bluuebunny/crossref_metadata_2025 huggingface dataset:
Resonances, scattering theory, and rigged Hilbert spaces
Authors: Parravicini Guido , Gorini Vittorio , Sudarshan E. C. G.
Published: March 2003

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,’’in,’’ and ’’out’’ eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ’’out’’ eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ’’complete’’ sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ’’out’’ eigenvectors. The free, ’’in’’ and ’’out’’ eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential.
A variational problem for the forward or backward scattering amplitude with three constraints
Authors: Sakmar I. A.
Published: March 2003

The problem of extremizing the slope of the imaginary part of either the forward or the backward scattering amplitude is treated as a variational problem with three constraints, one of which is the other slope and the other two σT and σel,im.
Canonical connections on Riemannian symmetric spaces and solutions to the Einstein–Yang–Mills equations
Authors: Harnad J. , Tafel J. , Shnider S.
Published: March 2003

It is shown that for any principal bundle over a Riemannian symmetric space G/G0 which admits G as automorphism group, the canonical G-invariant connection satisfies the source free gauge field equations. Extending this to product manifolds V×G/G0 and assuming the metric and gauge fields decompose in a natural way, this result is still valid and the Einstein equations with gauge fields as source may also be satisfied. For G/G0, this is so automatically, but with a cosmological term present. For dimV=1 or 2, solutions are found, yielding metrics of the Robertson–Walker and Reissner–Nordstrom type.
On the stationary Einstein–Maxwell field equations
Authors: Das A. , Kloster S.
Published: March 2003

The stationary gravitational equations in the presence of the electromagnetic fields, outside charged gravitating sources, are investigated. (i) The action integral of Kramer–Neugebauer–Stephani (K.N.S.) is derived from the Hilbert action integral by using new variational techniques. (ii) It is shown that the classification scheme for the system of partial differential equations of general relativity depends on the coordinate system used. In particular, if orthogonal coordinates are chosen for the associated space then the system of Einstein–Maxwell equations is a hyperbolic one. (iii) The eigenvalues of the Ricci tensor of associated space are expressed in terms of the invariants of stationary electro-gravitational fields. It is proved that if these eigenvalues are equal then the fields must belong to the class of Peres–Israel–Wilson (PIW) solutions. (iv) The global integrability of some of the stationary Einstein–Maxwell equations and the consequent equilibrium conditions of the ’’bodies’’ are investigated. (v) Boundary value problems for some of the field equations are pursued. It is proved that ω≡ln‖g44‖ is neither subharmonic nor superharmonic and the boundary value problem for this function does not yield a unique solution in general. A nontrivial solution of the stationary equations with ω≡0 is given. A special boundary value problem is explicitly solved. (vi) The PIW solutions are generated from the charged Kerr–Tomimatsu–Sato–Yamazaki (KTSY) solutions. The complex axially symmetric harmonic functions of these PIW solutions can be obtained from the real axially symmetric harmonic functions of the static Weyl class of electrovac solutions by a complex scale transformation of the coordinates.
Some electrovac models of homogeneous gravitational force fields in general relativity
Authors: Srinivasa Rao K. N. , Gopala Rao A. V.
Published: March 2003

In this paper we consider the problem of defining and constructing the general relativistic analog of the Newtonian homogeneous gravitational force field. With this purpose, the Newtonian definition of homogeneity is first reformulated in a manner suitable for nonflat space sections and is then shown to lead to a covariant characterization of static space–times admitting uniform gravitational force fields. This covariant characterization is both necessary and sufficient and is consistent with the necessary conditions of homogeneity introduced by Goodinson. Further, a whole class of static solutions of the Einstein–Maxwell equations, all admitting homogeneous gravitational force fields, is obtained and some of their properties are discussed. In particular, this class of electrovac solutions appears to exhibit the remarkable property that the metrics and the source electromagnetic fields are free of singularities.
Analyticity in the coupling constant of the λ P(φ) lattice theory
Authors: Constantinescu Florin
Published: March 2003

Consider the lattice λP(φ) theory in an arbitrary number of dimensions. The single spin distribution is given by λP(φ)+m2/2φ2. We show that if ϑ<n+1/2π̄, then there is a constant ε≳0 such that the correlations are analytic in ‖ λ ‖<ε, ‖ arg λ ‖ <ϑ provided m is sufficiently large. This result implies Borel summability of the lattice (Euclidean) λP(φ) quantum field theory for small coupling constants.
Theory of involutional transformations applied to the Dirac theory of the electron. I. Remarks on the Dirac plane waves
Authors: Kim Shoon K.
Published: March 2003

The involutional transformations are shown to play a fundamental role in the Dirac relativistic theory of electron. The symmetric plane waves in the momentum representation, which are the simultaneous eigenfunctions of the energy and helicity operator, are given by the columns of a unitary matrix defined by U=YEYs, where YE and Ys are IUH (involutional, unitary, and Hermitian) matrices which diagonalize the Dirac Hamiltonian and the helicity of a free particle respectively. It is shown that all the known properties of the Dirac plane waves stem from the properties of the involutional transformations YE and Ys.
Global existence of Maxwell–Klein–Gordon fields in (2+1)-dimensional space-time
Authors: Moncrief Vincent
Published: March 2003

