bluuebunny/crossref_metadata_2025 huggingface dataset:
Differential and integral methods for multidimensional inverse scattering problems
Authors: Yagle Andrew E.
Published: July 2002

A layer stripping procedure for solving three-dimensional Schrödinger equation inverse scattering problems is developed. This procedure operates by recursively reconstructing the Radon transform of the potential from the jump in the Radon transform of the scattered field at the wave front. This reconstructed potential is then used to propagate the wave front and scattered field differentially further into the support of the potential. The connections between this differential procedure and integral equation procedures are then illustrated by the derivations of two well known exact integral equation procedures using the Radon transform and a generalized Radon transform. These procedures, as well as the layer stripping procedure, are then reduced to the familiar Born approximation result for this problem by neglecting multiple scattering events. This illustrates the central role of the Radon transform in both exact and approximate inversion procedures.
An investigation of (nonadditive) scattering invariants in classical mechanics and quantum theory by differential topological methods
Authors: Requardt Manfred
Published: July 2002

The structure of invariants of the scattering transformation in (relativistic and nonrelativistic) classical mechanics and quantum theory is investigated and a constructive approach to finding and classifying them by exploiting and developing certain differential topological methods is provided. While, in the form of various by-products, results about the perhaps better known so-called additive scattering invariants are (re)derived, the primary concern here is with the less well-known nonadditive (i.e., several particle) conserved quantities.
Exact solutions in 1+1 dimensions of the general two-velocity discrete Illner model
Authors: Cornille Henri
Published: July 2002

The Illner model is the most general two-velocity discrete model of a Boltzmann equation in one spatial dimension which satisfies an H-theorem. It includes, as particular cases, both the Carleman and the McKean models. ‘‘Solitons’’ (one-dimensional solutions) and ‘‘bisolitons’’ (two-dimensional, space-plus-time, solutions), which are defined as rational fractions, and solutions with one or two exponential variables are determined. The model is treated as a nonintegrable nonlinear one, and from the solitons the possible class of bisolitons is guessed. Two classes of physically acceptable bisolitons are found. The first class is distributions positive only along one semiaxis and identically zero outside. These are interpreted physically by introducing elastic walls plus source or sink terms which become negligible at infinite time. The second class is periodic solutions which can be seen as damped sound waves. Essentially the same tools are used as in a companion paper for the six-velocity Broadwell model, where the two bisoliton classes mentioned above also exist. This suggests that general methods for obtaining nontrivial exact solutions could exist for the hyperbolic semilinear discrete Boltzmann models.
Lie transformations, similarity reduction, and solutions for the nonlinear Madelung fluid equations with external potential
Authors: Baumann G. , Nonnenmacher T. F.
Published: July 2002

The application of Lie-group methods to a system of coupled nonlinear partial differential equations representing what is usually called a Madelung fluid is shown. The generating operators of the transformation group that depends on five arbitrary group constants will be constructed, and all subclasses of systems of ordinary differential equations derived by similarity reduction will be presented in tabular form. Two subclasses of physical interest are investigated in detail and the similarity solutions are compared with solutions found earlier by the application of inverse scattering transform techniques to the cubic nonlinear Schrödinger equation. Similarity solutions for the Madelung equations with linear external potential Γ(x)=−f0x are presented.
Self-energy operator for an electron in an external Coulomb potential
Authors: Hostler Levere C.
Published: July 2002

The self-energy operator for an electron in an external Coulomb potential is investigated analytically using a mass eigenfunction expansion concept reported earlier. Contour integration techniques in the complex m2 plane are used to combine bound state and continuum contributions into a single integral. The result is a relatively simple integral representation for the mass operator. Only terms ignoring the ‘‘shift correction’’ are considered in this preliminary study. A transformation to a basis of relativistic Coulomb Sturmian functions exhibits the Zα dependence of the integrand in a strikingly simple way. The entire investigation is set in the framework of the ‘‘scalar formalism’’ for quantum electrodynamics investigated earlier by a number of authors and based on the ‘‘second-order’’ Dirac equation, {Π⋅(1+iσ)⋅Π+m2}Φ=0, where Φ is a 2×1 Pauli spinor.
Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Two- and three-resonance cases
Authors: Lewis H. Ralph , Goedert João
Published: July 2002

The momentum-moment formulation [Ann. Phys. (NY), 164, 47 (1985)] of Goedert and Lewis [J. Math. Phys. 28, XXX (1987)] and the momentum-resonance formulation of Lewis and Leach are used to study one-dimensional, time-dependent potentials that admit invariants which are rational functions of momentum with two or three simple poles. New examples are presented.
The hydrogen atom in phase space
Authors: Chetouani L. , Hammann T. F.
Published: July 2002

The Hamiltonian of the three-dimensional hydrogen atom is reduced, in parabolic coordinates, to the Hamiltonians of two bidimensional harmonic oscillators, by doing several space-time transformations,separating the movement along the three parabolic directions (ξ,η,φ), and introducing two auxiliary angular variables ψ and ψ′, 0≤ψ, ψ′≤2π. The Green’s function is developed into partial Green’s functions, and expressed in terms of two Green’s functions that describe the movements along both the ξ and η axes. Introducing auxiliary Hamiltonians allows one to calculate the Green’s function in the configurational space, via the phase-space evolution function of the two-dimensional harmonic oscillator. The auxiliary variables ψ and ψ′ are eliminated by projection. The thus-obtained Green’s function, save for a multiplicating factor, coincides with that calculated following the path-integral formalism.
Stability and bifurcation of a rotating planar liquid drop
Authors: Lewis D. , Marsden J. , Ratiu T.
Published: July 2002

