bluuebunny/crossref_metadata_2025 huggingface dataset:
On a model of a harmonic oscillator coupled to a quantized, massless, scalar field. I
Authors: Arai Asao
Published: March 2003

As a first step towards giving a rigorous mathematical interpretation to the Lamb shift, a system of a harmonic oscillator coupled to a quantized, massless, scalar field is studied rigorously with special attention to the spectral property of the total Hamiltonian. It is proved that the point spectra of the harmonic oscillator disappear completely into the continuous spectrum due to the interaction with the quantized field.
An expansion for power-law wavefunctions
Authors: Johnson Bruce R.
Published: March 2003

The regular and irregular solutions of the radial wave equation for rα potentials are given in terms of simultaneous power series in r2 and rα+2 . These results are shown to generalize to a potential with an arbitrary number of power-law terms.
Monodromy preserving deformation of ramified solutions to (Δ−m2)u = 0
Authors: Jimbo M. , Kashiwara M. , Miwa T.
Published: March 2003

Monodromy preserving deformation is discussed for solutions of (Δ−m2)u = 0, which are axially symmetric and with a given monodromy around a circle in R3. A holonomic system of linear differential equations is derived for appropriately normalized solutions. Their integral representations are also given, through which the deformation equations reduce to the fifth Painlevé equation. This problem can be related to the scattering of a spherical wave by a circular plate.
Spacetime G structures and their prolongations
Authors: Coleman Robert Alan , Korte Herbert
Published: March 2003

An elementary procedure for obtaining the prolongations of arbitrary G structures is described and applied to the affine, projective, Lorentz, conformal, and Weyl structures. Also, the condition that a projective and conformal structure be compatible and thereby define a unique Weyl structure is discussed from the G-structure viewpoint. Throughout, an invariant notation for jets is employed.
Dual-mass in general relativity
Authors: Ramaswamy Sriram , Sen Amitabha
Published: March 2003

A general notion of dual-mass, the gravitational analog of the magnetic monopole, is formulated in space-times that are asymptotically empty and flat at null infinity and in which the Bondi news vanishes. Dual-mass is specified by a real valued linear function on the asymptotic infinitesimal translation symmetries which, furthermore, depends on the asymptotic dual Weyl curvature tensor. It is shown that space-times with nonzero dual-mass are characterized by a null boundary (null infinity) having the structure of a principal S1 fiber bundle over S2 such that the dual-mass is proportional to the number of twists, n, in the bundle. Thus the topology of null infinity is that of a lens space L(n,1). A consequence of the existence of dual-mass is that the space-time is acausal. The NUT space-time is shown to be an example exhibiting these features, with a null infinity having the three-sphere topology.
General relativity: Dynamics without symmetry
Authors: Kuchař Karel
Published: March 2003

The concept of conditional symmetry is introduced for a parametrized relativistic particle model and generalized to geometrodynamics. Its role in maintaining a one-system interpretation of the quantized theory is emphasized. It is shown that geometrodynamics does not have any conditional symmetry: Such a symmetry should be generated by a dynamical variable K[gab, pab] which is linear and homogeneous in the gravitational momentum pab and which has a weakly vanishing Poisson bracket with the super-Hamiltonian and supermomentum. The generators K fall into equivalence classes modulo the supermomentum constraint. It is shown that each equivalence class can be represented by a member which is a spatial invariant. The remaining weak equations are turned into strong equations by the method of Lagrange multipliers. The local structure of the super-Hamiltonian and supermomentum imposes locality restrictions on the multipliers. These restrictions imply that the generator must be weakly equivalent to a local generator. A recursive argument then shows that the local generator must actually be weakly ultralocal. This uniquely determines the generator as the conformal Killing (super)vector of the local supermetric. However, the curvature scalar in the super-Hamiltonian breaks the conditional symmetry of the supermetric term and turns geometrodynamics into a theory without any symmetry. This result is generalized to inhomogeneous generators.
The equivalence of electromagnetic fields and viscous fluids in general relativity
Authors: Tupper B. O. J.
Published: March 2003

It is shown that spacetimes satisfying the Einstein–Maxwell equations, either in vacuo or coupled with a perfect fluid, may also satisfy the field equations for a viscous fluid. The necessary conditions for this alternative interpretation are found and examples of Einstein–Maxwell solutions admitting, and also not admitting, the viscous fluid interpretation are given.
Analytical solution for the change of Raman transitions quantum statistics
Authors: González-Díaz P. F.
Published: March 2003

By using the Laplace transform method we give exact analytical solutions for the time development of the diagonal and off-diagonal elements of the photon density matrix in Raman transitions.
Nonperturbative confinement in quantum chromodynamics. I. Study of an approximate equation of Mandelstam
Authors: Atkinson D. , Drohm J. K. , Johnson P. W. , Stam K.
Published: March 2003

An approximated form of the Dyson–Schwinger equation for the gluon propagator in quarkless QCD is subjected to nonlinear functional and numerical analysis. It is found that solutions exist, and that these have a double pole at the origin of the square of the propagator momentum, together with an accumulation of soft branch points. This analytic structure is strongly suggestive of confinement by infrared slavery.
Generalization of Stokes theorem and pure gauge fields
Authors: Iyanaga M.
Published: March 2003