We study the global existence problem for the Maxwell–Klein–Gordon equations in (2+1)-dimensional, Minkowski spacetime. We first establish local existence, in a suitable Sobolev space, by specializing to the Lorentz gauge and applying standard techniques. We then prove global existence by showing that an appropriate norm of the solutions cannot blow up in a finite time. An essential step in the proof involves showing that a certain second order ’’energy’’ does not blow up.
Periodic solutions of the classical polaron and bipolaron systems
Authors: Peeters F. , Devreese J. T.
Published: March 2003

It is shown that the exact solutions for the classical polaron model derived by Evrard et al. (the electron rotates about a fixed polaron centre with frequency Ω≫ω) exist also for the discrete frequencies Ω=ω/(n+ 1/2 )(ω is the longitudinal optical phonon frequency and n is an integer). For an infinite Brillouin zone radius the radius of the electron orbit is finite; this is in contrast with the behavior of the solutions found by Evrard et al., where the radius diverges with the Brillouin zone radius. Ringwood and Devreese have obtained the same set of solutions as proposed here with a different method. The present calculation shows clearly that the discrete frequencies arise as a consequence of the fact that the electron has to move in such a way that the different divergent contributions to the self-interaction cancel each other. For the bipolaron system similar exact solutions are found. It is shown that the orbit frequency of the electrons, in the bipolaron system, can have the values Ω=ω/(2n+1).
Thermal excitations in Heisenberg-x
y systems
Authors: Puga M. W.
Published: March 2003

The finite temperature excitations of the anisotropic chain in a magnetic field are calculated in the region ‖Δ‖<1. Some special solutions are given, which point out several changes with respect to the T=0 case.
Quantum friction in the c-number picture: The damped harmonic oscillator
Authors: Brinati J. R. , Mizrahi S. S.
Published: March 2003

Considering the Lagrangian proposed by Havas, that describes the classical damped motion of a particle, new momentum and position are defined in order to write a Hamiltonian that is subsequently quantized and expressed in terms of non-Hermitian operators. Using the c-number formalism proposed by Lax and Yuen, we associate to the quantum Liouville equation a Fokker–Planck one in terms of c-numbers. From the properties of this equation we obtain the mean values of the position, momentum, and energy of a brownian particle and we also verify the uncertainty principle. We observe that when the system is considered under the Markov hypothesis, the stochastic force is intimately related to the uncertainty principle and to the zero point energy.
Upper and lower bounds in nonrelativistic scattering theory
Authors: Darewych J. W. , Pooran R.
Published: March 2003

We consider the problem of determining rigorous upper and lower bounds to the difference between the exact and approximate scattering phase shift, for the case of central potential scattering. The present work is based on the Kato identities and the phase-amplitude formalism of potential scattering developed by Calogero. For nonstationary approximations, a new first-order (in small quantities) bound is established which is particularly useful for partial waves other than s waves. Similar, but second-order, bounds are established for approximations which are stationary. Some previous results, based on the use of the Lippman–Schwinger equation are generalized, and some new bounds are established. These are illustrated, and compared to previous results, by a simple example. We discuss the advantages and disadvantages of the present results in comparison to those derived previously. Finally, we present the generalization of some of the present formalism to the case of many-channel scattering involving many-particle systems, and discuss some of the difficulties of their practical implementation.
Properties of a covering space defined by Hawking
Authors: Haggman B. C. , Horndeski G. W. , Mess G.
Published: March 2003

We investigate the topological properties of a covering space introduced by Hawking in 1967 to assist in his derivation of some singularity theorems.
Relationships between the group-theoretic and soliton-theoretic techniques for generating stationary axisymmetric gravitational solutions
Authors: Cosgrove Christopher M.
Published: March 2003

We investigate the precise interrelationships between several recently developed solution-generating techniques capable of generating asymptotically flat gravitational solutions with arbitrary multipole parameters. The transformations we study in detail here are the Lie groups Q and Q̃ of Cosgrove, the Hoenselaers–Kinnersley–Xanthopoulos (HKX) transformations and their SL(2) tensor generalizations, the Neugebauer–Kramer discrete mapping, the Neugebauer Bäcklund transformations I1 and I2, the Harrison Bäcklund transformation, and the Belinsky–Zakharov (BZ) one- and two-soliton transformations. Two particular results, among many reported here, are that the BZ soliton transformations are essentially equivalent to Harrison transformations and that the generalized HKX transformation may be deduced as a confluent double soliton transformation. Explicit algebraic expressions are given for the transforms of the Kinnersley–Chitre generating functions under all of the above transformations. In less detail, we also study the Kinnersley–Chitre β transformations, the non-null HKX transformations, and the Hilbert problems proposed independently by Belinsky and Zakharov, and Hauser and Ernst. In conclusion, we describe the nature of the exact solutions constructible in a finite number of steps with the available methods.
Quantum field theory of particles of indefinite mass. I
Authors: Hostler Levere
Published: March 2003

