bluuebunny/crossref_metadata_2025 huggingface dataset:
Implementability of gauge transformations and quantization of fermions in external fields
Authors: Grosse H. , Karner G.
Published: July 2002

Quantization of fermions in an external soliton field, leading to a representation of the canonical anticommutation relation (CAR), which is inequivalent to the representation connected to the massive Dirac operator, is studied. Classes of gauge and axial gauge transformations that can be unitarily implemented are determined. In the latter case quantization conditions for gauge functions are obtained; integers entering can be interpreted as winding numbers.
Gell-Mann formula for simple complex Lie groups and geometric quantization
Authors: Šťovíček P.
Published: July 2002

A Lie–Poisson isomorphism for Lie algebras 𝔤 and 𝔮 =𝔨 ×𝔨 is derived in a closed form, where 𝔤 is complex and simple, and 𝔨 is the maximal compact subalgebra in 𝔤 . This isomorphism enables one to find a generalized Gell-Mann formula relating unitary irreducible representations of the corresponding Lie groups G and Q. The case 𝔤 =sl(n,C), 𝔨 =su(n) is considered in detail. A simple relation between characters is obtained.
A relativistic quantum mechanical harmonic oscillator without space-time variables
Authors: Blood F. A.
Published: July 2002

Solutions of a linear harmonic oscillatorlike second-order differential equation in a set of complex variables are investigated. This equation has an invariance group homomorphic to the inhomogeneous Lorentz group, IG14. Because of this, it has solutions with particlelike properties—mass, energy, momentum, and spin. These results are interesting for an equation without space-time variables.
An embedding problem
Authors: Ozsváth István
Published: July 2002

This paper contains two results. First it is shown that the three-dimensional Riemannian space, which is invariant under the transformations of the rotation group, cannot be embedded in a four-dimensional Euclidean space (except, of course, for the three-dimensional sphere). Second, the one parametric family of three-spaces with the above symmetry, which can be embedded in a four-dimensional unit sphere, is found and the embedding is constructed.
Scattering of waves from a random cylindrical surface
Authors: Ogura Hisanao , Nakayama Hiroshi
Published: July 2002

The present paper deals with the scattering of waves in two-dimensional space by the random surface of a circular object, which is meant to be a preliminary study for treating three-dimensional scattering by a random sphere. The theory is formulated using a stochastic functional method and a group-theoretic consideration related to the rotation of the circle, in a manner analogous to the authors’ previous treatment of the scattering by a planar random surface [Radio Sci. 15, 1049 (1980); J. Math. Phys. 22, 471 (1981); Radio Sci. 16, 831, 847 (1981); J. Opt. Soc. Am. A 2, 2208 (1985)]. First, the randomly scattered wave for cylindrical wave injection is given in terms of the Wiener–Hermite functional of the random field on the circle, and then the scattered field for plane-wave injection is synthesized by superposing cylindrical waves. The differential cross sections for the coherent and incoherent scattering are obtained, and a statistical version of the optical theorem is shown to hold. Some numerical calculations are made for the Mie scattering by the random circular surface with Dirichlet and Neumann conditions.
Nonlinear ‘‘self-interaction’’ Hamiltonians of the form H (0)+λ〈r p〉 r q and their Rayleigh–Schrödinger perturbation expansions
Authors: Vrscay Edward R.
Published: July 2002

Rayleigh–Schrödinger perturbation expansions for eigenvalues E(λ) of nonlinear Hamiltonians of the form Ĥ(0)+λ〈r p〉rq, p,q≥1 are calculated using hypervirial (HV) and Hellmann–Feynman (HF) theorems. Such Hamiltonians are similar in form to those employed in the study of ‘‘self-interacting’’ systems, e.g., solute–solvent interactions. The specific cases considered for H(0) are one-dimensional harmonic oscillators and hydrogen atoms. The eigenvalue expansions for the nonlinear problems are compared with those of the linear problems where p=0, whose large-order behavior and summability properties are well-known. Also examined are the perturbation expansions for the expectation values 〈rk〉, which are also products of the HVHF method.
Second-degree kinematical constraints associated with dynamical symmetries
Authors: Iosifescu Mircea , Scutaru Horia
Published: July 2002

The tensor operators that transform under subrepresentations of the symmetrized Kronecker square of the adjoint representation for the classical semisimple Lie algebras have been determined. All irreducible representations that satisfy the identities obtained by the vanishing of these tensor operators have been deduced. The pairs of irreducible representations of nonexceptional semisimple Lie algebras, the Kronecker product of which decomposes into two irreducible components, have been pointed out. As a consequence of this result, a comparison of the identities, derived in the way indicated before, with those resulting by the application of a method due to Hannabuss, Kostant, and Okubo, has been obtained. Connections between these results and those obtained by Drinfeld, concerning the solutions of quantum Yang–Baxter equations, have been established.
On the generalized multiplication and addition of complex numbers
Authors: Tikochinsky Yoel
Published: July 2002

