bluuebunny/crossref_metadata_2025 huggingface dataset:
Application of a novel interpolative perturbation scheme to the determination of anharmonic oscillator wavefunctions
Authors: Ginsburg Charles A. , Montroll Elliott W.
Published: March 2003

This paper is concerned with a scheme for finding approximate wavefunctions and energy levels of anharmonic oscillators with even power anharmonicities. Generally one can easily find simple asymptotic forms for wavefunctions for small and large oscillator displacements y. In the case of a quartic oscillator the wavefunction with anharmonicity parameter λ, ψ0(y) =exp{−[a11(λ) y4+(2λ/9) y6]1/2} (A) with a11(λ) =E20 and E30−(1/4) E0−(1/3) λ=0, (B) while not exact for all y, does have the correct asymptotic properties. Furthermore, the appropriate root of the cubic equation for E0 deviates by no more than 4% from the exact values of E0 in the range 0⩽λ<∞. In our interpolative method of improving ψ0(y), the correct asymptotic behavior of ψ0(y) is preserved by introducing an extra function of λ into the exponential function (A) and changing the power of the polynomial in the exponent: ψ0(y) =exp{−[a21(λ) y8+a22(λ) y10 +(2λ/9)2y12]1/4}. (C) Through the proper choice of a21(λ) and a22(λ) one obtains ground state energies which deviate by no more than 0.5% over the full range 0⩽λ<∞. Futher improvement is achieved by increasing the degree of the polynomial in the exponential. Excited state wavefunctions are obtained by multiplying exponentials such as (A) and (C) by polynomials in y.
Nontranslationally covariant currents and associated symmetry generators
Authors: Garber W. D. , Reeh H.
Published: March 2003

Within the framework of axiomatic field theory, the general case of a translationally noncovariant conserved local current is investigated. It is shown that the associated symmetry does not change the particle number nor the mass or the momentum of one-particle states. There is an integer N such that the N-fold commutators of the generator with the momentum as well as with the mass operator vanish.
On the wave-mechanical representation of a Bose-like oscillator
Authors: Ohnuki Y. , Kamefuchi S.
Published: March 2003

A detailed study is made of the wave-mechanical representation of a one-dimensional Bose-like oscillator whose canonical variables satisfy the general commutation relations first proposed by Wigner. The eigenvalue problems of the momentum and Hamiltonian operators are completely solved, and this is made possible only when wavefunctions in general are allowed to be hyperfunctions. The equivalence between the wave- and matrix-mechanical representations is thereby established for any value of c (a characteristic parameter of the theory), contrary to the conclusion reached previously by Yang. It is also found that for the case −1/2<c<0 or 0<c<1/2 there exist two classes of eigenfunctions that are mutually separated by a superselection rule.
Perturbation theory for Coulomb scattering
Authors: Zorbas J.
Published: March 2003

Perturbation series for the ’’renormalized’’ complex-energy distorted plane waves (RCEW’s) are defined and shown to converge to the series expansions for the physical distorted plane waves (PW’s) for two-particle scattering via Coulomb-like potentials V (x) =e1e2‖x‖−1+Vs(x), where Vs ∈ ℒ2 has compact support. A perturbation series for the ’’renormalized’’ half-off-shell T matrix is defined and shown to converge to the series expansion for the pure Coulomb physical T matrix.
On the relationship between conservation laws and invariance groups of nonlinear field equations in Hamilton’s canonical form
Authors: Kumei Sukeyuki
Published: March 2003

It is shown that whenever fields governed by the equations ∂/∂tpα=−δH/δqα, ∂/∂tqα =δH/δpα allow a conservation law of the form ∂ρ/∂t+divJ=0, there exists a corresponding Lie–Bäcklund infinitesimal contact transformation which leaves the Hamiltonian equations invariant. A condition that an invariant Lie–Bäcklund infinitesimal contact transformation gives rise to a conservation law is established. Each such transformation, which may involve derivatives of arbitrary order, yields a one-parameter local Lie group of invariance transformations. The results are established with the aid of a Lie bracket formalism for Hamiltonian fields. They account for a number of recently discovered conservation laws associated with nonlinear time evolution equations.
A variational derivation of the Bach–Lanczos identity
Authors: Ray John R.
Published: March 2003

A discussion of a modified Hilbert variational principle is presented. The Bach–Lanczos identity is then derived from this variational principle.
Fluctuation theories and Gaussian stochastic processes
Authors: Fox Ronald Forrest
Published: March 2003

The theory of fluctuations for systems near equilibrium has given rise to two developments which generalize the theory in two distinct ways. One of these developments is focused on the theory of fluctuations far from equilibrium where the dynamics is nonlinear. The other development has focused on extending the class of fluctuating forces to include forces with non-delta function correlations. The near equilibrium theory corresponds with the theory of stationary, Gaussian, Markov processes; the nonlinear, far from equilibrium theory corresponds to the theory of nonstationary, Gaussian, Markov processes; and the non-delta function, force correlation theory corresponds to the theory of stationary, Gaussian, non-Markovian processes in one form, and to the theory of nonstationary, Gaussian, non-Markovian processes in another form. The common feature found in all these theories is Gaussianness.
A derivation of the virial expansion with application to Euclidean quantum field theory
Authors: Menikoff R. , Sharp D. H.
Published: March 2003