A generalization of the Stokes theorem is derived for the path-order phase factor in nonabelian gauge theories. It is proved that the curvature form vanishes identically if and only if the connection form is pure gauge.
Quasi-abelian and fully non-abelian gauge field copies: A classification
Authors: Doria Francisco Antonio
Published: March 2003

We show that a theorem by S. Solomon on quasi-abelian gauge fields extends to a full classification of ambiguous potentials for any general non-abelian field which exhibits this phenomenon. A characterization for such fields is given, as well as a criterion that distinguishes in a straightforward manner between potentials that are at least locally gauge-equivalent to a fixed canonical potential and those which are not equivalent to that potential anywhere inside a neighborhood of space–time. Our results are obtained for R4 with an arbitrary non-degenerate metric, but can be easily extended to any space–time. Three examples (due to S. Deser and F. Wilczek, S. Coleman, and T. T. Wu and C. N. Yang) are discussed in order to clarify our analysis.
Democracy of internal symmetries in supersymmetrical quantum field theory
Authors: L/opuszański Jan T.
Published: March 2003

The freedom of choice of some discrete and internal symmetries in the supersymmetric, massive, interacting quantum field theory is discussed. It is shown that the discrete symmetry consisting of changing the sign of some (not all) scalar fields is incompatible with the supersymmetric structure of the theory. It is further demonstrated that an internal symmetry which transforms only some of the fields of fixed spin leaving the other fields invariant and which acts nontrivially on the supercharges can not be admitted as a symmetry; although it can be a good internal symmetry in absence of supersymmetric covariance. Moreover, in case of a model consisting of scalar, spinor and vector fields even a symmetry which transforms all of the scalar (vector) fields leaving spinor and vector (scalar) fields unaffected is ruled out provided it acts nontrivially on some of the supercharges.
On a new Bose–Fermi mixing symmetry
Authors: Nash Patrick L.
Published: March 2003

The Bose–Fermi symmetry manifest in supersymmetry has non-super-symmetric realizations. Two examples of a new Bose–Fermi symmetry, called Clifford symmetry, are discussed. In the first example, the spin content of the Clifford multiplet (the analog of a supersymmetry particle multiplet) is 4(0,0)+2{( 1/2 ,0)+(0, 1/2 )}+( 1/2 , 1/2 ); in the second example it is 25(0,0)+20{( 1/2 ,0)+(0, 1/2 )}+5{(1,0)+(0,1)}+16( 1/2 , 1/2 )+4{(1, 1/2 )+( 1/2 ,1)}+(1,1). The mass matrix for a Clifford multiplet is, in general, not a multiple of the unit matrix (which it is, however, required to be for an irreducible supersymmetry particle multiplet).
On approximating the solutions and critical points of some nonlinear phenomena
Authors: Vatsya S. R.
Published: March 2003

We consider a nonlinear differential equation which arises in some heat transfer problems and study the applicability of Newton’s method in approximating the physical solution. Also two methods are devised to approximate the physically interesting critical point, one based on the iterative method and the other on the Newton method. Using these methods, we obtain a sequence of linear-operator valued functions. The approximations are in the form of the fixed points of certain eigenvalues of the operators thus obtained. Some comments on numerical approximations of these fixed points are made.
Dynamic polarizability of the double quadratic and multiquadratic chains with anharmonic coupling
Authors: Peyrard M.
Published: March 2003

We study the dynamic polarizability of a linear chain of atoms interconnected by springs and subjected to a double quadratic (D-Q) or multiquadratic (M-Q) substrate potential in the presence of a weak nonlinear coupling term between adjacent particles. The results obtained by Trullinger on the D-Q model with linear coupling are reviewed and the same formalism is extended to calculate the modified kink waveform in the presence of nonlinear coupling and the dynamic polarizability of this modified kink. The simplicity of the model allows us to carry out analytically all the calculations. We show that the presence of kinks in such an anharmonic chain enhances the effect of coupling nonlinearities.
A null tetrad analysis of the Ernst metric
Authors: Bose S. K. , Esteban E.
Published: March 2003

The Ernst metric is analyzed in terms of the null tetrad formalism of Newman and Penrose. Some applications of the formalism are also given.
Perturbed Hamiltonian systems
Authors: Case K. M. , Roos A. M.
Published: March 2003

It is shown that when a completely integrable Hamiltonian system is perturbed about a particular solution the resulting equations to all orders are completely integrable Hamiltonian systems. Numerous examples are worked out and some new constants for the original system are obtained.
Partitioning lower bounds for Bubnov–Galerkin’s eigenvalues
Authors: Abdel-Raouf M. A.
Published: March 2003

Löwdin’s partitioning technique is extended for calculating energy-lower bounds in Bubnov–Galerkin’s eigenvalue problems.
The domain of definition of bundle representations
Authors: Sen R. N.
Published: March 2003

It is proved that the equivalence class of bundle representations of a group G on the product bundle ℬ0 with total space B0=X×Y includes all representations of G on bundles ℬ which are homeomorphic (but not necessarily naturally homeomorphic) to the product X×Y, provided the G has the same action on the fibres of ℬ0 and ℬ. The group A of the bundle ℬ is immaterial.
On the Abel summability of partial wave amplitudes for Coulomb-type interactions
Authors: Gesztesy F. , Lang C. B.
Published: March 2003