A quantum field theory of particles of indefinite mass is derived using rigorous correspondence arguments starting with a classical theory of particles of indefinite mass. The classical theory can be recovered in a suitable limiting case as h/→0 by means of Ehrenfest’s theorem. Our deviation leads to a quantum mechanical wave equation which turns out to be basically the same equation investigated earlier by Fock, Nambu, and others, but differs from this earlier equation in our use of a new evolution parameter—herein called ’’evolution-time’’—defined as proper time divided by the classical mass. Owing to our use of evolution time as the development parameter of the system our Fock equation is without any reference to a mass parameter, in contrast to the older Fock equation. The indefiniteness of the particle mass frees the ordinary time, t—herein called ’’observer’s time’’—of any fixed relationship to the evolution time, and the two times becomes quite independent parameters. The Hamiltonian of our system turns out to be (minus half) the total mass squared of the system and is a constant of the motion. In order to guarantee negative definiteness of the Hamiltonian of the second quantized system, it is necessary to quantize our Fock equation using Fermi–Dirac statistics. A real scalar field is described by an equation which is second-order in the evolution time, obtained by iterating our first-order Fock equation. The second-order Fock equation must be second quantized using Bose–Einstein statistics, in order to preserve the interpretation of the Fourier amplitudes as creation and annihilation operators. The propagator for the second-order Fock equation has a Pauli–Villars type sum of terms, in which one term describe the propagation of timelike states, the other term describes space-like states.
On computing eigenvalues in radiative transfer
Authors: Siewert C. E.
Published: March 2003

The Wiener–Hopf factorization of the dispersion function is used to deduce explicit expressions for the discrete eigenvalues in the theory of radiative transfer.
Shift operators for discrete representations of O(p, q)
Authors: Murphy T.
Published: March 2003

Shift operators for discrete representations of O( p,q) are found in product form. Their normalization is found and conditions are derived for the weight components of such representations.
The character generator of SU(n)
Authors: Stanley Richard P.
Published: March 2003

A simple combinatorial method for writing the character generator of SU(n) is described.
On a new relation between semisimple Lie algebras
Authors: Patera J. , Sharp R. T. , Slansky R.
Published: March 2003

A recently discovered relation between pairs of semisimple Lie algebras is further investigated. This relation, which is called subjoining and denoted by ’’≳’’, is a generalization of inclusion, where a subalgebra is embedded in an algebra. Nontrivial subjoinings of two algebras of the same type are described. New chains of algebras involving proper inclusions and subjoinings can be formed. Infinite families of maximal subjoinings Cn≳Bn and Bn≳Cn are shown.
Gauge invariance and the Helmholtz conditions
Authors: Cawley Robert
Published: March 2003

In a previous work I have outlined a new formalism of theoretical mechanics, extending the traditional subject in a new way to elementary systems whose second-order dynamical equations do not satisfy the classical Helmholtz conditions for the existence of a Lagrange function. In the present paper I determine the role of a new gauge invariance (’’dynamical’’ gauge invariance), satisfied by the equations of motion of systems covered by the formalism, and the relationship this bears to the Helmholtz conditions. A certain subgroup, of ’’kinematic’’ gauge transformations, is singled out: the kinematic gauge transformations correspond for the Lorentz force law to the usual gauge transformation of electromagnetism, general dynamical gauge transformations correspond to minimal substitutions. An analogue for the nonalbelian gauge force law is discussed briefly. An implication of the present work is the result, in a sense made explicit within, that (the usual) gauge invariance is an intrinsic property of classical Hamiltonian systems.
Relativistic covariance and rotational electrodynamics
Authors: Corum James F.
Published: March 2003

The following article demonstrates how the logical coherence of relativistic electrodynamics is maintained for a particular family of rotational paradoxes. The internal computational unity, for rotation, is preserved through the manifestation of a commonly unrecognized geometrical property of tensor calculus.
Number operators for composite particles in nonrelativistic many-body theory
Authors: Brittin Wesley E. , Sakakura Arthur Y.
Published: March 2003

Commuting physical occupation number operators for composite particles are constructed using projection operator techniques. The composite particle occupation number operators are constructed from creation and annihilation operators of the elementary particles which make up the many-body system. They appear as positive operators in any given second quantized theory and represent observables within the framework of that theory. Bose-type composites have number operators with eigenvalues 0,1,2,..., and Fermi-type composites have number operators with eigenvalues 0,1. There does not arise here any problem having to do with exchange symmetry—exchange symmetry is exact, since the number operators act in the Fock space of the elementary particles. The composite particle number operators may be used in the construction of theories of composite particle reactions or equilibrium from a first principles standpoint. The construction used here not only establishes the existence of composite particle number operators but also provides some computational machinery which hopefully will aid in more practical applications.
An integral transform related to quantization
Authors: Daubechies I. , Grossmann A.
Published: March 2003