In this paper we give a derivation of the virial expansion and some of its generalizations. Our derivation is based on the generating functional which defines a representation of the density operator ρ (x) in a nonrelativistic local current algebra. The virial expansion results from solving a functional differential equation for this quantity. We exploit the well-known analogy between quantum field theory and classical statistical mechanics to explore the use of the virial expansion in Euclidean quantum field theory. Specifically, we show that the virial expansion can be used to derive Feynman’s rules and to provide a perturbation expansion about a static ultralocal model. The latter is worked out in detail in the case of a free neutral scalar model, and outlined in the case of a λφ4 model.
Multiple steady states in a simple reaction–diffusion model with Michaelis–Menten (first-order Hinshelwood–Langmuir) saturation law: The limit of large separation in the two diffusion constants
Authors: Ibañez J. L. , Velarde M. G.
Published: March 2003

The admissible multiple nonuniform steady states of a model bimolecular autocatalytic reaction–diffusion system with Michaelis–Menten (first-order Hinshelwood–Langmuir) saturation law are constructed in the case of large scale separation in the two diffusion constants. Both the Dirichlet and the Neumann problems are discussed in a one-dimensional geometry, and the corresponding bifurcation pictures are given.
Expanding shearfree spatially homogeneous universes with a nonsynchronous time coordinate and anisotropy of the universe
Authors: Fennelly A. J.
Published: March 2003

The apparent isotropy of the microwave background radiation on all angular scales and regions thus far observed is usually accepted as evidence of the isotropy of the universe. Current applications of the Einstein theory of gravitation in cosmology couples all rotation or peculiar velocity to anisotropy in the background radiation. Rotation in particular is coupled to shear. These are based on a number of results that apply to spatially homogeneous cosmologies with a synchronous time coordinate. While the models allow the past of our universe to be rather interesting, they constrain the present to be quite boring. We introduce a nonsynchronous time coordinate and show that the present could allow more interesting fluid motions, including rotation and peculiar velocity in spite of the microwave background’s isotropy. We use the formalism to construct rotating Friedman universes and study observations in them. Almost all other cosmological data are consistent with a rotation of the universe.
’’IST-solvable’’ nonlinear evolution equations and existence—An extension of Lax’s method
Authors: Miodek I.
Published: March 2003

We present here a new and easy method, a natural extension of Lax’s method, for obtaining general ’’IST-solvable’’ nonlinear evolution equations. These are evolution equations for the potential function(s), v, of a Hamiltonian, H, when the logarithmic t derivatives of H’s inverse scattering data are given by a t-dependent ratio of entire functions of E, Ω (t,E). Here E is the energy variable and Ω is the ’’dispersion relation’’ of Abowitz, Kaup, Newell, and Segur (AKNS). We pose the question of existence of the evolution equation’s solution. This question is answered completely in the one-dimensional Schrödinger case (first example). In a second example we derive the evolution equation for an n×n matrix generalization of the Zakharov–Shabat–AKNS equation. Our method displays the central role of analyticity in E in the IST method as a whole.
Symmetry and separation of variables for the Hamilton–Jacobi equation W2t−W2x −W2y =0
Authors: Boyer C. P. , Kalnins E. G. , Miller W.
Published: March 2003

We present a detailed group theoretical study of the problem of separation of variables for the characteristic equation of the wave equation in one time and two space dimensions. Using the well-known Lie algebra isomorphism between canonical vector fields under the Lie bracket operation and functions (modulo constants) under Poisson brackets, we associate, with each R-separable coordinate system of the equation, an orbit of commuting constants of the motion which are quadratic members of the universal enveloping algebra of the symmetry algebra o (3,2). In this, the first of two papers, we essentially restrict ourselves to those orbits where one of the constants of the motion can be split off, giving rise to a reduced equation with a nontrivial symmetry algebra. Our analysis includes several of the better known two-body problems, including the harmonic oscillator and Kepler problems, as special cases.
Symmetries in gauge theories
Authors: Bergmann Peter G. , Flaherty Edward J.
Published: March 2003

A general definition of symmetry for solutions of the field equations of gauge theories is proposed, and some of its properties and consequences are discussed.
Coherent electromagnetic waves in pair-correlated random distributions of aligned scatterers
Authors: Twersky Victor
Published: March 2003

Recent results for the corresponding scalar problem are generalized to coherent electromagnetic waves in random distribution of pair-correlated obstacles (aligned or averaged over alignment). Proceeding essentially as before, we obtain dispersion equations by averaging the vector–dyadic functional equation relating the multiple and single scattered amplitudes of the obstacles. In general, for aligned nonradially symmetric scatterers, the resulting bulk indices of refraction specify anisotropic media; the anisotropy arises either from the scatterers’ properties (physical parameters or shape, or both) or from their distribution, or from both. The illustrations include both isotropic and anisotropic cases, and the explicit results generalize earlier ones.
A no-go theorem concerning the cluster decomposition property of direct-interaction scattering theories
Authors: Mutze U.
Published: March 2003