We prove that the sum of partial wave amplitudes for Coulomb-type potentials [e.g., V(r) =γ/r+O(r−2)] is convergent in the Abel sense although it diverges in the ordinary sense. The method of Abel summation is a generalization of the ordinary summation and allows one to sum certain divergent series explicitly. It is closely connected with analytic continuation; with the help of optimal conformal mappings the convergence of the Abel sum (for long- and short-range interactions) can be improved substantially. This enables us to obtain values of the scattering amplitude for each scattering angle (except forward direction). In particular, we show that the screened scattering amplitude converges in the Abel sense up to a phase factor to the unscreened one if the screening is removed.
On the Lorentz dipole approximation in static electrodynamics
Authors: Dolzycki Stanislaw J.
Published: March 2003

The energy specification S{We}=〈[P]l=0, φ〉 of electrostatic sources introduced in the preceding paper is further developed. The electrostatic potential Φ due to a source distribution is defined as a generalized function satisfying the energy specification equation S{We} =〈−ε0∇(n) ⋅∇(n)Φ, φ〉, where n denotes the order of a multipole approximation is reviewed. Specifically, the generalized function of an equivalent field corresponding to a classical field intensity E is introduced in terms of a given energy specification S{We}. Besides the equivalent field, a family of generalized functions Dn referred to as the characteristic fields is introduced to deal with the displacement vector D. A formal description of the so-called polarization charges comes out of an analysis of an equivalent field. Equivalent fields of magnetostatic problems are discussed on the basis of the magnetostatic energy specification S{Wm}.
Linearization stability of Einstein equations coupled with self-gravitating scalar fields
Authors: Saraykar R. V. , Joshi N. E.
Published: March 2003

In this paper, we extend the work of Fischer–Marsden and Moncrief on the linearization stability of vacuum spacetimes to the case of vacuum Einstein equations coupled with self-gravitating scalar fields. We prove that the coupled system is linearization stable under some suitable conditions. We also prove the relation between linearization stability and the condition that spacetime admits Killing fields analogous to the work of Moncrief.
Massive spin-1 field in expanding universes and the quantum equivalence principle
Authors: Foussats Adriana , Laura Roberto , Zandron Oscar
Published: March 2003

In this work, we develop the quantum field theory formalism in the curved space-time for the case of massive vector field, using the Quantum Equivalence Principle previously introduced. With this principle and for a particular model for expanding universe—spatially flat Robertson–Walker metric—an adequate particle model is obtained. The mean density of created particles for the corresponding Bogolyubov transformation is finite.
Wick polynomials with a mass gap are not infinitely divisible
Authors: Baumann Klaus
Published: March 2003

We show that Wick polynomials of a generalized free field with a mass gap are not infinitely divisible.
Quantum tachyons in Schwarzschild space–time
Authors: Talukdar B. , Sen M. , Sen D.
Published: March 2003

The wave equation of a spinless tachyon is studied in Schwarzschild space–time. In contrast to earlier approaches to the problem, it is shown that tachyonic static solutions satisfy a simple second-order linear differential equation regardless of the mass of the black hole and the mass parameter of the tachyon. Physical implication of the present approach is discussed. Using Langer modification of the WKB (Wentzel–Kramers–Brillouin) boundary condition an expression similar to the Bohr–Sommerfeld quantization condition is derived.
The set of all projective limits of a projective system of state operators
Authors: Ochs Wilhelm
Published: March 2003

Let {WK} be a projective system of state operators defined on the finite tensor products of some family {ℋt} of Hilbert spaces. We prove that all projective limits of {WK} on the complete tensor product ⊗t∈T ℋt can be generated from every single projective limit by certain operations. In addition, we provide a necessary and sufficient condition for {WK} to have projective limits on incomplete tensor products of the ℋt’s.
Representation matching and the gauge invariant energy-momentum tensor
Authors: Dongpei Zhu
Published: March 2003

We atttack the problem of finding appropriate representations of symmetry groups so that a conserved quantity derived by the Noether theorem from one symmetry of a theory preserves the other symmetry. This representation matching problem is well solved in two-dimensional gauge theory where we find a new representation of the translation group which leads straightforwardly to the symmetric, gauge-invariant energy-momentum tensor.
Relativistic quantum dynamical group for hadrons
Authors: Roman P. , Haavisto J.
Published: March 2003

Motivated by previous work on relativistic quantum dynamics expressed in algebraic terms, we introduce a fully relativistic generalization of the Hooke group. The mathematical properties, relation to other proposed quantum dynamical groups, and the unitary ray representations of this group are studied. Hadrons are viewed as de Sitter type microuniverses, where the quantum dynamics is then determined by the relativistic Hooke group. Wave equations are studied, a mass formula is derived, the emergence of a Regge type formula is deduced, and correspondence with other extended hadron models is noted.
Affine transformations and the geometry of superspace
Authors: Tucker R. W.
Published: March 2003