We study in some detail the correspondence between a function f on phase space and the matrix elements. (Qf)(a,b) of its quantized Qf between the coherent states ‖ a〉 and ‖ b〉. It is an integral transform: Qf(a,b) = ℱ{a,b ‖ v}f(v) dv, which resembles in many ways the integral transform of Bargmann. We obtain the matrix elements of Qf between harmonic oscillator states as the Fourier coefficients of f with respect to an explicit orthonormal system.
Nature of superspace
Authors: Bugajska Krystyna
Published: March 2003

It is demonstrated that the superspace of the supersymmetry theory can be identified in a natural manner with a family of concrete spinor structures over space–time.
Generalized Bessel functions and the representation theory of U(2) σ C2×2
Authors: Holman Wayne J.
Published: March 2003

We construct the matrix elements of both finite transformations and infinitesimal generators in irreducible representations of the motion group U(2) σ C2×2 with the aid of the contraction limit of the analogous structures of U(4). The matrix elements of finite transformations are found to have a structure similar to that of the classical Bessel function in that they contain two inverse gamma matrices which couple Wigner D functions. An integral representation is established and related to the matrix-valued Bessel functions of Gross and Kunze. By means of the representation property of the matrix elements we obtain a new sum rule for classical Bessel functions and an analog of the binomial theorem for the sum of two 2×2 matrices which involves the U(2) gamma matrix instead of the classical gamma function.
Selection rules for P
n3′n
Authors: Dirl R.
Published: March 2003

Clebsch–Gordan coefficients for the type II Shubnikov space group Pn3′n are calculated in terms of such coefficients for the unitary subgroup Pn3n.
Simple derivation of the Newton–Wigner position operator
Authors: Jordan Thomas F.
Published: March 2003

The kind of operator algebra familiar in ordinary quantum mechanics is used to show formally that in an irreducible unitary representation of the Poincaré group for positive mass, the Newton–Wigner position operator is the only Hermitian operator with commuting components that transforms as a position operator should for translations, rotations, and time reversal and does not behave in a singular way that contradicts what can be learned from Lorentz transformations in the nonrelativistic limit.
On six-dimensional canonical realizations of the so(4,2) algebra
Authors: Iosifescu Mircea , Scutaru Horia
Published: March 2003

On each six-dimensional symplectic manifold a coordinate-free realization of the so(4,2) algebra can be constructed, the generators of which satisfy the polynomial relations fulfilled by the so(4,2) generators associated with the Kepler problem. This realization contains as a particular case several realizations of so(4,2) known in the literature. An expression of the symplectic form on a six-dimensional symplectic manifold, in terms of the so(4,2) generators defined on this manifold, is obtained. In particular, on the six-dimensional orbit of the SO(4,2) group in so(4,2) this symplectic form coincides with the symplectic form introduced by Kirillov Kostant and Souriau. The symplectic form is given a Darboux expression with the aid of three pairs of canonically conjugated variables, which are a generalization of the Delaunay elements defined in the Kepler problem.
WKB method for systems of integral equations
Authors: Berk H. L. , Pfirsch D.
Published: March 2003

The WKB theory for vector systems of integral equations is developed herein. A variational technique is used to derive the equations for the WKB amplitudes in x-space or its dual k-space. Compact, explicit solutions are obtained in one dimension. When a solution breaks down at a turning point, the dual-space representation can be used to derive the connection formulas between WKB solutions. These connection formulas are equivalent to the rules of the Furry method. The Furry method is used to show how general golbal-dispersion relations can be constructed.
On a remarkable class of two-dimensional random walks
Authors: Wiegel F. W.
Published: March 2003

This study describes some properties of random walks in a plane which differ from free random walks through an extra weightfactor (−1) for every crossing of some branchline T. The statistical distribution of these walks is derived, asymptotically for very long walks, in the case that T consists of a half-line. It is pointed out that these walks are relevant to (1) self-avoiding random walks in a plane; (2) the simple entanglement problem in polymer physics.
Poincaré–Cartan integral invariant and canonical transformations for singular Lagrangians
Authors: Dominici D. , Gomis J.
Published: March 2003

In this work we develop the canonical formalism for constrained systems with a finite number of degrees of freedom by making use of the Poincaré–Cartan integral invariant method. A set of variables suitable for the reduction to the physical ones can be obtained by means of a canonical transformation. From the invariance of the Poincaré–Cartan integral under canonical transformations we get the form of the equations of motion for the physical variables of the system.
Spectral broadening of waves propagating in a random medium
Authors: Wenzel Alan R.
Published: March 2003