Let x○y and x⊕y denote complex valued generalized multiplication and addition of complex numbers. If (a) multiplication is associative, (b) addition is associative and commutative, (c) there exists a complex number e satisfying x⊕e=x for all x, (d) multiplication is distributive with respect to addition, and (e) both operations are analytic functions in the two variables, then there exists a mapping x′→x such that (x○y)′=x′⋅y′ and (x⊕y)′=x′+y′. This result is used in the derivation of the multiplication and addition laws for quantum amplitudes.
Super-Selberg trace formula from the chaotic model
Authors: Uehara Shozo , Yasui Yukinori
Published: July 2002

A nonrelativistic superparticle moving freely on the super-Riemann surface of genus g≥2 is investigated. The classical motion is characterized by the super-Fuchsian group. The periodic orbits are unstable and the system is classically chaotic. Quantization is performed in the path integral method. The kernel function is explicitly given in the semiclassical approximation. The quantized energy spectrum is related to the length spectrum of the classical periodic orbits, which is a superanalog of Selberg’s trace formula.
On the many-time formulation of classical particle dynamics
Authors: Longhi G. , Lusanna L. , Pons J. M.
Published: July 2002

Starting from the standard one-time dynamics of n nonrelativistic particles, the n-time equations of motion are inferred, and a variational principle is formulated. A suitable generalization of the classical Lie–König theorem is demonstrated, which allows the determination of all the associated presymplectic structures. The conditions under which the action of an invariance group is canonical are studied, and a corresponding Noether theorem is deduced. A formulation of the theory in terms of n first-class constraints is recovered by means of coisotropic imbeddings. The proposed approach also provides for a better understanding of the relativistic particle dynamics, since it shows that the different roles of the physical positions and the canonical variables is not peculiar to special relativity, but rather to any n-time approach: indeed a nonrelativistic no-interaction theorem is deduced.
Chemical potential of a D-dimensional free Fermi gas at finite temperatures
Authors: Lee M. Howard
Published: July 2002

The chemical potential of a D-dimensional free Fermi gas at low temperatures has been obtained using some ideas due to Barker and Blankenbechler [J. Math. Phys. 97, 302 (1986); Am. J. Phys. 25, 279 (1957)]. There is an interesting even–odd-dimensional effect in the behavior of the chemical potential, also observed in other properties of a free Fermi gas, such as the susceptibility. For D=2, it is possible to give a closed form expression, thus valid both in the high- and low-temperature regions, probably not possible in any other even or odd dimensions.
Duality and conformal structure
Authors: Dray Tevian , Kulkarni Ravi , Samuel Joseph
Published: July 2002

In four dimensions, two metrics that are conformally related define the same Hodge dual operator on the space of two-forms. The converse, namely, that two metrics that have the same Hodge dual are conformally related, is established. This is true for metrics of arbitrary (nondegenerate) signature. For Euclidean signature a stronger result, namely, that the conformal class of the metric is completely determined by choosing a dual operator on two-forms satisfying certain conditions, is proved.
Coherent states for the noncompact supergroups Osp(2/2N,R)
Authors: Balantekin A. B. , Schmitt H. A. , Halse P.
Published: July 2002

An analysis of the coherent states for the noncompact supergroup Osp(2/2N,R) is presented. In contrast to Osp(1/2N,R), both typical and atypical representations have to be considered. The measure of integration, in general, for Osp(2/2N,R) coherent states is calculated; it is then used to construct the decomposition of unity for the special case of Osp(2/2,R). It is found, however, that the typical and atypical representations of Osp(2/2,R) have to be treated separately. It is verified that the coherent states for Osp(2/2,R) are ‘‘closest to classical’’ in the sense of Perelomov.
Local and global spectral shift functions in R2
Authors: Bollé D. , Danneels C. , Osborn T. A.
Published: July 2002

The energy-dependent trace-class time-delay operator associated with the transit time of a scattering system through a finite space region Σ⊆R2 is used to define a local (Σ-dependent) version of the Krein spectral shift function. If the region Σ is a disk of radius r, it is proved that as r→∞ the local spectral shift function converges, for almost all energies, to the original spectral shift function of Krein. This result continues to be valid for systems exhibiting zero-energy resonance behavior.
The relativistic coma aberration. II. Helmholtz wave optics
Authors: Atakishiyev Natig M. , Lassner Wolfgang , Wolf Kurt Bernardo
Published: July 2002

The relativistic coma aberration of geometric optics was examined in the first paper [J. Math. Phys. 30, 2457 (1989)]. Here is a study of a unitary realization of the Euclidean group, the dynamic group for global optics, on the space of solutions of the Helmholtz equation. Deformation to the Lorentz group of relativity yields the self-adjoint generators of boost transformations on that space. Graphic results for the action of a boost normal to the screen on an off-axis Gaussian beam, that may be compared with classical wave optics results on diffraction in aberration, are presented.
Relativistic and nonrelativistic plasma dispersion functions
Authors: Robinson P. A.
Published: July 2002

A number of new results involving the functions that determine the emission, dispersion, and absorption of waves in nonrelativistic and weakly relativistic plasmas are presented. These results comprise series, integrals, recursion relations, symmetry properties, interrelations, approximations, and connections with standard transcendental functions.
Integrability and orbits in quartic polynomial potentials
Authors: Cleary Paul W.
Published: July 2002