The stability and symmetry breaking bifurcation of a planar liquid drop is studied using the energy-Casimir method and singularity theory. It is shown that a rigidly rotating circular drop of radius r with surface tension coefficient τ and angular velocity Ω/2 is stable if (Ω/2)2 <3τ/r3. A new branch of stable rigidly rotating relative equilibria invariant under rotation through π and reflection across two axes bifurcates from the branch of circular solutions when (Ω/2)2=3τ/r3.
Cohomology of supermanifolds
Authors: Bartocci Claudio , Bruzzo Ugo
Published: July 2002

The cohomological properties of supermanifolds (intended in the sense of De Witt [Supermanifolds (Cambridge U. P., London, 1984)] and Rogers [J. Math. Phys. 21, 1352 (1980)]) are investigated, paying particular attention to the de Rham cohomology of supersmooth differential forms (SDR cohomology). The SDR cohomology of De Witt supermanifolds is shown to be equivalent to the de Rham cohomology of their body. The SDR cohomology is explicitly computed for some topologically nontrivial supermanifolds and some general conclusions concerning the geometric structure of supermanifolds and the properties of the SDR cohomology are drawn. In particular, it is shown that the SDR cohomology is neither a topological nor a real differentiable invariant, but rather a ‘‘superdifferentiable’’ invariant.
Geometric properties of transition amplitude spaces
Authors: Pulmannová Sylvia , Gudder Stanley
Published: July 2002

The investigation of transition amplitude spaces (tas’s) introduced by Gudder and Pulmannová [J. Math. Phys. 28, 376 (1987)] is continued. In particular, ordered structures related to tas’s are considered. Under some conditions, which are analogous to the conditions obtained for transition probability spaces by Pulmannová [J. Math. Phys. 27, 1791 (1986)], the ordered structure related to a tas can be represented by the orthocomplemented lattice of all f-closed subspaces of a generalized Hilbert space (𝒱,𝒟,θ, f ). It is shown that, provided that the above representation takes place for a total tas, the division ring 𝒟 must be isomorphic with a subfield C1 of the field of complex numbers C. Sufficient conditions are also given under which the ordered structure of a tas can be represented by the lattice of all closed subspaces of a complex Hilbert space.
A note about closed timelike curves in Gödel space-time
Authors: Malament David B.
Published: July 2002

A greatest lower bound for the total (integrated) energy of closed timelike curves in Gödel space-time is derived. (Here ‘‘energy’’ is determined relative to the velocity field of the major mass points of the universe.) The derivation is then used to reconstruct and extend a remark of Gödel’s concerning total (integrated) acceleration requirements for ‘‘time travel’’ in his model universe.
Quantum theory on a regular tetrahedron
Authors: Dowker J. S.
Published: July 2002

Quantum theory on the surface of a regular tetrahedron is discussed. The fact that the net of the tetrahedron tiles the plane allows the propagators to be constructed as image sums of standard ones. The effect of a constant magnetic field is discussed. The field theory Casimir energy is found.
Exponential time-evolution operator for the time-dependent harmonic oscillator
Authors: Fernández Francisco M.
Published: July 2002

The time-evolution operator for the time-dependent harmonic oscillator H= (1)/(2) {α(t)p2 +β(t)q2} is exactly obtained as the exponential of an anti-Hermitian operator. The method is based on the equations of motion for the coordinate and momentum operators in the Heisenberg representation. The problem is reduced to solving the classical equations of motion.
The Gel’fand realization and the generating function of the Clebsch–Gordan coefficients of SL(2,R) in the hyperbolic basis
Authors: Basu Debabrata
Published: July 2002

It is shown that the canonical realization of the representations of SL(2,R) proposed by Gel’fand and co-workers yields a generating function of the Clebsch–Gordan coefficients of the group in the hyperbolic basis. This function is the coupled state and appears as the solution of an ordinary differential equation reducible to the hypergeometric equation. The desired expansion of the generating function that yields the Clebsch–Gordan coefficients is essentially a generalization of Barnes’ theory of analytic continuation of the hypergeometric function. In this paper the normalized Clebsch–Gordan coefficients for the coupling of two representations of the positive discrete class are calculated. The final result is an analytic continuation of the corresponding expression in the SO(2) basis. The possible application of the generating function to the reduction of the Kronecker product of three irreducible representations is discussed.
The semiclassical limit of quantum dynamics. I. Time evolution
Authors: Robinson Sam L.
Published: July 2002

The ℏ→0 limit of the quantum dynamics determined by the Hamiltonian H(ℏ) =−(ℏ2/2m)Δ+V on L2(Rn) is studied for a large class of potentials. By convolving with certain Gaussian states, classically determined asymptotic behavior of the quantum evolution of states of compact support is obtained. For initial states of class C10 the error terms are shown to have L2 norms of order ℏ1/2−ε for arbitrarily small positive ε.
A new eight-vertex model with an infinite number of commensurate phases
Authors: Sen Diptiman
Published: July 2002