Formulas for the cross-correlation and spectral density functions of the scalar wave field radiated by a random point source in a weakly inhomogeneous three-dimensional time-dependent random medium are derived. The medium is assumed to be statistically homogeneous and isotropic and to be statistically independent of the source. The analysis is based on a modification of the smoothing method. An approximate expression for the power spectrum of the wave as a function of the source-field point distance (or propagation distance) is obtained for the case in which the characteristic frequency of the source is much greater than that of the medium. This expression shows that the wave spectrum approaches a limiting form, which is referred to here as the fully developed spectrum, with increasing propagation distance. It is also found that the total signal power is conserved as the spectrum evolves. Results obtained for the case of a narrow-band source indicate that the spectral bandwidth increases initially as the square root of the propagation distance, but that at larger distances it approaches a limiting value. Numerical results obtained for the narrow-band case show a progressive broadening of the wave spectrum with increasing propagation distance and/or with increasing strength of the randomness of the medium, in agreement with observations.
Quality factor constrained, antenna pattern synthesis using a restricted class of aperture functions
Authors: Jarem John M.
Published: March 2003

The quality factor [Q] for the E-plane strip source antenna is minimized with respect to a class of aperture functions for which the [Q] converges. A complete basis for the above class of functions is constructed for the first time and this basis is used to minimize the above mentioned [Q]. The functions which minimize the above [Q] turn out to be doubly orthogonal and are used to implement a constrained aperture synthesis procedure. New results concerning the maximum bandwidth (or minimum [Q]) of the E-plane strip source antenna are given.
Some remarks on the classical vacuum structure of gauge field theories
Authors: Asorey M.
Published: March 2003

A simple and useful characterization of the global copies of any classical gauge vacuum is given. When the gauge group is abelian we obtain through that characterization a necessary and sufficient condition for the equivalence of the principal fiber bundles on which any two of such copies are defined. We compute by using also that characterization the classical vacuum structures of some non-abelian gauge field theories defined on different space–times.
Inverse problem transport calculations for anisotropic scattering coefficients
Authors: McCormick N. J. , Sanchez R.
Published: March 2003

One-speed transport anisotropic scattering coefficients are calculated by an inverse transport model which requires only emerging angular distributions from a homogeneous slab uniformly irradiated by a monodirectionally incident beam. The solution of the direct problem used to test the inverse calculations is obtained with the FN method of Siewert. New numerical schemes are developed which are applicable for the FN solution of other one-speed problems. The inverse transport method shows promise for characterizing media by only measurements of reflected and transmitted laser light from a slab.
On the scattering of plane electromagnetic waves off spherically confined cold plasmas with overdense and steep densities
Authors: Kriegsmann Gregory A.
Published: March 2003

In this paper we study the scattering of a plane electromagnetic wave off a spherical plasma pellet. The plasma density is taken to be overdense and very steep. This causes the cut off radius, r0, to be within a fraction of a wavelength from the spherical boundary. The problem is studied in the asymptotic limit (aω/c)→ ∞ with 0<1−r0=O(c/aω). Here a is the radius of the sphere, ω is the frequency of the incident radiation, and c is the velocity of light in free space. We develop an asymptotic technique which reduces Maxwell′s equations to three ordinary differential equations within the plasma. Our method is a blend of geometrical optics and boundary layer techniques. Straightforward geometrical optics is used to describe the scattered field.
On the topology of charged spherical collapse
Authors: Hiscock William A.
Published: March 2003

It is shown that in the gravitational collapse of a charged fluid sphere only one of the two Reissner–Nordström curvature singularities is present, under the assumption that the charge density evaluated at the surface of the sphere and the total charge on the sphere do not have opposite sign. Arguments are presented to show that this assumption is physically reasonable. Ignoring possible naked singularities formed within the collapsing matter, this implies that the only Cauchy horizon in the interior of a charged black hole is the future inner event horizon (r=r−, t=+∞), which is known to be both classically and quantum mechanically unstable.
Observer frame rotation rates and magnetic fields in spatially homogeneous universes
Authors: Fennelly A. J.
Published: March 2003

We discuss how the rotation of an observer’s Cartesian reference frame is related to the precession of the shear tensor’s principal axes and to the rotation vector of the fluid. An approximate solution of Einstein’s equations illuminates this relationship further. In the case with a magnetic field and fluid flow a vorticity is allowed in Bianchi I cosmologies.
On the matrix elements of the U(n) generators
Authors: Gould M. D.
Published: March 2003

A straightforward derivation of the matrix elements of the U(n) generators is presented using algebraic infinitesimal techniques. An expression for the general fundamental Wigner coefficients of the group is obtained as a polynomial in the group generators. This enables generalized matrix elements to be defined without explicit reference to basis states. Such considerations are important for treating groups such as Sp(2n) whose basis states are not known.
A Bessel–Watson transform pair
Authors: Samaddar S. N.
Published: March 2003

A Bessel–Watson type of transform pair is developed. Since this result differs from a previously published result, a comparison between these two results is also presented.
Stability of constant-amplitude motions in slow-fluctuation approximation
Authors: Augusteijn Marijke F. , Breitenberger Ernst
Published: March 2003