The effect of enlarging the class of admissible movable singularities in Painlevé analysis to include all rational algebraic branch points is examined for a class of quartic polynomial potentials. Eight homogeneous quartic potentials are found in addition to the seven integrable cases given by weak Painlevé analysis. They are examined using various numerical techniques and Ziglin’s theorem. Only one of them remains a candidate for integrability, which indicates that, in general, most rational algebraic branch points are incompatible with integrability. Movable logarithmic singularities also appear to be inconsistent with integrability. However, the remaining potentials are either regular or nearly regular for the energies examined, and are therefore still of interest for numerical purposes. The corresponding surfaces of section are found to be particularly simple in structure and belong to a small number of topologically distinct classes. Their stable and unstable periodic orbit structures are examined to provide information about their regularity and for use in Ziglin’s theorem. There appears to be a correlation between the resonances of the stable periodic orbits and the order of the corresponding movable singularities.
Twistors for uniform acceleration
Authors: Harnett Gerald
Published: July 2002

The skew tensor field and twistor descriptions of the momentum and angular momentum of a classical relativistic particle are adapted to describe a uniformly accelerated particle. An extension, natural within the twistor framework, of the usual duality between Poincaré momenta and symmetries yields osculating planes together with acceleration scalars as momenta of uniformly accelerated particles. The adapted twistor description leads to the construction of a local twistor attached to an arbitrary world line in a general space-time and a conformally invariant prescription for uniform acceleration.
Generalized relations among N-dimensional Coulomb Green’s functions using fractional derivatives
Authors: Blinder S. M. , Pollock E. L.
Published: July 2002

Hostler [J. Math. Phys. 11, 2966 (1970)] has shown that Coulomb Green’s functions of different dimensionality N are related by G(N+2)=𝒪G(N), where 𝒪 is a first-order derivative operator in the variables x and y. Thus all the even-dimensional functions are connected, as are analogously the odd-dimensional functions. It is shown that the operations of functional differentiation and integration can further connect the even- to the odd-dimensional functions, so that Hostler’s relation can be extended to give G(N+1)=𝒪1/2G(N).
Well-posedness of stationary and time-dependent Spencer–Lewis equations modeling electron slowing down
Authors: van der Mee C. V. M.
Published: July 2002

The unique solvability of the time-dependent and stationary Spencer–Lewis equations is established under natural assumptions on the solution and the data of the problem. The strategy used is the method of characteristics followed by perturbation and monotone approximation arguments. The evolution operator in the time-dependent Spencer–Lewis equation is proved to generate a strongly continuous contraction semigroup.
A spherical collapse solution with neutrino outflow
Authors: Glass E. N.
Published: July 2002

A three-parameter family of solutions of Einstein’s field equations is given that represents a collapsing perfect fluid with outgoing neutrino flux. Solutions with ‘‘naked’’ singularities are exhibited. They can be forbidden by requiring pressure less than or equal to the density as a condition of cosmic censorship.
On a Lie algebra of vector fields on a complex torus
Authors: Bremner Murray R.
Published: July 2002

This paper discusses a modification of the Krichever–Novikov Lie algebra of vector fields on the torus in which the two specified points where singularities can occur are points of order 1 and 2 rather than points of infinite order.
Trivector Fourier transformation and electromagnetic field
Authors: Jancewicz Bernard
Published: July 2002

A new kind of Fourier transformation is proposed for distributions taking values in the Clifford algebra of three-dimensional space, with the unit imaginary replaced by the unit trivector. The transformation is used to introduce special distributions that describe the free electromagnetic field.
Application of optimal control theory for selective vibrational excitation in molecules modeled as harmonic physical systems
Authors: Beumee J. G. B. , Rabitz H.
Published: July 2002

The design of optimal electromagnetic fields producing selective vibrational excitation in molecules modeled as harmonic physical systems is shown to be equivalent to minimizing a quadratic cost functional balancing the energy distribution in the molecule and the fluence of the input. In the control problem, two approaches are employed to insure that the final excitation is attained. One method uses a control strategy that employs a terminal constraint and in the other approach the cost functional is augmented with a terminal cost. The asymptotic form of the state and costate is investigated for both strategies in the limit that the final time approaches infinity, and some mathematical results on the form of the Lagrange parameter are presented for the first type of controller. These two results allow for a detailed discussion on the appropriate choice of practical design constants. For the example of a linear chain molecule, and approximation for the eigenvalues of the Hamiltonian matrix is derived for the limiting case where the weighting on the fluence of the optical field in the cost functional increases to infinity. Also, for the linear chain it is shown that the eigenvalues are bounded and that this bound does not depend on the length of the chain.
Representations of the braid group obtained from quantum sl(3) enveloping algebra
Authors: Ma Zhong-Qi
Published: July 2002

The quantum Clebsch–Gordan (CG) coefficients for the coproduct 6×6 of the quantum sl(3) enveloping algebra are computed. Based on the representation 6, the representation of the braid group and the corresponding link polynomial are obtained. The link polynomials based on the representations of the quantum sl(3) enveloping algebra with a one-row Young tableau are discussed.
Complete integrability and analytic solutions of a KdV-type equation
Authors: Chen Zhi-xiong , Guo (Pen-yu Ben-yuKuo) , Xiang Long-wan
Published: July 2002