An axiomatic framework for relativistic direct-interaction single channel scattering theories is formulated in terms of two representations U’ and U of the Poincaré group. The infinitesimal generators P (momentum), J (angular momentum), E (energy), N (’’boost’’) of U, and P’, J’, E’ N’ of U’ are assumed to be related by the formulas of Bakamjian, Thomas, and Foldy: P’=P, J’=J, E’= (M’2+RP2)1/2, and N’= (E’X+XE’)/2+(J−X×P)(M’+E’)−1, where X is the center-of-mass position operator of U given by X=T−P× (J−T×P) M−1(M+E)−1 with T= (E−1N+NE−1)/2 and M’ is a positive operator that commutes with P, J, and X. Then, it is proved that, within the above-mentioned framework, the Moller operators W±=lim exp(−itE’)exp(itE) for t→±∞ cannot satisfy the cluster decomposition property (also known as separability) except for interactions that vanish if any one of the particles is removed to infinity.
Uniqueness of solutions to the linearized Boltzmann equation
Authors: Freede Garbanati L. , Greenberg William , Zweifel P. F.
Published: March 2003

Uniqueness theorems are proved for the linearized Boltzmann equation for both the ’’exterior’’ and ’’interior’’ problems under generalized Maxwell boundary conditions. The solution space is a weighted Lp space, and agrees with the space in which solutions have previously been constructed.
Diagonalization methods for the general bilinear Hamiltonian of an assembly of bosons
Authors: Tsallis Constantino
Published: March 2003

The problem of the exact diagonalization of the Hamiltonian of an assembly of N bilinearly interacting bosons is discussed in what concerns the eigenvalues as well as for the expression of the new boson operators in terms of the old ones. The method is equivalent to the standard equation-of-motion approach, nevertheless sensibly more concise. Three sets of operational rules are indicated, and their use is exhibited in some examples. In some particular cases of practical importance (for example, when all the coefficients of the Hamiltonian are real), the research of the eigenvalues has been compacted as much as possible.
Solitons and rational solutions of nonlinear evolution equations
Authors: Ablowitz M. J. , Satsuma J.
Published: March 2003

Rational solutions of certain nonlinear evolution equations are obtained by performing an appropriate limiting procedure on the soliton solutions obtained by direct methods. In this note specific attention is directed at the Korteweg–de Vries equation. However, the methods used are quite general and apply to most nonlinear evolution equations with the isospectral property, including certain multidimensional equations. In the latter case, nonsingular, algebraically decaying, soliton solutions can be constructed.
Isometries compatible with asymptotic flatness at null infinity: A complete description
Authors: Ashtekar Abhay , Xanthopoulos Basilis C.
Published: March 2003

The following results concerning isometries of space–times which are asymptotically empty and flat at null infinity are established: (i) The isometry group is necessarily a subgroup of the Poincaré group; (ii) if the asymptotic Weyl curvature is nonzero—more precisely, in the standard notation, if Kabcdnd does not vanish identically on ℐ—the space–time cannot admit more than two Killing fields unless the metric is Schwarzschildean in a neighborhood of ℐ; if it does admit two Killing fields, they necessarily commute; one (and only one) of them is a translation; the radiation field as well as the Bondi news vanishes everywhere on ℐ; and, finally, if the translational Killing field is timelike in a neighborhood of ℐ, the other Killing field is necessarily rotational. Several implications of these results are pointed out.
Geometry of the roots of matrices with Onsager–Casimir symmetry
Authors: van Oost E. , Lekkerkerker H. N. W.
Published: March 2003

The condition under which a matrix with Onsager–Casimir symmetry describing the coupling between m variables that are even (odd) under time reversal and 1 variable that is odd (even) has a pair of complex eigenvalues are analyzed, both graphically as well as algebraically.
Fibre bundle analysis of topological charges in spontaneously broken gauge theories
Authors: Schaposnik F. A. , Solomin J. E.
Published: March 2003

We study the topological properties of spontaneously broken gauge theories in the context of fibre bundle theory. In particular, we discuss the conditions under which the topological charges of gauge and Higgs fields are the same.
The energy eigenvalue equation for the linear potential
Authors: Phares Alain J.
Published: March 2003

Recently the solution of the linear potential problem for any value of the orbital quantum number l was given via a new class of combinatorics functions. This paper deals with the eigenvalue problem and presents a further reduction of the energy eigenvalue equation leading to a general method for obtaining numerical results. Originally the eigenvalue equation was obtained by requiring the vanishing of an infinite order polynomial, Hl(t) =𝒥∞m=02(l +1) Km(l) tm−1, that should reduce to the Airy function, Ai(−t), in the case l=0. The expansion coefficients Km(l) were in turn given as the limit for infinitely large integer k values of some other coefficients K(k)m(l). These latter coefficients were given explicitly in terms of combinatorics functions, σl(k,p), that individually diverge in the limit as k goes to infinity. No real attempt was made to show that H0(t) ≡Ai (−t), to calculate the limit as k→∞, or even prove the cancellation of infinities. This work has three objectives: (i) Show the complete equivalence between the combinatorics function solution and the Airy function at l=0; (ii) Obtain a closed form expression for the expansion coefficients 2(l+1) Kp(l) by relating them in a very simple manner to the finite part fp(l) of σl(k,p) in the limit as k→∞; (iii) Calculate a few lower order coefficients fp(l) and obtain some numerical results.
On the polynomial expansion of the Hill–Wheeler integral for the rotational energies
Authors: Ullah Nazakat
Published: March 2003