Oscillatory motions at constant amplitude admit of an especially simple description of their stability in phase space: orbital stability is equivalent to stability of the amplitudes alone, regardless of phase behavior, while Liapunov stability can subsequently be inferred from the phases alone. Stability arguments simplify further in slow-fluctuation approximation because of the availability of explicit quadratures for the amplitudes and phases depending ultimately on a single polynomial. Thus, all orbital stability information about near-resonant constant-amplitude motions in conservative, autonomous systems can be extracted solely from that one polynomial. Explicit analytic criteria for orbital stability are derived, and auxiliary methods for the construction of stability charts are developed. Liapunov stability is shown to be a rare exception, but Liapunov instability is encountered in distinctly varying degrees; a fairly wide class of motions in a fairly wide class of systems is shown to be Liapunov–unstable only in the third order of a certain approximation. Five examples are given at some length; they differ starkly in detail. Owing to their tractable stability properties the abundant constant-amplitude motions play in slow-fluctuation approximation the role of the often nonexistent, purely periodic solutions of the traditional theories.
Independent variables in quantum mechanics
Authors: Blood F. A.
Published: March 2003

It is conjectured that the particle states of quantum mechanics are represented by functions of independent variables. These functions obey a linear differential equation which has an invariance group homomorphic to the inhomogeneous Lorentz group, thus giving a linear, Lorentz-invariant theory. Simple one-particle examples of equations which lead to a discrete particle spectrum are given, using both space–time variable, xμ, and sets of spinlike variables (pairs of complex numbers). Some of the examples have internal symmetry. No examples of realistic ’’many-body’’ particle theories are given, but we can deduce general characteristics. The differential equation must be of second or higher order to give an interaction. Products of single-particle states will be solutions of the equation and will form a complete set for widely separated particles. But products of one-particle states are not solutions of the equation for strongly interacting particles, and this permits the creation of particles. The origin of antisymmetry in such a theory is not clear.
On the existence of real Clebsch–Gordan coefficients
Authors: Damhus Ture
Published: March 2003

The question of the possible general existence of real Clebsch–Gordan coefficients (coupling coefficients) for compact groups is considered. Criteria are established for a group to be susceptible to the classical rotation group approach in which a choice of standard irreducible matrix representations is made such that there is a fixed inner automorphism of the group carrying all standard representations into their complex conjugate. In connection with a generalization of this approach the concept of quasi-ambivalence of a group is shown to be relevant.
Invariant connections and magnetic monopoles
Authors: Cant A.
Published: March 2003

Given a Lie group K acting on a principal fiber bundle P(M, G), we study the K-invariance of connections in P and in bundles associated to P. The geometry of spontaneous symmetry breaking is discussed from this point of view. The results are applied to the Wu–Yang and ’t Hooft–Polyakov models of a magnetic monopole.
Plane waves and topology
Authors: Ross D. K.
Published: March 2003

We investigate particles which can be described in terms of plane waves and find that the number of topologically distinct such particles is the same as the number of disconnected pieces of the gauge group or structure group of the appropriate fiber bundle.
A new method of constructing the symmetry coordinates of molecular vibrations based on the correspondence theorem
Authors: Kim Shoon K.
Published: March 2003

A general method of constructing the symmetry coordinates of molecular vibrations is presented via the correspondence theorem which describes the parallelism between a SALC (symmetry adapted linear combination) and an elementary basis function belonging to the same irreducible representation of the symmetry group of the molecule.
Quantum field theory of particles of indefinite mass. II. An electromagnetic model
Authors: Hostler Levere
Published: March 2003

A new model of the electromagnetic field is postulated. The model is designed within the conceptual framework of the quantum field theory of particles of indefinite mass. The model is built around an interaction Lagrangian of the type ℒI = (1/2) ρV−JμAμ, where (Jμ;ρ) is a conserved c-number 5-current. A gauge invariance principle is thereby built into the theory. The object (1/2) V is a new 5th component of the vector potential. Due to the use of the new evolution parameter τ, second quantization in the Lorentz gauge ∂μAμ = 0 parallels Coulomb gauge quantization in ordinary quantum electrodynamics. The Hamiltonian of the free electromagnetic field is negative definite and has the physical interpretation of minus half the sum of the squares of the masses of the photons present. The inner product in Hilbert space is not positive definite, spacelike states with timelike polarization having negative norm.
Shift operator techniques for the classification of multipole-phonon states. VIII. R(5) ↓ SU(2) ⊗ SU(2) reduction for obtaining quadrupole O
l eigenvalues
Authors: Vanden Berghe G. , De Meyer H. E.
Published: March 2003