A graded Cartan-type connection is devised on a bundle of graded affine frames over superspace. The relation of the gauged graded affine group to the geometry of superspace is discussed in the context of bundle reduction to simulate spontaneous symmetry breakdown. A complex quaternionic calculus is used to simplify the algebraic analysis.
Techniques for naturality isolation: I. With a Bosonic t channel
Authors: Stacey Richard
Published: March 2003

We develop the mathematical apparatus necessary to isolate pure naturality contributions from the helicity amplitudes for an arbitrary 2→2 scattering process (with a Bosonic t channel). We prove that certain combinations of the amplitudes and their (multiple) energy-derivatives suffice, and that no simpler methods exist. For high spin processes, where our methods might be overcomplicated, we develop a simple and accurate approximation using just a single energy-derivative.
Techniques for naturality isolation. II. With a Fermionic t channel
Authors: Stacey Richard
Published: March 2003

We develop the mathematical apparatus necessary to isolate pure naturality contributions from the helicity amplitudes for an arbitrary 2→2 scattering process (with a Fermionic t channel). In their exact form they are unlikely to be useful; in fact we prove that an exact isolation is impossible using only a finite combination of the amplitudes and their energy derivatives. However, we derive an approximation series consisting of such finite combinations which converges quickly to an exact separation of naturalities. The first term in the series—the single derivative approximation—is likely to give a good approximation. We comment on the application of our techniques to πN backward scattering.
Upper bound on the spin-flip cross section from unitarity, total cross section and the forward slope
Authors: Sakmar I. A.
Published: March 2003

For the spin 0–spin 1/2 particle scattering we give a method to construct an upper bound on the spin-flip cross section with the variational calculus using as constraints the total cross section, the forward slope and the full unitarity.
Confrontation of macroscopic and microscopic nuclear collective models
Authors: Chacón E. , Moshinsky M. , Vanagas V.
Published: March 2003

Since its start nuclear theory has lived with the dichotomy of viewing the nucleus microscopically, as a system of nucleons, or describing it macroscopically in terms of collective coordinates. In the last decade though, a point transformation has been introduced in which single particle coordinates can be expressed in terms of collective ones plus others, opening the possibility of deriving a microscopic collective model. In the present paper we confront the macroscopic and microscopic collective models, first in a space of two dimensions, in which we find explicitly the unitary representation in quantum mechanics of the canonical transformation that relates them. We then show how to extend every step of the analysis to the three-dimensional problem, though there some of the states required are not yet available in analytic form. One of the fundamental problems in collective models of the nucleus is that of shape. We indicate what are the operators whose expectation values give a reasonable description of the shape in the macroscopic and microscopic collective models and confront them critically.
Bianchi type IX cosmological models with homogeneous spinor fields
Authors: Obregón Octavio , Ryan Michael P.
Published: March 2003

The diagonal and symmetric Bianchi type IX models are coupled to a homogeneous spinor field. An action for the combined fields is constructed, where the orthonormal basis used is given explicitly in terms of the metric. This allows one to vary the action with respect to the metric and the spinor fields only. Next, a Hamiltonian formulation is given, and a qualitative solution for the problem is presented. We also show that the k = +1 FRW (Friedmann–Robertson–Walker) model is not compatible with a homogeneous spinor field, while the more complicated models are.
The Lipkin model and coherent states
Authors: Bhaumik Debajyoti , Choudhury Ajoy , De Mira , Roy Binayak Dutta
Published: March 2003

It is shown that the Bloch or angular momentum coherent states furnish a particularly efficacious basis for a discussion of various aspects of the Lipkin model of the ’’nucleus.’’ The Hartree–Fock description (as well as its projected version) is elegantly obtained in this framework. It is demonstrated that the ’’transition probability’’ between the first excited and ground states is proportional to the square of the number of ’’nucleons,’’ representing (in contrast to what obtains in the random phase approximation) a cooperativity of the ’’super-radiant’’ type. The extension of the model through the introduction of bosons permits, with the use of Bloch and Glauber coherent states, a succinct description of the phenomenon of boson condensation.
Expansion around instantons in quantum mechanics
Authors: Zinn-Justin J.
Published: March 2003

We calculate numerically a few terms of the corrections to the large-order behavior of the ground state energy of the O(N) anharmonic oscillator by analyzing the perturbation series. We then generate 94 terms of the perturbative expansion of the difference between the energies of the two low lying states of the double-well potential and analyze their large-order behavior.
Fiber bundles, superspace, and the gravitational field
Authors: Ross D. K.
Published: March 2003

We develop a new theory of the pure gravitational field by treating superspace as a fiber bundle with space–time as the base space, and Fermi space, with anticommuting Majorana spinor coordinate qi, as the typical fiber. In the fiber bundle geometry, a spin-3/2 field arises automatically. It comes in through the commutation relations of the basis vectors in the horizontal lift basis, or through the metric in the local direct-product basis. The Lagrangian is taken to be the scalar curvature of the fiber bundle, in analogy with general relativity with no source terms. The theory is self sourced and the spin-3/2 field and usual spin-2 field appear as gauge fields. The theory is also completely basis invariant. The field equations correctly describe a spin-3/2 field coupled to general relativity, with the correct ’’energy–momentum tensor’’ of the spin-3/2 field appearing automatically. We thus end up with a very simple, geometrical theory which contains far fewer fields that the geometrical work of Arnowitt and Nath while keeping their elegance of formulation. The resulting field equations are similar to those of simple supergravity with only a spin-3/2 field appearing in addition to the spin-2 Einstein field, however, supersymmetry invariance seems to play little or no direct role in the present theory.
Gauge groups in a fiber bundle approach to superspace and the gravitational field
Authors: Ross D. K.
Published: March 2003