A symmetric eight-vertex model, containing four even vertices with reak weights and four odd vertices with imaginary weights, is found to exhibit an infinite number of commensurate phases. The phase diagram is conjectured to be a complete devil’s staircase similar to that of certain one-dimensional systems. Associated naturally with the model are two diffeomorphic one-dimensional maps whose aymptotic trajectories are either stable cycles or intermittently chaotic, depending on the phase.
Solutions of Einstein’s equations relevant to the description of ‘‘bubbles’’ in the early universe
Authors: Ponce de Leon J.
Published: July 2002

A new class of spherically symmetric solutions of the Einstein field equations is presented. Their main features are that (i) the azimuthal metric coefficient depends on time only, and (ii) they possess similarity symmetry. The physical motivation for the study of such class of solutions is that according to recent investigations [R. N. Henriksen, A. G. Emslie, and P. S. Wesson, Phys. Rev. D 27, 1219 (1983); P. S. Wesson, Phys. Rev. D 34, 3925 (1986)], they can be relevant to ‘‘bubbles’’ of new phases, in phase transitions typical of inflationary universe models. The solutions have shear, are inhomogeneous, and may be interpreted as ‘‘mixtures’’ of perfect fluids. They have some adjustable parameters which can be used to assure the fulfillment of the energy conditions. There are two different types of solutions. One of them has similarity symmetry of the first kind and negative total pressure. These models can be used in a classical description of particle production phases in the early universe. The other type of solution has similarity of the second kind, i.e., it represents models with dimensional constraints. Explicit solutions representing mixtures of fluids with equations of state p=nρ and ρ=p of this type are given. They may be useful for cosmological models in closed universes. The dimensional constraints are found to be due to the ‘‘boundary conditions’’ in such universes. The specific characteristics of both types of solutions suggest that a transition from a particle-production phase to a radiation-dominated era can be described by means of bubbles of a ‘‘broken-symmetry’’ phase with positive pressure growing into a region of ‘‘unbroken-symmetry’’ phase with negative pressure.
Collision of impulsive gravitational waves followed by dust clouds
Authors: Taub A. H.
Published: July 2002

The evolution of a space-time containing two colliding plane impulsive gravitational waves each of whose leading edges is followed by a distribution of null dust is determined. The conditions on the Ricci tensor that ensure that the evolution of such a space-time is unambiguous are determined. These are the same as those that apply in the planar case. The equations of motion of the medium contained in the region of interaction of the dust clouds are determined. These equations determine the change in energy density of each dust cloud as the interaction proceeds and involve the functions whose specifications ensure that the evolution of the space-time is unambiguous.
On the uniqueness of prescriptions for spurious poles in Feynman integrals
Authors: Skarke Harald
Published: July 2002

It is shown that one loop Feynman integrals containing spurious poles (kn)−1 are completely determined by consistency properties, if they are allowed to depend either on one nonlightlike or on two lightlike vectors. Although no Ε prescription is given to the spurious poles, the results are identical either with the principal value or with the Leibbrandt/Mandelstam results.
Inelastic two-composite-particle system scattering theory at high energy
Authors: Yu-shun Zhang
Published: July 2002

In this paper, the methods of nucleons outside the closed shell (NOCS) and nucleons inside the closed shell (NICS) is introduced into the composite-particle systems, and Glauber’s multiple scattering theory is used to divide the multiple scattering amplitude (between two composite particle systems) into NOCS–NOCS, NOCS–NICS, NICS–NOCS, and NICS–NICS scattering amplitudes. In order to apply these concepts to our research, an effective approximate method is used for each scattering amplitude. For example, an independent particle model approximation has been used for the NOCS–NOCS scattering amplitude. As for the NICS–NICS and NICS–NOCS scattering amplitudes, the geometrical model and Bohr’s collective model are adopted, respectively. It can be shown that the high-energy scattering S matrix elements for composite-particle systems present a clear physical picture and render convenience to calculation.
Positive (2+1)-dimensional exact shock waves solutions to the Broadwell model
Authors: Cornille Henri
Published: July 2002

The exact solutions for the discrete Boltzmann models are sums of similarity shock waves: at least three for the (2+1)-dimensional solutions (two spatial coordinates). Here, for the three-dimensional, six velocities, Broadwell model shock waves solutions are also constructed. The difficult problem is the determination of solutions with positive density. It is proven that in the arbitrary parameters space, from which the solutions are constructed, there exists a domain leading to positivity. As an illustration, a numerical example is discussed. In the spatial coordinate plane both shock waves along one axis and bumps along the other are observed. The movement of these structures with time is discussed.
Approximate relativistic quantum Hamiltonians for N interacting particle systems
Authors: Ruiz E.
Published: July 2002

Time evolution of relativistic particle systems can be accomplished by means of a Schrödinger wave equation, provided the Hamiltonian of the N particle system satisfies some commutator equations involving the other generators of a suitable representation of the Poincaré group on the initial data space of the Schrödinger equation. This set of operator equations is solved in the N free particle case. Further, the structure of N interacting particle Hamiltonians is worked out to include second-order relativistic corrections, i.e., (1/c2)-terms. It is shown that Breit and Barker–O’Connell Hamiltonians (nonzero spin particles) and the Bažański Hamiltonian (zero-spin particles) are particular cases of this more general Hamiltonian.
Scattering of a wave packet by an interval of random medium
Authors: Faris William G. , Tsay Woody J.
Published: July 2002