With the aid of previously derived expressions for the reduced matrix elements of the R(5) generators, which are obtained by considering R(5) ↓ SU(2) ⊗ SU(2) reduction, a method is set up to evaluate analytical expressions for the eigenvalues of the quadrupole scalar shift operator O0l. Explicit expressions are listed for states with angular momenta l = 2v−k (k = 0 up to 13).
Shift operator techniques for the classification of multipole-phonon states. IX. Properties of nonscalar R(3) product operators in the G2 group
Authors: Vanden Berghe G. , De Meyer H.E. , Van der Jeugt J.
Published: March 2003

Expressions connecting nonscalar R(3) products of operators shifting the eigenvalues of L2 are constructed within the group G2.
The inverse problem of the shear modulus and density profiles of a layered earth—torsional vibration data
Authors: Coen Shimon
Published: March 2003

This paper shows that the shear modulus and density profiles of a layered earth are uniquely determined by the torsional stress and displacement on its surface at two frequencies. An analytical example is given in which these profiles are deduced from analytic data.
The behavior at infinity of isotropic vortices and monopoles
Authors: Plohr Bradley
Published: March 2003

We derive detailed asymptotic formulae for the behavior at infinity of isotropic vortex solutions of the abelian Higgs model and monopole solutions of the Yang–Mills Higgs model. In particular we find that the classical mass of the Higgs field is the smaller of m and twice the mass of the gauge field, where (mc/h/)2 is the curvature of the Higgs self-interaction potential at the classical vacuum.
Algebras with three anticommuting elements. I. Spinors and quaternions
Authors: Ilamed Yehiel , Salingaros Nikos
Published: March 2003

A general construction of alternative algebras with three anticommuting elements and a unit is given. As an exhaustive result over the real and complex fields, we obtain the Clifford algebras H (quaternions), N1 (dihedral Clifford algebra which is related to real 2-spinors), and S1 (algebra of Pauli matrices which is related to complex 2-spinors). What is important is that the algebras N1 and S1 possess inverses everywhere except on a region akin to the light cone of the Minkowski space, while the quaternion algebra H has inverses everywhere except at the zero element. We discuss the reasons why the three algebras N1, H, and S1 are so difficult to distinguish in the representation space of 2×2 complex matrices.
Algebras with three anticommuting elements. II. Two algebras over a singular field
Authors: Salingaros Nikos
Published: March 2003

The Clifford algebra Ω generated by the elements {1,ω} with (ω)2 = +1, is an abelian ring of dimension two with properties analogous to the complex field C. The ring Ω has a string of singular inverses, and may be regarded as a ’’singular field’’ which circumvents both the fundamental theorem of algebra and the Frobenius theorem. We construct two associative algebras of dimension four over Ω: the Clifford algebra Ω1 and the biquaternions of Clifford Ω2, and demonstrate that both algebras possess inverses everywhere except on a singular region akin to the light cone of the Minkowski space. Matrix representations are discussed, as well as the importance of the algebras Ω1 and Ω2, in the description of physical vector fields.
A unified theory of the point groups and their general irreducible representations
Authors: Kim Shoon K.
Published: March 2003

Point groups and their general irreducible (vector and projective) representations are characterized by the subgroup conditions for SU(2) in a unified scheme: these conditions are given by simple polynomial equations imposed on the matrix elements of the 2×2 unitary matrices of SU(2). The general irreducible representations for the point groups D∞,Dn (with arbitrary integer n?2), O, and T are given by four simple and effective tables.
On the parametrization of certain finite groups and their representations
Authors: Bovier Anton , Wyler Daniel
Published: March 2003

We discuss a convenient way of parametrizing certain finite groups. They comprise groups with abelian normal subgroups and central extensions thereof; they include the groups Dn, T, O, and their double groups, as well as the SU(3) subgroups Tn, Δ(3n2), Δ(6n2), Σ(72), Σ(216), Σ(36) and their Z3-extensions. The method allows for a rapid calculation of representations and coupling coefficients; in particular, it solves the ’’multiplicity problem’’ of nonsimply reducible groups. We illustrate the method treating the Hessian group Σ(216) and its central extension.
The Racah algebra for groups with time reversal symmetry .II
Authors: Newmarch J. D. , Golding R. M.
Published: March 2003

In a previous paper, J. Math. Phys, 22, 233 (1981) it was shown that a Racah algebra could be developed for groups containing the antilinear operator of time reversal. Here the 1jm and 2jm symbols are constructed explicitly, and it is shown that the 3jm symbols may be found in terms of those of the linear subgroup. Thus the Racah algebra of these groups is known once the Racah algebra of the linear subgroup is known.
Fredholm determinants associated with Wiener integrals
Authors: Nelson Bruce , Sheeks Benny
Published: March 2003

We present a method for evaluating a large class of Fredholm determinants that are associated with the evaluation of certain Wiener integrals. The infinite-dimensional determinant is shown to be equal to a single finite-dimensional determinant.
Modified singular perturbation method for a stiff system of linear evolution equations
Authors: Bl/eński Tomasz
Published: March 2003