A semisimple Lie group is incorporated into our fiber bundle model of superspace and the gravitational field. The Lagrangian density is taken to be the scalar curvature of the (8+n)-dimensional fiber bundle where n is the dimensionality of the Lie group. The resulting field equations describe a nonabelian gauge field correctly coupled to the spin-3/2 gravitino and the spin-2 graviton.
Some examples of compact supermanifolds with non-Abelian fundamental group
Authors: Rogers Alice
Published: March 2003

A detailed construction is given of a supermanifold which is compact and has far from trivial topology. Higher dimensional examples are also described. The Grassmann algebra from which the supermanifolds are constructed may have finite or infinite dimension.
On the nature of the Gardner transformation
Authors: Kupershmidt B. A.
Published: March 2003

It is shown that every higher Korteveg-de Vries equation can be included in a one-parameter family of integrable equations.
Analytical expansions for Fermi–Dirac functions
Authors: Bañuelos Alicia , Depine Ricardo Angel , Mancini Roberto Claudio
Published: March 2003

We obtain a fast convergent series expansion for the Fermi–Dirac function Fs(a) for −10<a⩽1. We give values of Fs(a) for s = n+ 1/2 (n = 0,1,⋅⋅⋅,6) with a in the same range.
On nearest neighbor degeneracies of indistinguishable particles
Authors: Kedem Benjamin
Published: March 2003

Arrangement degeneracies suggested by sufficient statistics associated with binary stationary mth order Markov chains are discussed, and are shown to correspond and generalize some degeneracies arising when indistinguishable particles are placed on a one-dimensional lattice with n compartments. From these statistics it is possible to define an mth order unit. The arrangement degeneracy obtained from s 1’s and n−s 0’s so that lower order units are placed in higher order is difficult. For this case only the third order arrangement degeneracy is obtained, the first and second orders being relatively simple. These results are applied in determining the asymptotic distributions of rare events.
Scattering of a scalar wave from a slightly random surface
Authors: Nakayama J. , Ogura H. , Sakata M.
Published: March 2003

Scalar wave scattering from a slightly random surface is analyzed by a probabilistic method. We make use of the homogeneity of an infinite random surface, that is, the shift invariance property of the strictly homogeneous random field. By the group-theoretic consideration of such a shift invariance property, the wave solution proves to be a homogeneous random field multiplied by an exponential function. Then such a homogeneous random field is approximately solved for a slightly random surface to yield a wave solution involving multiple scattering. Several statistical properties of the scattering are calculated and shown in the figures. The accuracy of the approximate solution is examined in terms of the error of the boundary-value equation.
Covariant electrodynamics of a dyon in a medium
Authors: Cohn J. , Hong N.
Published: March 2003

A covariant formulation of electrodynamics of a dyon in a uniform, isotropic, and transparent medium is discussed. Using generalized Maxwell’s equations admitting magnetic charge, the 4-potentials of a dyon of electric charge e and magnetic charge m and the corresponding field tensor are calculated. This field tensor is then used to calculate the various stress tensors of Minkowski, Abraham, and Marx. And it is found that the dyon behaves like an electrically charged particle of ’’effective’’ charge e*, where e* = e[1+(e/m)(m/e)2]1/2, where e and m are the electric and magnetic permeabilities of the medium.
A multipole formalism for material media
Authors: Frahm Charles P.
Published: March 2003

It is shown that it is possible to make a meaningful multipole expansion for the electromagnetic fields produced by localized charge and current distributions embedded in material media—provided the media possess certain reasonable properties. The result is similar to the well-known multipole expansions for localized sources in vacuum but differs from it primarily because of induced charge and current density contributions to the various multipole coefficients.
Energy-particle-number inequality in nonlinear complex-scalar field theory
Authors: Rosen Gerald
Published: March 2003

For a self-interaction energy density U(‖ψ‖2) that is positive-definite, monotone-increasing with increasing ‖ψ‖2, and concave-saturating, it is shown that the total field energy E and particle number N satisfy the general inequality E⩾ (function of ξ) ‖N‖(3−ξ)/2(2−ξ) in which the positive parameter ξ≡min [dlnU( ρ)/dlnρ] is less than unity.
Lattice Green’s functions for a linear chain with next nearest neighbor interactions
Authors: Bahurmuz A. A. , Loly P. D.
Published: March 2003

The lattice Green’s functions for a linear chain with next nearest neighbor (NNN) interactions, Gl(t,A) = (1/r)ℱr0 coslxdx/[tie−(cos x+Acos2x)] are studied for various values of A, the ratio of NNN to nearest neighbor (NN) interactions. It is shown that Gl(t,−A) = (−1)l+1[Gl(−t,A)]*, thereby allowing attention to be restricted to the positive range of A which further divides into the two cases, (a) 0⩽A⩽1/4, with band edge singularities, and, (b) 1/4<A<∞, with an additional in-band singularity. Exact results are then obtained for the imaginary parts of Gl and for the real parts of G0 and G1. Finally a recurrence relation enables the real parts of Gl for arbitrary l to be found from those for l = 0 and 1.
Aesthetic field theory—Extended particles in four-dimensional space–time
Authors: Muraskin M.
Published: March 2003