This paper deals with the scattering theory for the one-dimensional discrete Schrödinger equation with a random potential having large support. The main result is that a fluctuation deep within the scattering region has a very small effect on the scattering of wave packets; the region of random potential is effectively opaque.
Weyl-ordered fermions and path integrals
Authors: Gavazzi Giuliano M.
Published: July 2002

It is shown that a correspondence exists between the Weyl-ordered Hamiltonian and the mid-point prescription in the discrete path integral for fermions. It is then proven that the Feynman rules obtained from the discrete and continuous path integral are equivalent.
Vertex operator representations of basic affine superalgebras
Authors: Frappat L. , Sciarrino A. , Sorba P.
Published: July 2002

Using the basic construction of the affine superalgebra OSp(M‖N)(1) in terms of vertex operators, vertex operator representations of a large class of untwisted and twisted affine basic superalgebras of the unitary and orthosymplectic series are found. The construction uses two methods: first, the regular embeddings of semisimple superalgebras (untwisted case) and, second, the folding method developed in a previous paper [Frappat et al., Nucl. Phys. B 305, 164 (1988)] to construct twisted vertex operators for Lie algebras with fermionic elementary fields (twisted case).
Mastersymmetries, angle variables, and recursion operator of the relativistic Toda lattice
Authors: Oevel Walter , Fuchssteiner Benno , Zhang Hongwei , Ragnisco Orlando
Published: July 2002

Conserved quantities, bi-Hamiltonian formulation, and recursive structure of the relativistic Toda lattice (RT) are obtained in an algorithmic way without making use of the Lax representation. Furthermore, for the multisoliton solutions the gradients of the angle variables are described in terms of mastersymmetries. A new hierarchy of completely integrable systems is discovered, which turns out to correspond to the ‘‘negative’’ of the hierarchy of RT. Thus it is shown that the full algebra of time-dependent symmetry group generators for each member of the RT hierarchy is isomorphic to the algebra of first order differential operators with Laurent polynomials as coefficients. The surprising phenomenon is revealed that the members of the RT hierarchy are connected to their negative counterparts by explicit Bäcklund transformation.
Uniqueness problems in formal nonlinear representations of the Poincaré group in 2+1 dimensions
Authors: Rideau G.
Published: July 2002

It is shown that the cocycles of extension of one massless representation of the Poincaré group  𝒫3 in 2+1 dimensions by the tensor product of n massless representations are coboundaries when the space of the representation is the space of the C∞ functions on R2 rapidly decreasing at infinity and at the origin. As a direct consequence, the equivalence classes of formal nonlinear representations of  𝒫3 with an irreducible physical representation as linear term are isomorphic to the classes of extension of the linear term by its symmetrical tensor product of order 2.
The elastoplastic shock problem as an example of the resolution of ambiguities in the multiplication of distributions
Authors: Colombeau Jean-François
Published: July 2002

One-dimensional collisions between two isotropic solids, in which the equations of physics lead to ‘‘multiplications of distributions,’’ are considered. Based on this example, a general physicomathematical method, to be adapted to each particular case, is proposed to resolve the ambiguity inherent in such products. This can be achieved with the aid of a new mathematical theory of generalized functions, which permits dealing with mathematical phenomena of a microscopic nature that govern products of distributions having singularities at the same point. This tool has recently been applied in various situations (in continuum mechanics) in which the equations of physics lead to ‘‘heuristic products of distributions.’’ One obtains new (algebraic) formulas in the simplest cases, and new numerical schemes in more general cases. The key to the resolution of ambiguities lies in more precise statements of the laws of physics than are permitted within distribution theory, and have no analog in classical analysis, so that in general a resolution cannot be obtained from ‘‘formal calculations.’’
The equivariant inverse problem and the uniqueness of the Yang–Mills equations
Authors: López M. C. , Noriega R. J. , Schifini C. G.
Published: July 2002

The equivariant inverse problem for Yang–Mills-type Euler–Lagrange expressions is solved in the affirmative. This leads to a proof of the uniqueness of the Yang–Mills equations.
Electromagnetic fields in an expanding universe
Authors: Hogan P. A. , Ellis G. F. R.
Published: July 2002

The asymptotic form of the electromagnetic field due to a bounded distribution of charge current in an open, expanding Friedmann–Lemaître–Robertson–Walker universe is studied. The technique used is to first describe a mechanism for passing from a solution of Maxwell’s vacuum field equations on Minkowskian space-time to a solution of Maxwell’s field equations in a region free of charge current on the cosmological background. This is tested on the field of an accelerating point charge and then applied to the rigorous treatment of the asymptotic electromagnetic field of a bounded charge-current distribution in Minkowskian space-time given by Goldberg and Kerr [J. Math. Phys. 5, 172 (1964)]. A ‘‘peeling expansion’’ of the electromagnetic field in the expanding universe is obtained in inverse powers of a parameter that is proportional to the area distance along the generators of future null cones with vertices on the world line of a fundamental observer. The algebraic character of the two leading coefficients in the expansion is the same as that of the two leading coefficients in the Goldberg–Kerr expansion in Minkowskian space-time. In addition, bounds can be calculated, at any instant in the history of a fundamental observer, on all the coefficients in the peeling expansion, as a consequence of the evaluation of such bounds by Goldberg and Kerr in the case treated by them.
A new generalization of the Hankel integral transform
Authors: Inayat-Hussain A. A.
Published: July 2002