A transformation is used which enables one to carry out exactly the integration of the Hill–Wheeler integral for the rotational energies. The expression for the energies EJ is shown to be the ratio of two polynomials in J (J+1), where J is the total angular momentum. A nice feature of the formulation is that the coefficients in the expansion involve only the matrix elements of the lowest rank independent HJ2r and J2r operators, 0⩽r⩽N−1, N being the number of J states contained in the given rotational band, and H being the Hamiltonian of the system.
Relativity and deformed Lie groups
Authors: Smrz P. K.
Published: March 2003

The concept of a deformed Lie group in which the structure coefficients are functions of the group coordinates is defined. Every Lie group can be deformed outside any of its subgroups. The affine group in four dimensions deformed outside Gl(4,C) has a variable group metric that is closely connected with the Ricci tensor of the four-dimensional manifold of translations. An analog of Einstein’s vacuum equations expresses the invariance of the metric with respect to the deformation. An enlargement of the affine group leads naturally to the appearance of the energy–momentum terms in the equations, while the gravitational interaction constant plays a role of a fundamental group constant (like c in the Lorentz group) which makes all generators of the gauge group dimensionless.
Para-Bose coherent states
Authors: Sharma J. K. , Mehta C. L. , Sudarshan E. C. G.
Published: March 2003

In place of the usual commutation relation [â,â†]=1 we consider the generalized commutation relation characteristic of the para-Bose oscillators, viz, [â, Ĥ]=Ĥ where Ĥ is the Hamiltonian (1/2)(ââ†+â†â). The number states and the representation of various operators in the basis formed by these states are obtained. We then introduce the para-Bose coherent states defined as the eigenstates of â for this generalized case. We consider some of the properties of these coherent states and also show that the uncertainty product 〈 (Δq̂)2〉 〈 (Δp̂)2〉 in this case could be made arbitrarily small.
An inverse scattering transform for potentials of compact support
Authors: Portinari João C.
Published: March 2003

We consider the inverse scattering problem for the one-dimensional Schrödinger equation on the whole line, (d2/dx2) φ (x,k)+[k2−V (x)]φ (x,k) =0. In some applications, as for example in the synthesis of electromagnetic media, it is important to have sufficient conditions on the scattering data such that the corresponding potential has compact support in some prescribed interval. The scattering data traditionally used in connection with the above ISP have been either one of the reflection coefficients (we are assuming that the potential V does not support bound states) r and ?—from the left and right, respectively. Although it is easy to obtain simple conditions on r (?) to ensure cutoff of the potential on the left (right), conditions on r (?) that guarantee cutoff on the right (left) are too complicated to be of any practical value. In this paper, we propose to use new scattering data, namely the ratio r/t (where r is either one of the reflection coefficients and t is the transmission coefficient), and give necessary and sufficient conditions for the corresponding potential to have support contained in [−a, a].
Super Clifford algebra
Authors: Dixon Geoffrey
Published: March 2003

An extension of su(2,2;2n) is presented which is based upon a theory of Z4 gradings of Clifford algebras. In the example given su(2,2;4) is extended and the Clifford algebra of an internal six-dimensional space is manifested. It is suggested that super Clifford algebras of this type can give valuable insight into the study of su(2,2;2n) supersymmetry theories.
The bound states for the symmetric shifted Coulomb potential
Authors: van Haeringen H.
Published: March 2003

We investigate the bound states for the symmetric one-dimensional shifted Coulomb potential, V (x) =−2s (‖x‖ +d)−1. Explicit approximate expressions for the infinite number of bound-state energies are obtained. For small s, the ground-state energy is O (s2 ln2sd), whereas the energies of the excited states are O (s2). We prove that the square roots of the binding energies form approximately a harmonic progression both for the even solutions and for the odd solutions. This is also true for the sequence of all solutions when sd is not small. However, when sd≪1, this sequence shows an interesting odd–even staggering phenomenon.
Almost-structures and structures in Lorentzian manifolds. I. Almost-Hermite- and almost-product- (2×2) -structures
Authors: Catenacci Roberto , Salmistraro Franco
Published: March 2003

We present a list of the most important almost-structures which have been found of interest in general relativity, in the null-bivectors formalism. We discusss some of the relevant properties of such almost-structures and various new or more or less known results. We also present theorems on the relations between almost-product-structures and almost-Hermitian-structures.
Conservation equations and the gravitational symplectic form
Authors: Palmer T. N.
Published: March 2003

By considering space–times whose metric is given by a perturbation expansion away from a background which admits a Killing vector, conservation equations, based on the energy–momentum tensor, are derived to first and second orders in the perturbation expansion. To the first order, equations are derived independently of the Einstein field equations, and describe secular changes in the energy–momentum distribution of the matter fields. To the second order, a gravitational energy–momentum contribution arises from the conservation equations which may be constructed from the symplectic inner product on the solution space of the linearized Einstein field equations. Considering a similar scheme based on the Bel–Robinson tensor, it is shown that whilst first order conservation equations can be formulated, the lack of a symplectic form for the perturbed Bel–Robinson tensor implies the nonexistence of second order conservation equations, except when the background is flat. The results are applied to perturbations of a stationary black hole, and simple expressions are found for the mass and angular momentum fluxes, through the event horizon, due to a gravitational perturbation. By considering a monochromatic wave, it is seen that the conservation of the gravitational symplectic form reduces, in suitable coordinates, to the Wronskian condition of Teukolsky and Press.
Constructing quantum fields in a Fock space using a new picture of quantum mechanics
Authors: Farrukh M. O.
Published: March 2003