We continue our study of complex aesthetic field theory using a set of group theoretical data introduced previously. Our more detailed study shows significant differences with the corresponding real theory. We find that our theory allows for a four-dimensional particle system, where the particle system is viewed as a bound state of a three-dimensional maximum and minimum. The magnitude of the field is large in this ’’confluence’’ region. This property persists in time. We can think of this as a form of nonattenuation. We never see a large magnitude ’’free’’ maximum or minimum (confinement). A problem with the particle system is that the confluence region extends to a greater degree in z for large ‖t‖ compared to the case at t = 0.
On the decoupling theorem in field theory
Authors: Manoukian Edward B.
Published: March 2003

An elementary proof of the decoupling theorem in field theory is given when all the masses in the theory are allowed to go to infinity. The proof is given directly in momentum space with the subtractions of the theory performed at the origin and containing nonzero mass particles. The theorem states that, in Euclidean space, if the masses of the theory are scaled by l and l is allowed to go to infinity then the corresponding Feynman amplitude vanishes not more slowly than l−1, i.e., ‖ 𝒜‖<l−1C, for l⩾1.
Linearly superposable and finite-action classical Yang–Mills fields
Authors: Oh C. H. , Teh Rosy
Published: March 2003

We show that in the Minkowski space, a self-dual gauge field can be linearly superposed with either another self-dual gauge field or a non-self-dual gauge field to give a new solution of the Yang–Mills equation. From these new solutions, Euclidean solutions are constructed. Some of these new solutions are valid in any dimensions of space–time.
An axiomatic framework for supersymmetries
Authors: Ghikas Demetris P. K.
Published: March 2003

A framework is proposed in which supersymmetries can be defined in the language of axiomatic quantum field theory. This framework contains a nuclear *-algebra into which the Borchers’ algebra of a general supermultiplet is embedded through a map which, in some sense, generalizes the concept of a superfield. The algebra of supersymmetry is represented on the constructed nuclear *-algebra as an algebra of graded derivations. Since a graded derivation cannot be integrated to a usual automorphism group (only to a formal group), it is assumed that conditions at the Lie algebraic level are strong enough to produce supersymmetric behavior. Thus it is conjectured that if a functional of the nuclear *-algebra is annihilated by the algebra of supersymmetry, and if this functional is related to a state of the Borchers’ algebra through the embedding map, this state through the GNS construction gives rise to a supersymmetric Wightman theory. This supersymmetric condition produces an infinite number of correlations among the n-point functions. The 2-point Wightman functions for a general supermultiplet are completely analyzed and it is found that their behavior is similar to the perturbative results. Finally it is proved that the free fields satisfy these supersymmetric conditions.
Sum rules in classical scattering
Authors: Bollé D. , Osborn T. A.
Published: March 2003

This paper derives sum rules associated with the classical scattering of two particles. These sum rules are the analogs of Levinson’s theorem in quantum mechanics which provides a relationship between the number of bound-state wavefunctions and the energy integral of the time delay of the scattering process. The associated classical relation is an identity involving classical time delay and an integral over the classical bound-state density. We show that equalities between the Nth-order energy moment of the classical time delay and the Nth-order energy moment of the classical bound-state density hold in both a local and a global form. Local sum rules involve the time delay defined on a finite but otherwise arbitrary coordinate space volume Σ and the bound-state density associated with this same region. Global sum rules are those that obtain when Σ is the whole coordinate space. Both the local and global sum rules are derived for potentials of arbitrary shape and for scattering in any space dimension. Finally the set of classical sum rules, together with the known quantum mechanical analogs, are shown to provide a unified method of obtaining the high-temperature expansion of the classical, respectively the quantum-mechanical, virial coefficients.
On the spontaneous magnetic order in the Hubbard model
Authors: Jedrzejewski J. , Verbeure A.
Published: March 2003

A rigorous proof is given of the absence of spontaneous magnetization in the Hubbard model in one and two dimensions.
Phase-space approach to relativistic quantum mechanics. III. Quantization, relativity, localization and gauge freedom
Authors: Kaiser Gerald
Published: March 2003

We examine the relationship between the mathematical structures of classical mechanics, quantum mechanics, and special relativity, with a view toward building a consistent framework for all three. The usual idea of ’’canonical quantization,’’ with its emphasis on the transition from functions over classical phase space to operators, appears to be inconsistent with relativistic covariance. On the other hand, the spectral condition of relativistic quantum mechanics, which is merely a covariant statement that the energy is nonnegative, naturally leads to the construction of a covariant extension of classical phase space. By giving up the idea of sharp ’’localizability’’ in space—known to be at odds with covariance— and adopting instead a notion of ’’soft’’ localizability in phase space, a consistent theory of relativistic quantum mechanics is seen to emerge whose structure naturally incorporates the classical sympletic geometry as well. Furthermore, the new theory deals directly and covariantly with extended particles rather than point particles and is free of the various inconsistencies known to plague the usual theory. The new notion of ’’microlocality’’ in phase space leads to a new form of gauge freedom which is similar to the usual one but simpler and more powerful, using methods of complex analysis. The phase-space version of Yang–Mills theory is worked out.
Path integrals with a periodic constraint: The Aharonov–Bohm effect
Authors: Bernido Christopher C. , Inomata Akira
Published: March 2003