A stiff system of linear evolution equations in Banach space is investigated. It is shown that the standard singular perturbation algorithm can be considerably simplified. In this modified algorithm the asymptotic solutions can be obtained in each order independently. The initial conditions are given explicitly so there is no need to solve the so-called ’’inner’’ equations. Two examples of application are considered.
Algebraic and geometric structure of linear filters and scattering systems. I
Authors: Hermann Robert
Published: March 2003

Some of the problems of linear filter and scattering theory are interpreted in terms of the theory of algebraic and analytical subvarieties of Grassman manifolds.
Incompressibility in relativistic continuous media
Authors: Ferrando J. J. , Olivert J.
Published: March 2003

A formalism of continuous media in general relativity is given and the concept of shock waves is defined using manifolds with boundary and the transversality theory of submanifolds. A definition of relativistic incompressibility is proposed and one gets that the shock waves are longitudinal with the speed of light.
Classical solutions of the equations of supergravity
Authors: Finkelstein Robert J. , Kim Jaegu
Published: March 2003

We describe an algorithm to solve the classical equations of supergravity for the coupled fields of helicity 2 and 3/2. The algorithm depends on an expansion in the associated Grassman algebra and leads to a sequence of coupled equations that may be solved in a step by step manner. The procedure begins with solutions of the usual empty space Einstein equations but the subsequent equations are all linear differential equations. To complete the method, it is necessary to generalize the supplementary conditions on the vector spinor field from flat to curved space. The algorithm also permits a classification of the complete solutions in terms of the associated gravitational fields. It is shown that vanishing curvature implies Minkowski space and does not permit other conceivable possibilities such as a Clifford space. Generalizations of the vanishing curvature space are suggested.
Charged Demianski metric
Authors: Krori K. D. , Chaudhury T. , Bhattacharjee R.
Published: March 2003

A solution of Einstein–Maxwell equations is presented. This solution is the charged version of the Demianski metric.
Viscous fluid interpretation of electromagnetic fields
Authors: Raychaudhuri A. K. , Saha S. K.
Published: March 2003

As observed by Tupper, if the Ricci tensor satisfies the Rainich conditions for a nonnull electromagnetic field, the energy stress tensor may sometimes be interpreted as due to a viscous fluid (apparently Tupper believed this to be possible for all electrovac solutions). The present paper shows that for such an interpretation to be possible, there must be an additional symmetry property. Even then in some cases the interpretation may not work due to unacceptable behavior of the fluid velocity vector.
Space–times with geodesic, shear-free, twist-free, nonexpanding rays. II
Authors: Ludwig Garry
Published: March 2003

Reduced gravitational field equations are obtained for space–times with geodesic, shear-free, twist-free, and nonexpanding rays. No restrictions are imposed on either the Weyl tensor or the Ricci tensor, and a further restriction made previously that the spin coefficient τ vanish is also dropped. Special cases of Einstein–Maxwell space–times are investigated further.
Coherent frequency modulation in Gaussian stochastic processes
Authors: Takimoto Noboru
Published: March 2003

A study is given of the stochastic properties of a system of classical harmonic oscillators, driven by a Gaussian fluctuation and with a periodically modulated frequency. It is shown that, when the condition for the parameter amplification is almost satisfied, a phase locking occurs between the modulation and oscillation, leading to a coherent motion of the system as a whole. The difference between this type of coherent motion and the one excited by a periodic external force is pointed out. The distribution function for the process is defined and is shown to satisfy a generalized Fokker–Planck equation. A discussion is also given of the conditional probability, and some of its characteristic properties are specified in connection with the phase-locking effects.
Generalized decoupling theorem in quantum field theory
Authors: Manoukian Edward B.
Published: March 2003

Previous analyses of the decoupling theorem, in Euclidean space, considered only one mass scale in the theory becoming large and had the stringent constraint of allowing no zero mass particles in the theory. We generalize the decoupling theorem in both respects. We prove the vanishing property of renormalized Feynman amplitudes, with subtractions, when any subset of the masses in the theory become large and, in general, at different rates, thus providing different large mass scales in the theory. This theorem is then extended and we give sufficiency conditions for the validity of the decoupling theorem when any subset of the remaining nonasymptotic masses are scaled to zero and, in general, at different rates. All the subtractions of renormalization are carried out at the origin of momentum space. The proof applies for theories with derivative couplings and with higher spin fields as well.
Linear equations invariant under arbitrary coordinate changes
Authors: Derrick G. H.
Published: March 2003

Linear homogeneous equations of the type i αλ∂ψ/∂xλ = βψ are considered, where αλ and β are constant Hermitian N×N matrices and ψ is an N component column vector. The conditions that this equation is invariant under arbitrary changes of coordinates are shown to be αλCκι+C†κιαλ = ακ δλι−αλδκι, βCκι+C†κιβ = −βδκι, αλCκι+ακCλι = 0, where Cκι is a set of 16 N×N matrices which specify the transformation law for the field components ψ. Some theorems are proved about solutions of these matrix relations and some explicit representations are given.