The complete integrability of the variable coefficient version of a KdV equation via the Painlevé approach is analyzed. Through the Painlevé–Bäcklund equations, its auto-Bäcklund transformation, Lax pairs, symmetry, strong symmetry, bilinear form, and analytic solutions are obtained.
New link polynomial obtained from octet representation of quantum sl (3) enveloping algebra
Authors: Ma Zhong-Qi
Published: July 2002

The quantum Clebsch–Gordan coefficients for the coproduct 8×8 of the quantum sl(3) enveloping algebra are computed. In the decomposition of the coproduct 8×8, there are two octet representations that are identified by the symmetry in changing the order of the factor octet representations. The corresponding Řq matrix and a new link polynomial are obtained.
Scattering of waves from a random spherical surface—Mie scattering
Authors: Ogura Hisanao , Takahashi Nobuyuki
Published: July 2002

The stochastic theory developed by the authors for the scattering from a random planar surface is extended to the case of a random spherical surface, which is assumed to be a homogeneous random field on the sphere, homogeneous with respect to spherical rotations. Based on the group-theoretical analogies between the two, the formulation of the theory is closely connected to the representation theory of the rotation group. The concept of the ‘‘stochastic’’ spherical harmonics associated with the rotation group and their several formulas are introduced and discussed at the beginning. For the plane wave incident on a random spherical surface, the scattered random wave field can be expanded systematically in terms of the stochastic spherical harmonics in much the same way as the nonrandom case, and several formulas are derived for the coherent scattering amplitude, the coherent and incoherent power flows, and the coherent and incoherent scattering cross sections. The power-flow conservation law is cast into the stochastic version of the optical theorem stating that the total scattering cross section consisting of the coherent and incoherent power flow is equal to the imaginary part of the coherent forward-scattering amplitude. Approximate solutions are obtained for the Mie scattering with a slightly random spherical surface where the single scattering approximation is valid due to the absence of a real resonance, as shown in the previous work on the two-dimensional case. Some numerical calculations are made for the coherent and incoherent scattering cross sections.
On the semigroup nature of superconformal symmetry
Authors: Duplij Steven
Published: July 2002

A semigroup of N=1 superconformal transformations is introduced and analyzed. Noninvertible ones can describe transitions from body to soul and form a proper ideal containing a set of nilpotent transformations. The projective superspace is also considered. Transformations twisting the parity of a tangent space are brought in. They can be a nonsuperconformal ‘‘square root’’ of noninvertible superconformal transformations and the analogs of the Poincaré metric and conformal invariance are suggested for them.
On the τ-function of matrix hierarchies of integrable equations
Authors: Dickey L. A.
Published: July 2002

Expressions of the Baker and of the τ-functions for algebraic geometrical solutions of the AKNS-D hierarchy of integrable equations are obtained (in terms of θ-functions) along with a formula connecting them.
Symplectic hidden-variables theories—The missing link in algebraic contextual approaches
Authors: Durdević Mićo , Vujičić Milan , Herbut Fedor
Published: July 2002

The three known demonstrations that there exist contextual hidden variables (HV) that reproduce quantum mechanics (the HV theories of Bohm–Bub, Wiener–Siegel, and Gudder) are shown to be special cases of a generalized Gudder’s theory defined in this work. Within this scheme, a symplectic HV theory is introduced for which it is argued that it is physically more useful than Gudder’s theory because it makes possible the definition of a Hamiltonian subquantum dynamical law that reproduces in a natural way the Schrödinger equation. On the other hand, the symplectic HV theory contains as concrete realizations a slightly modified theory of Bohm–Bub and the theory of Wiener and Siegel.
Graded C*-algebras in the N-body problem
Authors: de Monvel-Berthier Anne Boutet , Georgescu Vladimir
Published: July 2002

An algebraic formalism is presented which simplifies and makes natural various arguments in the theories where some notion of ‘‘connected operator’’ appears. As a first example, in this paper the case of N-body systems is considered.
Reflection coefficient beyond all orders for singular problems. II: Closed-spaced critical points on the nearest critical level line
Authors: Hu Jishan , Kruskal Martin
Published: July 2002

A crucial connection formula with closed-spaced critical points on the nearest critical level line is established in this paper in order to use the generalized Pokrovskii–Khalatnikov method to calculate the nontrivial behavior of the reflection coefficient for singular problems.
Sum rules for SU(2) Racah coefficient from group integral
Authors: Tanimura N. , Tanimura O.
Published: July 2002

New sum rules are derived for the SU(2) Racah coefficients by means of the group integral. The general graphic rules of calculating the multifold group integral for the product of the SU(2) characters in terms of the Racah coefficients are presented.
Integrable dynamical systems with quadratic and cubic nonlinearities related to graded Lie algebras
Authors: Jiang Zhuhan , Rauch-Wojciechowski S.
Published: July 2002

Practical implementation of two important methods of constructing integrable dynamical systems, the Lax pair method and the Adler–Konstant–Symes theorem, is studied. General considerations are illustrated by several examples that contain multiwave interaction systems and interacting Garnier systems as particular cases.
Remarks on continuity of entropy of states on C*-dynamical systems
Authors: Muraki Naohumi
Published: July 2002

Lower semicontinuity of Ohya’s 𝒮-entropy with respect to the state space and to the space of invariant states is shown for some C*-dynamical systems. Lower semicontinuity of the 𝒮-entropy in the weak* topology is also shown for compact convex sets 𝒮 satisfying certain conditions.
q-analogs of IU(n) and U(n,1)
Authors: Chakrabarti A.
Published: July 2002

