων +C (t) to the time-independent form H̄= (1/2) δμνω̄μω̄ν using the linear transformation ω̄μ=sμ ν(t) ων +rμ(t). Differential equations are obtained for the parameters sμ ν and rμ. The transformed Hamiltonian enables the construction of an invariant I and an invariant matrix [Iμν]. These invariants apply to both the classical and quantum mechanical problems. The invariant I has the dynamical symmetry group SU(n), and this characterizes all systems with Hamiltonians of the form of H.
Impedance, zero energy wavefunction, and bound states
Authors: Martin André , Sabatier Pierre C.
Published: March 2003

We show that the presence, or absence, of bound states in the three-dimensional Schrödinger equation directly depends on the existence of zeros for a function which is a zero energy solution of the equation and which has the meaning of an impedance in a related equation. Several inequalities that are sufficient to prevent the existence of bound states are obtained from this remark. Some of them are new and bridge the gap between previous results.
Spontaneous symmetry breaking of U1(M) ⊗U2(M) ⊗U3(M) with colored Higgs particles
Authors: Schorr Amir
Published: March 2003

In a previous article a general method for finding the symmetry-breaking directions in a theory which is symmetric under a group U(N1) ⊗⋅⋅⋅⊗U(Nj) ⊗SU(M1) ⊗⋅⋅⋅⊗SU(Mk) was presented. In order to explain and exhibit its utility, we derive in this paper the possible directions of spontaneous symmetry breaking in a U1(M) ⊗U2(M) ⊗U3(M) theory with ’’colored’’ Higgs particles. As an example we discuss the symmetry breaking in the Pati–Salam model which is found to be a legitimate one. A simple explanation of the stability of the quarks inside a ’’particle-phase’’ is exhibited.
Symmetries of the stationary Einstein–Maxwell field equations. I
Authors: Kinnersley William
Published: March 2003

The Einstein equations for stationary axially symmetric gravitational fields are written in several extremely simple forms. Using a tensor generalization of the Ernst potential, we give forms that are manifestly covariant under (i) the external group G of coordinate transformations, (ii) the internal group H of Ehlers transformations and gage transformations, and (iii) the infinite parameter group K of Geroch which combines both. We then show how the same thing can be done to the Einstein–Maxwell equations. The enlarged internal group H′ now includes the Harrison transformations, and is isomorphic to SU(2,1). The enlarged group K′ contains even more parameters, and generates even more potentials and conservation laws.
Symmetries of the stationary Einstein–Maxwell field equations. II
Authors: Kinnersley William , Chitre D. M.
Published: March 2003

From Einstein–Maxwell fields which are stationary and axially symmetric, we show how to construct an infinite hierarchy of potentials. The potentials form a representation of K′, the infinite-parameter symmetry group of the Einstein–Maxwell equations. For flat space, the hierarchy is calculated explicitly.
Wavepacket scattering in potential theory
Authors: Weber T. A. , Hammer C. L.
Published: March 2003

A contour integration technique is developed which enforces the initial conditions for wavepacket-potential scattering. The expansion coefficients for the exact energy eigenstate expansion are automatically expressed in terms of the plane wave expansion coefficients of the initial wavepacket thereby simplifying what is usually a tedious, mathematical process. The method is applicable regardless of the initial spatial separation of the wavepacket from the scattering center.
Causally symmetric spacetimes
Authors: Tipler Frank J.
Published: March 2003

Causally symmetric spacetimes are spacetimes with J+(S) isometric to J−(S) for some set S. We discuss certain properties of these spacetimes, showing for example that if S is a maximal Cauchy surface with matter everywhere on S, then the spacetime has singularities in both J+(S) and J−(S). We also consider totally vicious spacetimes, a class of causally symmetric spacetimes for which I+(p) =I−(p) =M for any point p in M. Two different notions of stability in general relativity are discussed, using various types of causally symmetric spacetimes as starting points for perturbations.
Nonlocal interactions: The generalized Levinson theorem and the structure of the spectrum
Authors: Newton Roger G.
Published: March 2003

Fredholm theory is applied to the Lippmann–Schwinger equation for nonlocal potentials without spherical symmetry. For a specified large set of trace-class interactions it is proved that when, for real k≠0, the Fredholm determinant vanishes, k2 is the energy of a bound state. The point k=0 is examined and the analog of the distinction between zero-energy bound states and zero-energy resonances for local central potentials is found. A generalized Levinson theorem is proved.
Inhomogeneous cosmologies: New exact solutions and their evolution
Authors: Szafron D. A.
Published: March 2003

An algorithm is presented for determining all solutions of the Einstein field equations representing a perfect fluid with metric of the form ds2=dt2−e2αdz2 −e2β(dx2+dy2) and fluid flow vector u=∂/∂t. The entire class of solutions is then invariantly characterized. These new solutions generalize Szekeres’ inhomogeneous cosmological models containing dust. A subclass of these solutions is studied in detail and it is interesting that some of these models approach isotropy but not homogeneity for large cosmological times.
The Clebsch–Gordan coefficients of S
n
Authors: Schindler Susan , Mirman R.
Published: March 2003

Ordering schemes for the frames and tableaux of Sn are presented, and some results, expressible in terms of these, are developed. A formula is derived for the sign function on tableaux. A table of the nonzero Clebsch–Gordon coefficients for the ’’working triplets’’ is given. Methods are described, and a needed table supplied, for finding the other coefficients from the tabulated ones. The values are for n=2,...,6, with the coefficients for n=6 relegated to PAPS.
Structural properties of the self-conjugate SU(3) tensor operators
Authors: Lohe M. A. , Biedenharn L. C. , Louck J. D.
Published: March 2003

Denominator functions for the set of self-conjugate SU(3) tensor operators are explicitly obtained and shown to be uniquely related to SU(3) -invariant structural properties. This relationship becomes manifest through the appearance of zeroes of the denominator functions which thereby express the fundamental null space properties of SU(3) tensor operators. It is demonstrated that there exist characteristic denominator functions whose zeroes, in position and multiplicity, possess the interesting, and unexpected, property of forming SU(3) weight space patterns (in which the zeroes play the role of weights).
On generating forms of K-generalized Lagrangian and Hamiltonian systems
Authors: Rodrigues Paulo R.
Published: March 2003

From a (n+1) -form Ω on the manifold JkM of k-jets of local sections of the vector bundle (M,π,N) we study the conditions to obtain the Lagrangian and Hamiltonian formalisms for a theory which involves higher order derivatives. The results generalize those of Gallissot and others for k=1.
Maxwell’s equations in an expanding universe
Authors: Malin S.
Published: March 2003

Schrödinger’s classical solutions of Maxwell’s equations in an expanding universe with positive spatial curvature are reformulated in terms of gorup theory. Euler angles are used as coordinates in spherical space; the equations satisfied by the components of the complex electromagnetic field tensor are then given in terms of Euler angles. It is shown that if the fundamental modes of the electromagnetic field are appropriately chosen, certain components of the tensor are given by matrix elements of the irreducible representations of the group SU(2).
On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
Authors: Glassey R. T.
Published: March 2003

Solutions to the Cauchy problem for the equation iut=Δu+F(|u| 2)u (x∈ℝn, t>0), u(x,0)=φ(x), are considered. Conditions on φ and F are given so that, for solutions with nonpositive energy, the following obtains: There exists a finite time T, estimable from above, such that ∥gradu(t)∥L2(ℝn)→+∞ as t→T−. It is also shown that other Lq-norms of a solution (including q=∞) blow up in finite time.