For any conventional nonrelativistic quantum theory of a finite number of degrees of freedom, we construct a picture which we call ’’the scattering picture,’’ combining the ’’nice’’ properties of both the interaction and the Heisenberg pictures, and show that, in the absence of bound states, the theory could be formulated in terms of a free Hamiltonian and an effective potential. We generalize the equations thus derived to the relativistic case and show that, given a Poincaré invariant self-adjoint operator D densely defined on a Fock space, there exists an interacting field which is asymptotically free and has as the scattering matrix the nontrivial operator S=eiD, provided that D annihilates the vacuum and the one-particle states. Crossing relations could easily be imposed on D, but, apart from a few comments, the problem of analyticity of S is left open.
Conditioning of states. II
Authors: Deliyannis Platon C.
Published: March 2003

An alternative axiomatic system describing the concept of conditioning (or preparation) of states in a quantum logic is proposed and its consequences developed. The main difference between this and the system proposed by Pool is our reliance on Mielnik’s idea of transition probabilities, thereby avoiding some ad hoc hypotheses as well as the theory of Baer *-semigroups.
Quantum field theory Potts model
Authors: Constantinescu Florin , Ruck Herbert M.
Published: March 2003

We consider a quantum field theory analog to the three states Potts model [R. B. Potts, Proc. Camb. Phil. Soc. 48, 106 (1952)] in two dimensions. Our model can be interpreted as a neutral vector model with discrete gauge symmetry. We prove the existence of the thermodynamic limit by using the lattice approximation and correlation inequalities.
Polynomial irreducible tensors for point groups
Authors: Patera J. , Sharp R. T. , Winternitz P.
Published: March 2003

Generating functions for (Γr,Γm) tensors for any point group G and any pair of its irreducible representations Γr and Γm are calculated explicitly. A (Γr,Γm) tensor transforms according to Γr, and its components are polynomials in another tensor transforming by Γm. Explicit integrity bases of (Γr,Γm) tensors are given for all pairs Γr and Γm for the groups Cn, Dn, T, and O, and for the same groups with reflections. A composition rule for extending the result to reducible representations is formulated. Point group tensors irreducible with respect to SO(3) are obtained, together with their generating functions.
A nonlinear scalar field theory in isotropic homogeneous space–time
Authors: Okolowski J. A.
Published: March 2003

A classical nonlinear scalar field theory in isotropic homogeneous space–time of uniform negative curvature is considered which admits a singularity-free spatially localized dynamically unstable solution. The associated field energy is obtained as a finite positive quantity only for suitably restricted values of a ’’size parameter’’ which measures the degree of spatial localization of the solution. The static flat space–time limit of the present field theory as well as a physically appropriate limitation on the magnitude of the field energy are discussed.
Energetically stable systems
Authors: Demoen Bart , Vanheuverzwijn Paul , Verbeure André
Published: March 2003

For quantum systems as well as for classical continuous systems energetic stability is defined. It is proved that stability, supplemented with a cluster property, characterizes equilibrium states.
An exact solution to Einstein’s equations with a stiff equation of state
Authors: Wesson Paul S.
Published: March 2003

A solution to the equations of general relativity is given which is spherically-symmetric and nonstatic with an inhomogeneous density profile ρ and a pressure p given by the stiff equation of state p=ρc2. The solution may be of use in representing collapsed astrophysical systems or the early stages of an inhomogeneous cosmology.
The conserved densities of the Korteweg–De Vries equation
Authors: McGuinness Mark J.
Published: March 2003

The conserved densities of the Korteweg–de Vries equation are identified as energy densities associated with higher order equations generated from the KdV equation and governing its solutions.
Second-quantization representation for a nonrelativistic system of composite particles. II. Kinematical properties of the multispecies Tani transformation
Authors: Girardeau M. D.
Published: March 2003

In previous publications a first-principles method was developed for constructing second-quantization representations for systems of composite bound states and their constituents. It is based on the introduction of redundant modes (’’ideal atom variables’’) which are given physical content by carrying out a suitable unitary transformation. A single transformed Hamiltonian explicitly and simultaneously exhibits all kinematically possible scattering and reaction channels. Most of the previous results were limited to the case of two fermion composites. This restriction is removed herein, in order to allow a first-principles approach to the many-particle quantum dynamics and statistics of chemical and nuclear reactions. The kinematical aspects of the relevant transformation are examined.
Polynomial basis for Yang–Mills invariants
Authors: Anandan J. , Roskies R.
Published: March 2003