The starting point is the nonsemisimple, inhomogeneous Lie algebra Un×I2n [denoted also as IU(n)], where I2n represents an Abelian subalgebra in semidirect product with the homogeneous part U(n). This is realized by explicitly giving the matrix elements of the generators on a modified Gelfand–Zetlin basis that allows representations of infinite dimensions. The enveloping algebra is q lifted by introducing q brackets in the matrix elements giving Uq(IU(n)). The deformation of the Abelian structure of I2n is studied for q≠1. Some implications are pointed out. The important invariants are constructed for arbitrary n. The results are compared to the corresponding ones for Jimbo’s construction of Uq (U(n+1)) on a Gelfeld–Zetlin basis. Finally, the related construction of Uq(U(n,1)) is presented and discussed. Here, Uq(SU(1,1)), the q-analog of relativistic motion in a plane, is analyzed in the context of this formalism.
Associated integrable systems
Authors: Alber Solomon J.
Published: July 2002

New class of integrable Hamiltonian systems is obtained as systems directly defined over Jacobi varieties. This approach enables one to establish a link between associated discrete and continuous systems. In particular, regular procedure is found for the discretization of the integrable continuous systems. Hierarchies of the continuous systems associated with Toda lattices, relativistic Toda lattices, and Volterra lattices are found and studied.
Stably causal Gödel-type models
Authors: Monteiro S. W.
Published: July 2002

The problem of finding stationary Gödel-type cosmological space-times endowed with stable causality is solved in general relativity. These models are generated by spin fluids with strong spin-vorticity coupling, and present interesting physical properties. Their intrinsic characterization is made by means of an invariant algebraic classification. A simple technique to test the stable causality is applied to new and old distinct stationary space-times.
Lie symmetries of Hirota’s bilinear equations
Authors: Tamizhmani K. M. , Ramani A. , Grammaticos B.
Published: July 2002

The existence of Lie-point symmetries for a family of partial differential equations (PDEs) written in Hirota’s bilinear formalism is investigated. These equations have been studied in previous publications from the point of view of the existence of multisoliton solutions and also of the Painlevé property and are either known as integrable or good candidates for integrability. For these equations, the Lie algebra of Lie-point symmetries is derived, which in some cases turns out to be an infinite-dimensional algebra.
Canonical perturbation expansions to large order from classical hypervirial and Hellmann–Feynman theorems
Authors: McRae S. M. , Vrscay E. R.
Published: July 2002

The classical hypervirial and Hellmann–Feynman theorems are used to formulate a ‘‘perturbation theory without Fourier series’’ that can be used to generate canonical series expansions for the energies of perturbed periodic orbits for separable classical Hamiltonians. As in the case where these theorems are used to generate quantum mechanical Rayleigh–Schrödinger perturbation series, the method is very efficient and may be used to generate expansions to large order either numerically or in algebraic form. Here, the method is applied to one-dimensional anharmonic oscillators and radial Kepler problems. In all cases, the classical series for energies and expectation values are seen to correspond to the expansions associated with their quantum mechanical counterparts through an appropriate action preserving classical limit as discussed by Turchetti, Graffi, and Paul. This ‘‘action fixing’’ is inherent in the classical Hellmann–Feynman theorem applied to periodic orbits.
Hyperbolic models for linear transport theory
Authors: Pennisi S. , Sammartino M.
Published: July 2002

The linear transport equation and taking its moments are considered for seeking a second-order closure. It is found that all closures consistent with an entropy principle are elements of a one-parameter family. It is also shown that all the Eddington factors appearing in literature are all elements of the above family.
The low-density limit in terms of collective squeezed vectors
Authors: Rudnicki Slawomir , Alicki Robert , Sadowski Slawomir
Published: July 2002

The low-density limit for a quantum system interacting with a free Bose or Fermi gas is considered. For the particular choice of reference vectors (collective squeezed vectors) one proves the convergence of the associated matrix elements of the evolution operator to the matrix elements of the unitary quantum stochastic process driven by the quantum Poisson noise.
Weight diagram construction of Lax operators
Authors: Carbon Steven L. , Piard Eric J.
Published: July 2002

It is demonstrated and proven that cyclic weight diagrams corresponding to representations of affine Lie algebras allow one to construct the associated Lax operator. The resultant Lax operator is in the Miura-like form and generates the modified KdV equations. The algorithm is extended to the supersymmetric case.
Cooper pairing in one, two, and three dimensions
Authors: Esebbag C. , Getino J. M. , de Llano M. , Moszkowski S. A. , Oseguera U. , Plastino A. , Rubio H.
Published: July 2002

The Cooper pair eigenvalue equation is solved exactly for the free-electron density of states in one, two, and three dimensions. The two-dimensional (2-D) case is essentially the original derivation of Cooper, as is the three-dimensional case if the interaction is restricted to the vicinity of the Fermi surface. The essential singularity in coupling, familiar in 2-D quantum binding in a well, and sometimes erroneously attributed to the two-dimensional character of the BCS model interaction which is nonzero only very near the Fermi surface, appears in all three cases.
An existence theorem for perturbed Newtonian cosmological models
Authors: Brauer Uwe
Published: July 2002