A study of the eigenfunction expansions associated with the Bessel equation defined on an unbounded composite region has yielded a new generalization of the Hankel integral transform. This generalization contains as a special case an integral transform that is the Neumann (in the sense of boundary value problem) counterpart of the (Dirichlet-type) Weber–Orr transform and which itself is new. It also contains as special cases certain curious integral representations of the Dirac δ function. These representations are in fact the orthogonality conditions for the quasiorthogonal (i.e., orthogonal with respect to a discontinuous weight function) kernels of the new integral transforms.
A new scheme for enumerating connected diagrams on the lattice
Authors: Song Yongxin , Dai Yuanben
Published: July 2002

In this article, a scheme based on recursive generation of connected diagrams is proposed for enumerating the connected diagrams in various expansions for lattice field theories. This scheme is rigorous and general, and can be applied to the analytical methods in various lattice field theories. Some notions and results of the modern graph theory in mathematics are used. As examples, the diagram theoretic factors that occur in the average link energy of the lattice chiral field model and in the external source parameter of the pure lattice gauge field model are calculated.
Lobachevskian Dirac fields
Authors: Kerimov G. A.
Published: July 2002

Free Dirac fields in a Lobachevskian space-time (the Euclideanization of the anti-de Sitter space-time) are studied. These fields, which are related in the flat-space-time limit to the Euclidean Dirac fields, act in a space ℋ, which again has Fock space structure. The two-point Green’s function for Lobachevskian Dirac fields is obtained in terms of intrinsic geometric objects.
On an exceptional nonassociative superspace
Authors: Günaydin M.
Published: July 2002

The Jordan superalgebra JF(6/4) is the unique exceptional Jordan superalgebra that has no realization in terms of Z2-graded associative supermatrices. It is proposed to be the basis of an exceptional superspace that is non-Clifford algebraic. The JF(6/4) is constructed in a basis that renders itself to such an interpretation and its derivation, reduced structure, and Möbius superalgebras are studied. These algebras are simply the Lie superalgebras of generalized rotation, the Lorentz group, and conformal supergroup of the Jordan superalgebra JF(6/4). We also comment on the implications of the exceptionality of JF(6/4).
Some remarks on the Gupta–Bleuler triplet
Authors: Pierotti Dario
Published: July 2002

Indecomposable representations of the Poincaré group associated to infrared singular field theory models are discussed in the framework of the general theory of the Gupta–Bleuler triplet formulated by Araki. It is shown that the definition of maximal Hilbert space structures, related to the infrared properties of the states of the models, can be exploited to construct representation spaces for the Gupta–Bleuler triplet. The examples of the two-dimensional massless scalar field and of the electromagnetic field in the Landau gauge are discussed. In particular, in the first example, the relation between the Gupta–Bleuler triplet and the algebraic treatment of the massless scalar field is investigated. In the case of electromagnetism, the structure of the representation of the Poincaré group in the Landau gauge is clarified. The explicit form of the corresponding Gupta–Bleuler triplet for the one-particle space of the electromagnetic field is exhibited.
Remarks on tensor operators
Authors: Flath Dan
Published: July 2002

The notion of an algebra of tensor operators for a simple Lie algebra is discussed. A model for the finite-dimensional irreducible representations of sl(4) is constructed. Explicit Wigner operators acting on the model are defined. Striking commutation properties for these operators are conjectured that resolve a sequence of nontrivial multiplicity problems.
Equivariant harmonic maps into homogeneous spaces
Authors: Negreiros Caio J. C.
Published: July 2002

This paper is about harmonic maps from closed Riemann surfaces into homogeneous spaces such as flag manifolds and loop groups. It contains the construction of a family of new examples of harmonic maps from T2=S1×S1 into F(n) or Ω(U(n)) that are not holomorphic with respect to any almost complex structure on F(n) or Ω(U(n)), where F(n) is the quotient of U(n) by any maximal torus and Ω(u(n)) consists of f: S1→U(n) smooth such that f(1)=I.
Hannay’s angles outside the adiabatic range: Coupled linear oscillators near resonance
Authors: Koiller Jair
Published: July 2002

The simple harmonic 2-degree of freedom (dof) oscillator with the potential V= (1)/(2) [(1+r sin εt)q21+(1−r sin εt) q22+2r cos εtq1q2] is considered. It is shown that a coupling parameter k∼r/ε determines the behavior of the system after a loop 0≤t≤2π/ε in parameter space. Somewhat unexpected mode conversion and phase corrections occur. An optical model is outlined.
The one-dimensional Coulomb potential as a generalized function and the hidden O(2) symmetry
Authors: Weber T. A. , Hammer C. L.
Published: July 2002

The one-dimensional hydrogen atom treating the potential, –λ /‖x‖, is solved as a generalized function. The solutions (although nondegenerate) are nonunique unless fixed by some physical constraint. It is also shown that the hidden O(2) symmetry is a consequence of using solutions that are eigenfunctions of the operator sgn x≡x/‖x‖.
Addendum to ‘‘The equivariant inverse problem in gauge field theories and the uniqueness of the Yang–Mills equations’’ [J. Math. Phys. 3
0, 2382 (1989)]
Authors: Noriega R. J. , Schifini C. G.
Published: July 2002