It is shown that any polynomial invariant of the SU(2) Yang–Mills field is a polynomial in a basic set of ten invariants, although only nine of them are functionally independent. Polynomial bases for the self-dual and anti-self-dual Yang–Mills fields are also presented.
Neutron stars: Analytical continuation of the ingoing gravitational wave amplitudes and asymptotic eigenfrequencies distribution for even modes
Authors: Cazzola P. , Lucaroni L.
Published: March 2003

With reference to a hot perfect fluid neutron star with an equation of state whose behavior is polytropic near the surface and in the framework of an arbitrary multipole of even order l?2, the ’’ingoing’’ gravitational wave amplitude of frequency ω is analytically continued to the region Imω<0. This is performed by suitable rotations of the integration paths in the multiple integrals expressing the successive iterations for such amplitude. The analytical continuation allows us to successively obtain the asymptotic eigenfrequency distribution for ω→∞. This differs in some cases from that obtained in a previous paper on the basis of a conjecture regarding the analytical continuation of the ingoing amplitude, although it maintains the same qualitative features.
Stochastic systems and integral inequalities
Authors: Rao A. N. V. , Tourgee R. A. , Tsokos C. P.
Published: March 2003

A stochastic control system of the form dx=F (t,x) dt+G (t,x) dβ (t) +ζ1(t) dt+ζ2(t) dβ (t), t ∈ R+≡ (0,∞), x,F,ζ1 ε Rn, G and ζ2 are n×p matrix-valued functions, and β (t) is a p-dimensional Brownian motion process, is investigated. Utilizing stochastic Lyapunov functions and the theory of stochastic integral inequalities, conditions are stated under which the above stochastic control is integrally stable in the mean and asymptotically integrally stable in the mean. Conditions are also developed for the stochastic differential system in finite time to be mean stable, uniformly stable in mean, quasiexpansively stable in the mean, and quasicontractively stable in the mean.
On the relativistic Boltzmann equation
Authors: Lucquiaud J. C.
Published: March 2003

Using harmonic analysis techniques, we construct orthogonal polynomials on Minkowski’s hyperboloid in order to interpret in the framework of the theory of group representation the tensorial polynomials introduced by Marle for the resolution of the relativistic Boltzmann equation by the Grad method. Calculations are performed in an adapted coordinate system by using zonal spherical functions on the hyperboloid of Minkowski, which as a matter of fact are Jacobi polynomials. Moreover, the homogeneous components of the Maxwell distribution function give an interpretation of Juttner’s formulas and, consequently, of the thermodynamic quantities of the fluid.
Addendum: The Clebsch–Gordan coefficients of S
n
Authors: Schindler Susan , Mirman R.
Published: March 2003

JMAPA,18,1697,1977
Analytic continuations of the Lauricella function
Authors: Sud A. R. , Sud K. K.
Published: March 2003

The Laplace transform of the product of three confluent hypergeometric functions is expressed in terms of Lauricella’s function FA(α,a1,a2,a3, b1,b2,b3; x,y,z). Two analytic continuation relations of the FA function are obtained by making use of its Barnes integral representation. One analytic continuation leads to a set of one term transformation relations and in the second, FA is expressed in terms of eight Lauricella FB series. Analytic continuations are given for the FB series, thereby allowing one to obtain a new analytic continuation for the FA series. Our result is useful for calculating the FA function when ‖x‖+‖y‖+‖z‖=2, which occurs in the analysis of the electron scattering from the nucleus.
Yang–Mills equations in Maxwell form
Authors: Maciejko R.
Published: March 2003

The Yang–Mills field equations are written in a form analogous to Maxwell’s equations. The inherent nonlinearities are to be thought of as arising from a medium: The gauge fields then look like waves propagating in a medium. Some well-known solutions are considered in this approach.
Explicit decomposition of tensor products of certain analytic representations of symplectic groups
Authors: Ton-That Tuong
Published: March 2003

For any integer k≳1 let E=C2k×1, E′ =C1×2k, and G=Sp(k,C). If Pm(E) denotes the linear space of all homogeneous polynomial functions of degree m on E, then the representation Lm of G, obtained by left translation on Pm(E), is irreducible with signature (m,0,⋅⋅⋅,0). Similarly, Pn(E′) and Rn are defined by replacing E by E′, m by n, and left translation by right translation. In this article, an explicit decomposition of the tensor product representation Rn⊗Lm on Pn(E′) ⊗Pm(E) is given in terms of the solid symplectic Stiefel harmonics.
Punctual Padé approximants as a regularization procedure for divergent and oscillatory partial wave expansions of the scattering amplitude
Authors: Garibotti C. R. , Grinstein F. F.
Published: March 2003

Previous theorems on the convergence of the [n,n+m] punctual Padé approximants to the scattering amplitude are extended. The new proofs include the cases of nonforward and backward scattering corresponding to potentials having 1/r and 1/r2 long-range behaviors, for which the partial wave expansions are divergent and oscillatory, respectively. In this way, the ability of the approximation scheme as a summation method is established for all of the long-range potentials of interest in potential scattering.
Renormalized plane wave-projected and Coulomb-projected T-matrices
Authors: Zorbas J.
Published: March 2003