Given a Newtonian Friedmann-like cosmological model ℳO, there exist, locally in time, spatially periodic solutions close to ℳO. Such solutions represent inhomogeneous models that are homogenous and isotropic on a large scale. The Euler–Poisson system is shown to be linearization stable at ℳO.
The curvature and the algebra of Killing vectors in five-dimensional space
Authors: Rcheulishvili G.
Published: July 2002

This paper presents the Killing vectors for a five-dimensional space with the line element (1). The algebras that are formed by these vectors are written down. The curvature two-forms are described.
Von Hove model of quantum field theory-from the point of view of infinite dimensional stationary Markov process theory
Authors: Wang Zheng Dong
Published: July 2002

There are two ways to quantize the classical von Hove model. One way is to quantize the classical von Hove field equation, and the other is to quantize the classical energy functional. In this paper, their relation to each other is pointed out. As an application the second-order approximate quantization of (φ4)2-kink field is studied.
Exact wave functions of an electron on a quasiperiodic lattice: Definition of an infinite-dimensional Riemann theta function
Authors: Iguchi Kazumoto
Published: July 2002

A scheme for obtaining the exact wave functions of an electron on a quasiperiodic lattice is presented. It is shown that the trace map plays a very important role for construction of the infinite-dimensional Riemann theta function in terms of which the wave functions can be represented.
Self-adjointness of the operators in Wigner’s commutation relations
Authors: Ohnuki Yoshio , Watanabe Shuji
Published: July 2002

Both self-adjointness and spectra of the momentum operator p and the Hamiltonian H are studied: p=−i{d/dx−(c/x)R}; H=2−1{−(d/dx)2+(c/x2)(c−R)+x2}, for a one-dimensional harmonic oscillator governed by Wigner’s commutation relations. Here, c is a real parameter and Rψ(x)=ψ(−x). First the essential self-adjointness of p and H are shown to obtain that the spectrum of H consists of eigenvalues only. Moreover, we clarify the meaning in L2(R) of the classical form H=2−1(p2+x2). Next it is shown that every real number is in the continuous spectrum of p, by introducing a kind of generalized Fourier transform B satisfying p=B−1xB for the multiplication x. In the case of c=0, B turns out to be the ordinary Fourier transform and p becomes the well-known operator. By the methods stated above, all the results of the recent papers, where some restrictions on the parameter c were imposed, are improved.
Quasiperiodic solutions for matrix nonlinear Schrödinger equations
Authors: Wisse M. A.
Published: July 2002

The Adler–Kostant–Symes theorem yields isospectral Hamiltonian flows on the dual ■erm>$$̃g+* of a Lie subalgebra ■erm>$$̃g+ of a loop algebra ■erm>$$̃g. A general approach relating the method of integration of Krichever, Novikov, and Dubrovin to such flows is used to obtain finite-gap solutions of matrix nonlinear Schrödinger equations in terms of quotients of θ functions.
Conditions for a symmetric connection to be a metric connection
Authors: Edgar S. Brian
Published: July 2002

A recent result−in ‘general circumstances’ for a four-dimensional space–time−giving algebraic conditions on a curvature tensor (of a symmetric connection) so that the connection be metric, is shown to be a special case of a more general result; both of these results are shown formally to be of a generic nature. In this new result the conditions are imposed on a tensor of a more general character than the curvature tensor. In addition it is shown that once the symmetric connection is known to be metric, the metric is uniquely defined (up to a constant conformal factor). For those special curvature tensors which are excluded from the original result, supplementary conditions are suggested, which, alongside the original conditions are sufficient to ensure that most of these excluded curvature tensors are also Riemann tensors.
On the solution of homogeneous generalized wave equation
Authors: Capelas de Oliveira E.
Published: July 2002

We present the solutions for the homogeneous generalized wave equation when we have a local problem.
Functional realization of quantum affine algebras
Authors: Tsukada Haruo
Published: July 2002

Functional realizations of vertex representations of quantum affine algebras are presented. The representation spaces are realized as functionals, and the integral kernels of products of q-deformations of vertex operators are computed.
On the q-symplecton realization of the quantum group SUq(2)
Authors: Nomura Masao , Biedenharn L. C.
Published: July 2002

A q-symplecton realization of the quantum group SUq(2) is constructed, giving explicitly the product law for the Weyl-ordered characteristic polynomials. A new form of the q-Racah coefficients is obtained, which is especially adapted to proving a new symmetry for these functions. A surprising result is that unlike the SU(2) case there are two distinct invariant q-triangle functions in the q-symplecton extension.
Path integral treatment for the one-dimensional Natanzon potentials
Authors: Chetouani L. , Guechi L. , Lecheheb A. , Hammann T. F.
Published: July 2002

The Green’s function relative to the one-dimensional Natanzon potentials is exactly calculated by the path integral approach. The energy spectrum, the wave functions, and the scattering function S are deduced.
Quasi exactly solvable extensions of the Lamé equation
Authors: Brihaye Y. , Godart M.
Published: July 2002