The main theorem of the previous paper is extended to the case where L=L(gi j ; Aαi; Aαi,j). References and notations are the same.
Beyond Gaussian integrals in Grassman algebra
Authors: de Souza S. M. , Thomaz M. T.
Published: July 2002

Using the properties of determinants, the exact expressions for integrals of functions of the type exp[ηAη̄+(ηBη̄)ℓ] and their moments, where η and η̄ are Grassman generators with N components are derived.
Explicit orthonormal Clebsch–Gordan coefficients of SU(3)
Authors: Ališauskas Sigitas
Published: July 2002

The construction of the explicit algebraic-polynomial expressions for the nonmultiplicity-free orthonormal Clebsch–Gordan (Wigner) coefficients of SU(3)⊇U(2) is completed in the case of the paracanonical coupling scheme related with the explicit minimal biorthogonal systems by means of the Hecht or Gram–Schmidt process. The direct and inverse orthogonalization coefficients (the first of them being equivalent to the boundary orthonormal isofactors) are expressed, up to explicitly given multiplicative factors, in terms of the numerator and denominator polynomials related with the auxiliary Aλ function of Louck, Biedenharn, and Lohe that appears as a fragment of the denominator G-functions of canonical SU(3) tensor operators.
Hearing the shape of a general doubly connected domain in R3 with impedance boundary conditions
Authors: Zayed E. M. E.
Published: July 2002

The basic problem in this paper is that of determining the geometry of a general doubly connected domain in R3 together with an impedance condition on its inner bounding surface and another impedance condition on its outer bounding surface, from the complete knowledge of the eigenvalues {λj}∞j=1 for the three-dimensional Laplacian using the asymptotic expansion of the spectral function θ(t)=∑∞j=1 exp(−tλj) for small positive t.
The Goursat problem for Maxwell’s equations
Authors: Hillion Pierre
Published: July 2002

Using the spinor formalism of electromagnetism, the Goursat problem for Maxell’s equations is defined and some examples of solutions are given.
Hidden local gauge invariance in the one-dimensional Hubbard model and its equivalent coupled spin model
Authors: Zhou Huan-Qiang , Jiang Lin-Jie , Wu Ping-Feng
Published: July 2002

Hidden local gauge invariance in the one-dimensional (1-D) Hubbard model and its equivalent coupled spin model is studied. It is found that Abelian U(1)⊗U(1) gauge transformations appear in both cases. Furthermore, it is shown that the energy spectrum is gauge invariant whereas the eigenvectors are explicitly gauge dependent. However, this result relies heavily on Shastry’s conjecture about the eigenvalue of the transfer matrix for the 1-D Hubbard model. Lastly, there is also a discrete symmetry associated to Z2⊗Z2. Once this symmetry is broken, one immediately obtains another nontrivial solution to the Yang–Baxter relations. UFaipxr
Remarks on the Sp(2)-covariant Lagrangian quantization of gauge theories
Authors: Batalin I. A. , Lavrov P. M. , Tyutin I. V.
Published: July 2002

The existence of a solution of the exact generating equations (with ℏ≠0) for the Sp(2)-covariant Lagrangian quantization scheme is established. The characteristic arbitrariness of this solution is also studied. The equivalence between the Sp(2)-covariant quantization and the standard one is proven.
Lie structures in parasupersymmetric quantum mechanics: II. The spin-orbit coupling supersymmetrization procedure
Authors: Beckers J. , Debergh N.
Published: July 2002

The spin-orbit coupling supersymmetrization procedure is considered in parasupersymmetric quantum mechanics describing oscillatorlike systems. The superposition of bosonic and parafermionic degrees of freedom is mainly studied in the cases of two and three spatial dimensions but the n-dimensional case is also determined. New Lie superalgebras and Lie parasuperalgebras are pointed out: They differ from those already obtained in connection with the standard procedure of supersymmetrization studied in Part I of this series [J. Beckers and N. Debergh, J. Math. Phys. ▪▪, ▪▪▪ (1991)].
A wavelet transform for the Poincaré group
Authors: Klauder J. R. , Streater R. F.
Published: July 2002

It is noted that certain reducible cyclic representations of the Poincaré group are square integrable in the sense of wavelet theory. The corresponding wavelet transform and resolution of the identity are constructed. An inversion formula for an irreducible representation is obtained by taking limits.
About the geometric structure of symmetry-breaking
Authors: Keyl Michael
Published: July 2002

Gauge invariant Lagrangians in terms of groupoid actions are described. A general procedure for extending and reducing gauge invariance of Lagrangians depending on principal connections is found. The procedure includes the Higgs mechanism as a special case.
Involutive systems of differential equations: Einstein’s strength versus Cartan’s degré d’arbitraire
Authors: Sué Michael
Published: July 2002

Three new theorems relating Einstein’s notions of ‘‘strength’’ and ‘‘compatibility’’ to the field of the initial-value problem are presented. These theorems result (i) in a first proof of Matthews’ conjectures concerning this relation for a wider class of systems of partial-differential equations, (ii) in a new interpretation of Einstein’s compatibility condition, and (iii) in the exact relation between Einstein’s strength and Cartan’s degré d’arbitraire.
On the uniqueness of the Berry connection
Authors: Bohm Arno , Boya Luis J. , Kendrick Brian
Published: July 2002