The plane wave-projected formulation of the half-shell T-matrix for ionization and the Coulomb-projected formulation of the half-shell T-matrices for excitation and ionization are shown to converge to zero in the energy-shell limit. ’’Renormalized’’ plane wave-projected and Coulomb-projected half-shell T-matrices are defined and are shown to have physical energy-shell limits.
An illustration of the Lie group framework for soliton equations: Generalizations of the Lund–Regge model
Authors: Corones James
Published: March 2003

The Lie group framework for soliton equations is illustrated. It is shown that the original Lund–Regge model is one of an infinite family of similar relativistically invariant models that possess associated eigenvalue problems and isospectral flows. The models are explicitly found and their associated structures displayed. The group theoretic significance of the soliton equations and associated structures are given in accordance with the general theory.
Tensor spherical harmonics on S2 and S3 as eigenvalue problems
Authors: Sandberg Vernon D.
Published: March 2003

Tensor spherical harmonics for the 2-sphere and 3-sphere are discussed as eigenfunction problems of the Laplace operators on these manifolds. The scalar, vector, and second-rank tensor harmonics are given explicitly in terms of known functions and their properties summarized.
Conformal two-structure as the gravitational degrees of freedom in general relativity
Authors: d’Inverno R. A. , Stachel John
Published: March 2003

In this paper, we suggest that what we shall call the conformal 2-structure may, in an appropriate coordinate system, serve to embody the two gravitational degrees of freedom of the Einstein (vacuum) field equations. The conformal 2-structure essentially gives information concerning the manner in which a family of 2-surfaces is embedded in a 3-surface. We show that, formally at least, this prescription works for the exact plane and cylindrical gravitational wave solutions, for the double-null and null-timelike characteristic initial value problems, and for the usual Cauchy spacelike initial value problem. We conclude with a preliminary consideration of a two-plus-two breakup of the field equations aimed at unifying these and other initial value problems; and a discussion of some aspirations and remaining problems of this approach.
The retarded Josephson equation
Authors: Schlup W. A.
Published: March 2003

The retarded Josephson equation, which takes into account, in a simplified form, retardation effects of the Werthamer equation, is a nonlinear, nonsimultaneous, causal integrodifferential equation. It will be solved for kernels which are essentially the asymptotic kernels from BCS theory. Of physical interest are the rotational solutions, especially the characteristics and dynamics, which describe the steady state of a Josephson junction.
Evolution of a stable profile for a class of nonlinear diffusion equations. II
Authors: Berryman James G. , Holland Charles J.
Published: March 2003

First, explicit formulas are found for all the eigenfunctions and eigenvalues of a Sturm–Liouville problem associated with the class of nonlinear diffusion equations studied previously. The formulas for the eigenfunctions are proportional to Gegenbauer polynomials whose argument depends on the separable solution shape function. Next, rigorous bounds on the asymptotic amplitude are found in terms of integrals of the initial data. These bounds are the best possible bounds of the given type since they produce the exact result for the separable solution. Finally, results of numerical experiments are reported for D∼nδ where δ=1, −1/3, −1/2, and −2/3. The rigorous bounds are compared to the perturbation estimates from the earlier work and to the computed values of the asymptotic amplitude.
An algebraically special subclass of vacuum metrics admitting a Killing motion
Authors: Zenk L. G. , Das A.
Published: March 2003

The subclass of vacuum metrics with a Killing vector field (which may be either timelike or spacelike), having two of the nonzero eigenvalues of the Ricci subtensor equal, is investigated. Invariant methods are used. A special triad is chosen for the associated space V3 which gives rise to a special tetrad for the space–time V4, and this choice simplifies the expressions for the Weyl tensor and Newman–Penrose coefficients for V4. This subclass of vacuum metric reduces to two cases depending on whether or not the complex dilatation vanishes. In the first case the metric reduces to an example of plane-fronted waves. In the second case the problem reduces to a difficult pair of partial differential equations which has not been solved in the fullest generality. However, it has been shown that this case includes Robinson–Trautman metrics, Held–Robinson metrics, and some additional new Petrov type-III metrics with twisting rays.
Isotropy subgroups of SO(3) and Higgs potentials
Authors: Ovrut Burt A.
Published: March 2003

A method is given for determining the isotropy subgroups of an arbitrary, irreducible representation of SO(3). These subgroups are explicitly worked out for low-dimensional representations. As an application of these results we contruct the most general, renormalizable, SO(3) invariant Higgs potentials for these representations, determine the local minima of the potentials and discuss patterns of spontaneous symmetry breaking.
Some static and nonstatic solutions of Brans–Dicke theory of gravitation
Authors: Goswami G. K.
Published: March 2003

Static and nonstatic vacuum solutions of Brans–Dicke field equations are derived. For this purpose, a new and convenient technique is proposed. Results are applied to some known solutions.
Quadratic Hamiltonians, quadratic invariants and the symmetry group SU(n)
Authors: Leach P. G. L.
Published: March 2003

We show that any 2n-dimensional quadratic Hamiltonian may be transformed by a (usually time-dependent) linear canonical transformation into any other 2n-dimensional quadratic Hamiltonian, in particular that of the isotropic harmonic oscillator. This latter Hamiltonian possesses the symmetry group SU(n) and n2−1 linearly independent quadratic invariants which provide a basis for the generators of the group. Every other quadratic Hamiltonian is shown to have a quadratic invariant possessing SU(n) symmetry. The free particle structure is given explicitly. The anisotropic oscillator is shown not to possess SU(3) symmetry based on quadratic invariants. However, its wavefunctions and energy levels may be obtained directly from those of the isotropic oscillator whether the frequencies are commensurable or not.
Conformal extensions of the Galilei group and their relation to the Schrödinger group
Authors: Havas Peter , Plebański Jerzy
Published: March 2003