Quasi exactly solvable equations are spectral equations which possess a finite number of algebraic eigenvectors. For a few of these equations, such as the Lamé equation, the number of algebraic solutions is larger than predicted by the general theory. A class of quasi exactly solvable equations in one variable is considered and the conditions under which a rich algebraization occurs is discussed. Families of equations, which by themselves are not quasi exactly solvable, but can be transformed into systems of coupled quasi exactly solvable equations, are discussed. These results suggest a scheme for the classification of quasi exactly solvable systems in one variable.
Diffeomorphism cohomology in Beltrami parametrization
Authors: Bandelloni Giuseppe , Lazzarini Serge
Published: July 2002

Considering local conformal field theories on a Riemann surface by coupling conformal matter fields with a complex structure parametrized by a Beltrami differential, the local diffeomorphism cohomology modulo d of the Becchi–Rouet–Stora operator is computed directly by means of the spectral sequences method. Then, thanks to both power counting and locality principles of the Feynman algorithm, the local theory is analyzed. On the one hand, in the ghost number one sector, consistent anomalies turn out to be exactly, after elimination of a trace anomaly involving matter fields, the well-known holomorphically split diffeomorphism anomaly due to the vacuum. On the other hand, in the ghost number zero sector, local observables of the theory, namely, the vertex operators, are generically calculated, as well as all possible classical actions for Lagrangian conformal models.
Functional calculus using wavelet transforms
Authors: Holschneider Matthias
Published: July 2002

It is shown how the wavelet transform may be used to compute for a function s the symbol s(A) for any (not necessarily) self-adjoint operator A whose spectrum is contained in the upper half plane. For self-adjoint operators it is shown that this functional calculus coincides with the usual one. In particular it is shown how the exponential eitA can be written in terms of the resolvent Rz=(A−z)−1 of A as follows: eitA=(1/c) ∫0∞da an−2∫−∞+∞ dbĝ̄ (at)eitbRb−ian(A), with c=−2iπ×∫0∞(dω/ω) (−iω)n−1ĝ̄(ω)e−ω, and n∈N, and the integral is understood as the Cesaro limit. This shows explicitly how the behavior for large t is determined by the behavior of Rz at ℑz≂1/t.
Yang–Mills theory on a cylinder coupled to point particles
Authors: Gupta K. S. , Henderson R. J. , Rajeev S. G. , Turgut O. T.
Published: July 2002

A model of quantum Yang–Mills theory with a finite number of gauge invariant degrees of freedom is studied. The gauge field has only a finite number of degrees of freedom since it is assumed that space–time is a two-dimensional cylinder. The gauge field is coupled to matter, modeled by either one or two nonrelativistic point particles. These problems can be solved without any gauge fixing, by generalizing the canonical quantization methods of S. G. Rajeev [Phys. Lett. B 212, 203 (1988)] to the case including matter. For this, the geometry of the space of connections is used, which has the structure of a principal fiber bundle with an infinite-dimensional fiber. Both problems are reduced to finite-dimensional, exactly solvable, quantum mechanics problems. In the case of one particle, it is found that the ground state energy will diverge in the limit of infinite radius of space, consistent with confinement. In the case of two particles, this does not happen if they can form a color singlet bound state (‘‘meson’’).
Nonlinear Schrödinger equations and the separation property
Authors: Goldin Gerald A. , Svetlichny George
Published: July 2002

Hierarchies of nonlinear Schrödinger equations were investigated for multiparticle systems, satisfying the separation property, i.e., where product wave functions evolve by the separate evolution of each factor. Such a hierarchy defines a nonlinear derivation on tensor products of the single-particle wave-function space, and satisfies a certain homogeneity property characterized by two new universal physical constants. A canonical construction of hierarchies is derived that allows the introduction, at any particular ‘‘threshold’’ number of particles, of truly new physical effects absent in systems having fewer particles. In particular, if single quantum particles satisfy the usual (linear) Schrödinger equation, a system of two particles can evolve by means of a fairly simple nonlinear Schrödinger equation without violating the separation property. Examples of Galilean-invariant hierarchies are given.
Kerr–Schild metrics revisited. I. The ground state
Authors: Gergely László Á. , Perjés Zoltán
Published: July 2002

The Kerr–Schild pencil of metrics gab+Λlalb is investigated in the generic case when it maps an arbitrary vacuum space-time with metric gab to a vacuum space-time. The theorem is proved that this generic case, with the field l shearing, does not contain the shear-free subclass as a smooth limit. It is shown that one of the Kóta–Perjés metrics is a solution in the shearing class.
Extended reflection equation algebras, the braid group on a handlebody, and associated link polynomials
Authors: Schwiebert Christian
Published: July 2002

The correspondence of the braid group on a handlebody of arbitrary genus to the algebra of Yang–Baxter and extended reflection equation operators is shown. Representations of the infinite-dimensional extended reflection equation algebra in terms of direct products of quantum algebra generators are derived; they lead to a representation of this braid group in terms of R-matrices. Restriction to the reflection equation operators only gives the colored braid group. The reflection equation operators, describing the effect of handles attached to a three-ball, satisfy characteristic equations that give rise to additional skein relations and thereby invariants of links on handlebodies. The origin of the skein relations is explained and they are derived from an adequately adapted handlebody version of the Jones polynomial. Relevance of these results to the construction of link polynomials on closed three-manifolds via Heegard splitting and surgery is indicated.
Modular invariant partition functions and method of shift vector
Authors: Shirzad A. , Arfaei H.
Published: July 2002