The Aharonov–Bohm effect is formulated in terms of a constrained path integral. The path integral is explicitly evaluated in the covering space of the physical background to express the propagator as a sum of partial propagators corresponding to homotopically different paths. The interference terms are also calculated for an infinitely thin solenoid, which are found to contain the usual flux dependent shift as the dominant observable effect and an additional topological shift unnoticeable in the two slit interference experiment.
Iteration of single- and two-channel Schrödinger equations
Authors: Müller R. , Müller–Kirsten H. J. W.
Published: March 2003

A general perturbation technique is developed for the iteration of one- and two-channel Schrödinger equations for potentials, which can be expanded around a minimum. The channel coupling is assumed to be weak. In order to facilitate the numerical or algebraic computer calculation of terms of higher order, a recurrence relation is derived for some particularly important coefficients. The eigenvalues and oscillatorlike solutions are then derived explicitly up to and including the third-order iteration. Furthermore, we demonstrate that certain parts of every nth order iteration can be lumped together in a manner which is independent of the specific form of the potential. Finally, these methods are applied to the calculation of the eigenvalues of the one-channel equation for linear and logarithmic potentials with or without a weak Coulomb contribution.
Derivation of ’’Bethe’s hypothesis’’ from the quantum inverse scattering transformation for the nonlinear Schrödinger equation
Authors: Wiesler Andreas
Published: March 2003

Using the quantum version of the inverse scattering transformation for the nonlinear Schrödinger equation, eigenstates of the Hamiltonian can be constructed. We show that these eigenstates are of the Bethe form.
Hypervirial relations and orthogonalization conditions
Authors: Fernández Francisco M. , Castro Eduardo A.
Published: March 2003

Through the imposition of orthogonalization conditions, a number of results are derived for wavefunctions and eigenvalues in the framework of hypervirial methodology. Some previous results are extended and various similar developments of off-diagonal Hellmann–Feynman and sum rule formulas are indicated.
Eigenvalue problem for an infinite tridiagonal matrix
Authors: Wongtawatnugool C. , Wu S. Y. , Shih C. C.
Published: March 2003

A method is developed for the calculation of the eigenvectors of an infinite tridiagonal matrix. Possible application of this method to study the problem of localization in a disordered linear chain is also discussed.
Perimeter expansion in the n-bug system and its relationship to stability
Authors: Behroozi F. , Gagnon R.
Published: March 2003

We consider a system of n bugs located at (x1,y1), ..., (xn,yn), where bug i runs away from bug i+1 with common speed v along the instantaneous line of sight. To close the cycle of flight, bug n runs away from bug 1. The computer simulation of this system indicates that random initial configurations evolve into stable regular center-symmetric patterns—all of which have a vertex angle of less than π/2. By utilizing the Lagrange multiplier method, we show that for these stable configurations the perimeter expansion rate ṗ is a local maximum. The most stable configuration has the smallest possible vertex angle and is associated with an absolute maximum for ṗ. The regular center-symmetric patterns with vertex angles greater than π/2 also have a stationary perimeter expansion rate. These are local minima rather than maxima, however, and belong to configurations which are unstable.
All algebraically degenerate ℋ spaces, via ℋℋ spaces
Authors: Finley J. D. , Plebański J. F.
Published: March 2003

Starting from a canonical ℋℋ space, which by virtue of the self-dual part of its conformal curvature tensor being algebraically degenerate, has a single congruence of totally null, extremal two-surfaces, along which the coordinates are built, we specialize to the case where the anti-self-dual conformal curvature vanishes, giving us an algebraically degenerate ℋ space with coordinates especially adapted to its degeneration. We then solve the ℋℋ equation in this case and obtain, at one stroke, all algebraically degenerate ℋ spaces in a simple, compact form, useful for later applications. The generic solution depends on four arbitrary holomorphic functions of two variables, and any special Petrov type desired is easily distinguished. Also, a special comparison is made for all such spaces of type D, showing the relation of their parameters to the usual real, type-D parameters of mass, Newman-Unti-Tamburino (NUT) parameter, rotation and acceleration. Lastly, a contraction to the special cases in which the leaves of the congruence are relatively plane is performed explicitly.
The wave equation in asymptotically retarded time coordinates: Waves as simple, regular functions on a compact manifold
Authors: Gowdy Robert H.
Published: March 2003

The Minkowski-space scalar wave equation is represented on a spatially compact manifold with an asymptotically retarded time. In this coordinate system, with hyperbolic space slices and space coordinates generated by a conformal map, the wave equation takes a simple time-independent form which may form a model for numerical integration calculations with nonlinear wave equations.
On the infinite volume limit of the strongly coupled Yukawa2 model
Authors: Battle Guy A. , Rosen Lon
Published: March 2003