Arguments are presented that make the choice of the connection, which gives rise to the Berry phase not only natural, but unique, both in the Abelian and the non-Abelian cases. Invariance is invoked under unitary transformations of the probability amplitudes in quantum systems to force the connection to be invariant under the unitary group. Because the action is not free, the horizontal subspace chosen by the connection has to be invariant under the little group, and that makes it orthogonal to the fiber’s direction, yielding the conventional Berry connection. The argument works just as well for the non-Abelian case, where the fibers are orthonormal frames (Stiefel manifolds), and the state space a Grassmanian, with a transitive but not free unitary action.
Radiation thermodynamics
Authors: Kremer G. M. , Müller Ingo
Published: July 2002

It is shown that the entropy principle provides a unique specific form of the radiative momentum flux. Also the nonequilibrium entropy and entropy flux of radiation thermodynamics are calculated explicitly. Waves are discussed in two limiting cases.
Bundle realizations and invariant connections in an Abelian principal bundle
Authors: Negro Javier , del Olmo Mariano A.
Published: July 2002

In this paper the concept of bundle realization of a Lie group on an Abelian principal bundle is defined. This definition is based on the theory of locally operating realizations of Lie groups. Afterward the bundle realizations are studied and characterized into pseudoequivalence classes. This theory is applied to a systematic study and classification of invariant connections under a Lie group. In particular, some examples of gauge invariant potentials under some subgroups of the Poincaré group are worked out.
Rotational diffusions as seen by relativistic observers
Authors: Garbaczewski Piotr
Published: July 2002

The major unsolved problem in the framework of Nelson’s stochastic mechanics is addressed and an attempt is made to provide a description of relativistic spin-1/2 particles in terms of Markovian diffusions on S3. Random rotations are here labeled by the proper time of a particle in relativistic motion and are continuously distributed along a space-time trajectory followed by the particle in Minkowski space.
C-statistical quantum groups and Weyl algebras
Authors: Majid Shahn
Published: July 2002

C-statistical quantum groups and algebras are obtained by a process of transmutation. They are like super-quantum groups and algebras but with statistics given now by a complex number. Among the examples, it is shown that the Weyl algebra of canonical quantization may be viewed equivalently as a C-statistical plane. Related examples are the ‘‘noncommutative torus’’ and a double loop-variable quantization of photons. These results lead toward a reformulation of ordinary quantum mechanics as a classical theory with C-statistics. In this reformulation, the role of the ±1 factors of super statistics is played by the free-particle time evolution.
Boson–fermion and baryon mapping: Construction of collective subspaces. III. Application of the baryon mapping to many-baryon states
Authors: Meyer Jutta
Published: July 2002

The theory developed in Paper I of this series is applied to the general case of a system consisting of colorfree quark triplets, whose quantum numbers are chosen as collective trifermion indices. The appropriate mapping technique to be used here is the baryon mapping. It is demonstrated that the original multiquark states can be exactly represented by states of colorfree ideal baryons. Besides, collective extended images are derived for a class of fermionic operators leaving the collective fermion space invariant.
Formal solutions of inverse scattering problems. V
Authors: Prosser Reese T.
Published: July 2002

In part III of this series [J. Math. Phys. 21, 2648 (1980)], it was shown that the backscatter function for the three-dimensional potential scattering problem can be used to recover the potential function, provided that either function is sufficiently small in a suitable norm. Here a new formula is given that relates the two functions directly, displays their invariance properties explicitly, and enables the inversion process to proceed under a more natural smallness condition.
Instanton-like solutions in conformal chiral superfield theories
Authors: Catto Sultan , Gürsey Yusuf
Published: July 2002

It is shown that previously developed supersymmetric field equations depending on a chiral supermultiplet admit instanton-like solutions.
Analytical solutions to classes of linear oscillator equations with time varying frequencies
Authors: Antone T. A. , AL-Maaitah A. A.
Published: July 2002

Analytical solutions to differential equations in the form of ÿ+[q(t)+q1(t)]y=0 are presented, where q1(t) is dependent on the solution of the basic equation ÿ+q(t)y=0. Various forms of the first equation are generated through a suggested procedure and their solutions should have some value in the mathematical physics field as well as in engineering applications.
Symmetry scattering on the hyperboloid SO(2,1)/SO(2) in different coordinate systems
Authors: Wehrhahn R. F. , Smirnov Yu. F. , Shirokov A. M.
Published: July 2002

The symmetry scattering theory based on the Harish-Chandra–Helgason theory of spherical functions on noncompact Riemannian symmetric spaces is extended to treat all spherical harmonics on the hyperboloid SO(2,1)/SO(2). The required conditions for an extension of the symmetry scattering theory to treat all spherical harmonics on arbitrary noncompact Riemannian symmetric spaces are elaborated.
Super angular momentum and super spherical harmonics
Authors: Daumens Michel
Published: July 2002

The usual quantum mechanics methods of defining angular momentum and spherical harmonics in the ordinary space E(3) are generalized to the real commuting super-space E(3‖2). The super angular momentum, generators of the super-rotation, is realized as differential operators acting on functions defined on E(3‖2). By solving the eigenvalue problem in spherical coordinates, a set of pseudo-orthonormalized functions is constructed, the super-spherical harmonics Ylmj, whose main properties are given.
Superconformally covariant operators and super-W-algebras
Authors: Gieres François , Theisen Stefan
Published: July 2002