Various authors have considered a conformal extension CG0 of the Galilei group which in some sense is the nonrelativistic limit of the conformal extension of the Poincaré group, and have also established an invariance group for the free-particle Schrödinger equation, the ’’Schrödinger group.’’ Here we establish the most general conformal extension CG of the Galilei group, which is found to be identical to the group of the most general coordinate transformations that permit the use of noninertial frames of reference and of curvilinear coordinates in Galilei-invariant theories, which was considered by one of us some time ago, and is a gauge group containing a number of arbitrary functions. Both CG0 and the Schrödinger group are subgroups of CG containing the Galilei group, but otherwise they do not overlap. The Hamilton–Jacobi and Schrödinger equations for particles which are free or interact via inverse-square potentials are shown to be invariant under the Schrödinger group, and a further invariance of the Hamilton–Jacobi equation is established.
Coping with different languages in the null tetrad formulation of general relativity
Authors: Ernst Frederick J.
Published: March 2003

We describe how, in spite of differing conventions regarding spacetime signature, sign of the Riemann tensor, and definition of the Ricci tensor, we were able to construct a precise dictionary relating various notations which are being employed in the null tetrad formulation of general relativity. In addition, we give in appendices the forms assumed by the Newman–Penrose equations and the corresponding abstract structural equations when nontraditional assumptions are made with respect to the three sign conventions.
Analytic continuation of an operator-valued H-function with applications to neutron transport theory
Authors: Kelley C. T.
Published: March 2003

An operator-valued generalization of Chandrasekhar’s H-function satisfies a nonlinear integral equation. A bifurcation analysis of this equation gives an analytic continuation of the H-function. This result is applied to a criticality problem in neutron transport theory, and asymptotic results are obtained.
Note on the Bertotti–Robinson electromagnetic universe
Authors: Tariq Nessim , McLenaghan Raymond G.
Published: March 2003

It is shown in a concise manner using Debever’s vectorial formalism that the Bertotti–Robinson solution is the most general conformally flat solution of the source free Einstein–Maxwell equations for nonnull electromagnetic fields.
Correlation functions and higher order coherence in inelastically scattered quantum radiation
Authors: Weiszmann Andrei N.
Published: March 2003

The concept of coherence is analyzed in a system of interacting radiation and matter. Using the projection technique, the reduced field density operator is found, and with it the first and higher order field correlation functions are computed. It is proved that the inelastically scattered field is, for the most part, incoherent in any order at any time interval after collision with an atomic ensemble, except some specific time intervals and positions, where the order of coherence is determined by the atomic correlations considered.
The reduced field density operator for an inelastically scattered quantum radiation
Authors: Weiszmann Andrei N.
Published: March 2003

The projection technique used for setting a non-Markoffian differential equation for the reduced field density operator is discussed, and a detailed solution of the equation is found.
A consequence of the invariance of Biot’s variational principle in thermal conduction
Authors: Lonngren K. E. , Hsuan H. C. S.
Published: March 2003

The invariance of Biot’s variational principle in thermal conduction suggests that this variational principle can be formulated in terms of a self-similar variational principle. This work presents such a derivation and applies it to a thermodynamics example.
Strings and gauge invariance
Authors: Milton Kimball A. , DeRaad Lester L.
Published: March 2003

Within the context of the nonrelativistic theory of dyons, we study a number of interrelated issues concerning the quantum formulation of magnetic charge. We begin by solving the two-body Schrödinger equation for an arbitrarily oriented singularity line (string) in terms of the known solutions with the string on the z axis. Charge quantization conditions emerge by requiring that the wavefunctions be single valued. The general solutions express the necessary gauge covariance of the wavefunctions. These results provide a basis for the reconsideration of the phase factor in the dyon–dyon scattering amplitude. Finally, the connection between the formulations in terms of vector potentials and in terms of intrinsic spin is investigated. This approach leads to a rederivation of the gauge transformation properties of the theory.
Subcriticality and supercriticality of energy dependent neutron transport in slab geometry
Authors: Pao C. V.
Published: March 2003

The energy dependent transport system in an anisotropic medium in slab geometry subjecting possible internal source q and incoming fluxes ψ0, ψ1 is discussed. It has been shown in an earlier paper that under certain conditions on the average number of secondary neutrons per collision c, the scattering cross section σ, and the optical slab length 2a, this system has a unique nonnegative solution for all inputs q, ψ0, ψ1. The aim of this paper is to establish analogous conditions on c, σ, a so that the system has no nonnegative solution when there is either internal source or incoming fluxes (or both), and it only has the trivial solution when neither internal source nor incoming fluxes are present in the system. This conclusion together with the earlier results yield explicit conditions for insuring the supercriticality and the subcriticality of the energy dependent system and therefore lead to analytical upper and lower bounds for the critical value c* in terms of σ and a.