Using the FKG inequality, we construct infinite volume expectations of products of boson fields and fermi currents (ψ̄)ren for the scalar Yukawa2 model with arbitrary coupling constant. These expectations satisfy the Osterwalder–Schrader axioms with the possible exception of clustering.
The path integral formulation of the dynamical map
Authors: Swanson Mark S.
Published: March 2003

A modified path integral form for the generating functional of the dynamical map is developed in terms of canonical field theory. The Yang–Feldman equation for arbitrary operator products is derived and a simple form of the boson theorem is proved. The effects of internal symmetry and broken symmetry upon the dynamical map are investigated. Simple applications to free fields and an interacting case are exhibited.
Bipolar expansion of tensor fields: Recurrence relations and analytic construction of form factors
Authors: Tang Henry H. K. , Vaagen Jan S.
Published: March 2003

Bipolar expansions of tensor under transformations of arbitrary translation and scaling of coordinates are obtained. The judicious choice of a coupled representation renders the expression compact and transparent. The radical coefficient functions (form factors) in this expansion can be given as integral transforms. They are shown to satisfy four-term recurrence relations, which together with an appropriate exploitation of the underlying symmetry result in a significant simplification of the original problem. A computational scheme is also worked out with which the radial form factors can be constructed analytically in terms of Gauss hypergeometric functions.
Linkages in general relativity
Authors: Geroch Robert , Winicour Jeffrey
Published: March 2003

For an asymptotically flat space–time in general relativity there exist certain integrals, called linkages, over cross sections of null infinity, which represent the energy, momentum, or angular momentum of the system. A new formulation of the linkages is introduced and applied. It is shown that there exists a flux, representing the contribution of gravitational and matter radiation to the linkage. A uniqueness conjecture for the linkages is formulated. The ambiguities due to the possible presence of supertranslations in asymptotic rotations are studied using the behavior of the linkages under first-order perturbations in the metric. While in certain situations these ambiguities disappear in the first-order treatment, an example is given which suggests that they are an essential feature of general relativity and its asymptotic structure.
Asymptotically flat ℋ spaces
Authors: Ludvigsen M. , Newman E. T. , Tod K. P.
Published: March 2003

A definition of an asymptotically flat ℋ-space is given. Using a technique for solving for all null geodesics in an ℋ-space, it is shown that the construction of another ℋ-space from a given asymptotically flat ℋ-space is idempotent, i.e., the new ℋ-space is isometric to the first one.
Static charged perfect fluid in a conformally flat spacetime
Authors: Banerjee A. , Santos N. O.
Published: March 2003

For static charged perfect fluid in a spacetime where gμν = e2σημν and σ = σ(x,y,z), assuming σ functionally related to the electrostatic potential, we prove that such solutions must be spherically symmetric. We consider two special cases. The first one is for an equation of state ρ = αp, with α being a constant. We arrive at exact solutions which have singularities. These include the case of a charged dust where α = 0, but the solution in this case is singular and is not included in those discussed previously by Das [A. Das, Proc. R. Soc. London, Ser. A 267, 1 (1962)] and also by De and Raychaudhuri [U. K. De and A. K. Raychaudhuri, Proc. R. Soc. London Ser. A 303, 97 (1968)]. The second case is for a constant mass density, where we prove that although the Schwarzschild interior solution is regular everywhere, the corresponding analog in the charged fluid case is not everywhere free from singularity.
Boundary conditions for zero-rest-mass fields in curved space-time: A regularity theorem
Authors: Anderson James L. , Kates Ronald E.
Published: March 2003

This paper shows that for gravitational radiation from slow-motion, harmonic sources, the formal power series obtained by expanding the O(ε5) wave-metric functions in inverse powers of r is a valid asymptotic expansion, provided the phase is expressed in terms of a properly strained null coordinate. The theorem proved here is useful for applying outgoing wave conditions in the neighborhood of ℐ+.
Amplitudes on von Neumann lattices
Authors: Boon M. , Zak J.
Published: March 2003

A formula is derived connecting any wave function 〈k,q‖f〉 in the kq-representation with the corresponding amplitudes of the state ‖f〉 on von Neumann lattices of states. The formula is used for establishing a possible interpretation for these amplitudes, for obtaining linear relationships between them, and for finding sum rules for the squares of their absolute values, and other related sum rules. It can also be used for establishing completeness criteria for the lattices of states and for defining a modified Hilbert space in which they become strictly complete. Particular attention is given to the coherent state lattice, but the discussion is extended to von Neumann lattices generated from an arbitrary state. Lattices generated from harmonic oscillator states are studied explicitly, and shown incidentally to lead to a wealth of summation expressions for Laguerre polynomials.
Inverse scattering of the permittivity and permeability profiles of a plane stratified medium
Authors: Coen Shimon
Published: March 2003

It is shown that the permittivity and permeability profiles of a lossless plane stratified medium can be uniquely determined from the reflection coefficient due to transverse electric plane waves at two angles of incidence and all the frequencies. The inverse scattering problem at oblique incidence is transformed to an equivalent inverse scattering problem at normal incidences. The latter is transformed to an inverse scattering problem for the one-dimensional Schrödinger equations, the solution of which is obtained by the Gel’fand–Levitan theory.