Superdifferential operators of order 2n+1 which are covariant with respect to superconformal changes of coordinates on a compact super-Riemann surface are studied herein. It is shown that all such operators arise from super-Möbius covariant ones. A canonical matrix representation is presented and applications to classical super-W-algebras are discussed.
Dynamical group of the relativistic Kepler problem
Authors: Horwitz L. P.
Published: July 2002

A manifestly covariant relativistic generation of the Lenz vector for the relativistic Kepler problem is constructed. The corresponding dynamical group for the bound state problem is SO(4,1).
Supersymmetries of the superspace E(3‖2)
Authors: Daumens M. , Minnaert P. , Noirot Y.
Published: July 2002

The superspace E(3‖2) is the simplest superspace that generalizes the three-dimensional ordinary space. A super-Euclidean metric is defined on this superspace through its isomorphy with the vectorial representation superspace of the super-rotation algebra osp(1‖2). The supergroup UOSP(3‖2) is defined as the largest supersymmetry group acting in E(3‖2) and preserving the scalar product. The vectorial representation of the superrotation group, UOSP(1‖2), acts also in E(3‖2). The relations between these two supersymmetries are studied exhaustively.
On the graded group U(1/1)
Authors: Guhr Thomas
Published: July 2002

A noncanonical parametrization for the graded group U(1/1) is introduced similar to the Euler angles for the ordinary group SU(2). Two differential representations for the underlying algebra of U(1/1) are constructed on the full and the restricted, i.e., coset, parameter space, respectively. A space of functions living on the latter is found exhibiting close formal similarities to a Hilbert space. Remarkably, the indices of those functions and thus the orthogonality and completeness relations involve anticommuting variables. Using this Hilbert space a representation of U(1/1) is evaluated which shows analogies to the Wigner functions for SU(2).
Nonperturbative treatment of singular potentials
Authors: Miller H. G.
Published: July 2002

A nonperturbative but absolutely convergent algorithm is applied to the determination of the eigenfunctions of Hamiltonian with a singular potential of the form H=−d2/dx2+x2+λ/xα in the domain [0, ∞] which obey Dirichlet boundary conditons. The formal structure of the algorithm is identical to that of the Lanczos algorithm when it is formally extended to self-adjoint operators.
Isometry groups of three-dimensional Lorentzian metrics
Authors: Bona C. , Coll B.
Published: July 2002

The necessary and sufficient conditions for a three-dimensional Lorentzian metric to admit a group Gr of isometries acting on s-dimensional orbits are given. These conditions are expressed in terms of the eigenvalues and eigenvectors of the Ricci tensor. As a by-product, the set of (abstract) groups that can act isometrically and maximally on such metrics is obtained.
Self-gravitating Yang–Mills solitons and their Chern–Simons numbers
Authors: Brodbeck Othmar , Straumann Norbert
Published: July 2002

A classification of the possible regular, spherically symmetric solutions of the Einstein–Yang–Mills system which is based on a bundle theoretical analysis for arbitrary gauge groups is presented herein. It is shown that such solitons must be of magnetic type, at least if the magnetic Yang–Mills charge vanishes. Explicit expressions for the Chern–Simons numbers of these self-gravitating Yang–Mills solitons are derived, which involve only properties of irreducible root systems and some information about the asymptotics of the solutions. It turns out, as an example, that the Chern–Simons numbers are always half integers or integers for the gauge groups SU(n). Possible physical implications of these results, which are based on analogies with the unstable sphaleron solution of the electroweak theory, are briefly indicated.
q-difference intertwining operators for a Lorentz quantum algebra
Authors: Da̧browski L. , Dobrev V. K. , Floreanini R.
Published: July 2002

Representations π̂r,r̄ of a Lorentz quantum algebra 𝒰 are constructed. They are labeled by two complex numbers r,r̄ and act in the space of formal power series of two noncommuting variables η,η̄. These variables are built from elements of the matrix Lorentz quantum group ℒ which is dual to 𝒰. The conditions for reducibility of π̂r,r̄ are given. q-difference intertwining operators in η, η̄, which realize partial equivalences of the representations π̂r,r̄ , are constructed explicitly. The whole construction is a generalization of a known procedure for q=1. The case when q is a root of unity is also considered in detail.
A generalized time-dependent relativistic wave equation
Authors: Awobode A. M.
Published: July 2002

A time-dependent, spin-1/2, relativistic wave equation is introduced, so that some difficulties associated with the free particle Dirac equation may be resolved in a natural and systematic way. It has been found possible to establish a connection between the fluctuation of the velocity and a mass function which describes the fluctuation of the rest mass, derived from the Dirac theory. The time-dependent equation obtained by substituting the mass function for the constant mass term allows the description of spin fluctuations, for example, as time-dependent transitions between nonstationary states.
Relativistic density-functional theory of a single-electron problem
Authors: Holas A. , March N. H.
Published: July 2002

The kinetic energy as a functional of the particle-number and current densities and the corresponding functional derivatives of this energy are discussed and constructed for a relativistic single-electron problem. By an additional assumption of slowly varying spatial potentials, a Klein–Gordon equation is established from which the ground-state electron density can be calculated, and an approximate form of the kinetic energy functional obtained. While there are local errors of O(1/c2) introduced by the mentioned assumption, it is shown that in calculating the energy of the system these errors average to zero, leaving errors only of O(1/c4).