Using the shift vector method a large class of self-dual lattices of dimension (l,l) is obtained, which has a one to one correspondence with modular invariants of free bosonic theory compactified on a coroot lattice of a rank l Lie group. Then a large number of modular invariants of affine Lie algebras are derived explicitly. Two applications of this method are a direct derivation of the D series of SU(N) and a new proof for the A-D-E classification of the SU(2)k partition functions.
A Nyström algorithm for electrostatics of an anisotropic composite
Authors: Helsing Johan
Published: July 2002

The construction of efficient numerical algorithms for the electrostatics of locally anisotropic composites seems to be a poorly explored area. In this paper coupled first and second kind Fredholm integral equations for the electrostatics of anisotropic inclusions in an anisotropic matrix are derived. For a square array of circular cylinders the integral equations are solved to high accuracy through pointwise discretization. In the process a recent renormalization method is extended for the evaluation of lattice sums [J. Math. Phys. 35, 6036 (1994)] to encompass the calculation of sums on stretched lattices. Conditionally convergent stretched lattice sums are computed from physical considerations.
Semiclassical determinants of Schrödinger operators on line bundles
Authors: Simon David S.
Published: July 2002

Heat kernel methods are used to compute asymptotic expressions for the zeta-regularized determinant and local heat invariants of a Schrödinger operator acting on sections of the kth tensor power of a line bundle, as k → ∞. The result is an infinite series representation involving Todd polynomials of the curvature.
Projective techniques and functional integration for gauge theories
Authors: Ashtekar Abhay , Lewandowski Jerzy
Published: July 2002

A general framework for integration over certain infinite dimensional spaces is first developed using projective limits of a projective family of compact Hausdorff spaces. The procedure is then applied to gauge theories to carry out integration over the non-linear, infinite dimensional spaces of connections modulo gauge transformations. This method of evaluating functional integrals can be used either in the Euclidean path integral approach or the Lorentzian canonical approach. A number of measures discussed are diffeomorphism invariant and therefore of interest to (the connection dynamics version of) quantum general relativity. The account is pedagogical; in particular, prior knowledge of projective techniques is not assumed.
Scattering on small three-dimensional, nonspherically symmetric potentials
Authors: Grinberg N. I.
Published: July 2002

Three-dimensional anisotropic inhomogeneous scatterer is considered, which is modeled by the Schrödinger operator with a pseudodifferential potential. Definition of the scattering amplitude is given based on the scattering of the plane wave. The amplitude, as well as the potential, depends on five real parameters. The correspondence between the scatterer (potential) and the scattering amplitude is discussed. It is stated, in particular, that any small nontrivial potential produces a nonzero scattering amplitude.
A simple method for constructing the inhomogeneous quantum group IGLq(n) and its universal enveloping algebra Uq
(igl(n))
Authors: Shariati A. , Aghamohammadi A.
Published: July 2002

We propose a simple and concise method to construct the inhomogeneous quantum group IGLq(n) and its universal enveloping algebra Uq(igl(n)). Our technique is based on embedding an n-dimensional quantum space in an n+1-dimensional one as the set xn+1=1. This is possible only if one considers the multiparametric quantum space whose parameters are fixed in a specific way. The quantum group IGLq(n) is then the subset of GLq(n+1), which leaves the xn+1=1 subset invariant. For the deformed universal enveloping algebra Uq(igl(n)), we will show that it can also be embedded in Uq(gl(n+1)), provided one uses the multiparametric deformation of U(gl(n+1)) with a specific choice of its parameters.
Asymptotic Clebsch–Gordan coefficients
Authors: de Guise Hubert , Rowe David J.
Published: July 2002

We present derivations of su(2) and su(3)⊇so(3) Clebsch–Gordan coefficients in the limit of large quantum numbers. For su(3), we derive simple analytic expressions for the asymptotic coefficients needed for the decomposition of the product (λ1,0)⊗(λ2,0), in the limit of λ1→∞, in an so(3) basis.
New spin-one gauge theory in three dimensions
Authors: Anco Stephen C.
Published: July 2002

This paper presents a new type of nonlinear gauge theory for spin-one fields in three dimensions. The theory is constructed by a systematic process of generalization applied to the linear gauge theory of spin-one fields. The process takes advantage of vector cross product and curl operations available only in three dimensions, leading to a highly novel form for the generalization of the field equations and gauge symmetry. Features of the new theory are discussed, and some possible generalizations are outlined.
Diffeomorphism cohomology in Beltrami parametrization. II. The 1-forms
Authors: Bandelloni Giuseppe , Lazzarini Serge
Published: July 2002

The 1-form diffeomorphism cohomologies within a local conformal Lagrangian field theory model built on a two dimensional Riemann surface with no boundary is studied. The case of scalar matter fields is considered and the complex structure is parametrized by Beltrami differential. The analysis is first performed at the classical level, and then we improve the quantum extension, introducing the current in the Lagrangian dynamics, coupled to external source fields. It is shown that the anomalies which spoil the current conservations take origin from the holomorphic region of the external fields, and only the differential spin 1 and 2 currents (as well as their c.c) could be anomalous.