bluuebunny/crossref_metadata_2025 huggingface dataset:
Vacuum solutions admitting a geodesic null congruence with shear proportional to expansion
Authors: Kupeli A. H.
Published: July 2002

Algebraically general, nontwisting solutions for the vacuum to vacuum generalized Kerr–Schild (GKS) transformation are obtained. These solutions admit a geodesic null congruence with shear proportional to expansion. In the Newman–Penrose formalism, if lμ is chosen to be the null vector of the GKS transformation, this property is stated as σ=aρ and Da=0. It is assumed that a is a constant, and the background is chosen as a pp-wave solution. For generic values of a, the GKS metrics consist of the Kasner solutions. For a=±(1±(2)1/2), there are solutions with less symmetries including special cases of the Kóta–Perjés and Lukács solutions.
Bianchi type VI0 space-times with perfect fluid source
Authors: Ram Shri
Published: July 2002

An analytic solution to Einstein’s field equations is presented for the Bianchi type VI0 class of models. The energy-momentum tensor is of the perfect fluid type. The solution corresponds to a locally rotationally symmetric and expanding cosmological universe which would give an essentially empty universe for large time. Some kinematical properties of the solution are discussed.
Behavior of dynamic soliton solutions in nonintegrable extended Klein–Gordon systems by means of a state plane technique
Authors: Tateno H.
Published: July 2002

The dynamic behavior of soliton solutions in nonintegrable extended Klein–Gordon systems as a continuum containing a dissipation term and an external force term, expressed by φxx−φtt−F(φ)=Gφt−JB, is investigated geometrically in a state plane by transforming the equation into three basic equations, each of which is associated with the derivative with respect to x, t, and φ, respectively. The initial and the boundary conditions are imposed so that the solution approaches asymptotically the stationary solitary-wave solution as ‖x‖ and ‖t‖ approach infinity. In the above treatment, the waves consisting of the pair of φx and φt are divided into two components, the traveling wave component, V(x,t), and the others. The state plane is then constructed by the coordinates consisting of V(x,t) and φ. The traveling wave component is defined with φT by introducing nonlinear coordinates Ξ(x,t)=X(x,t)−uT(x,t) instead of the linear coordinates ξ=x−ut, and travels with a constant velocity of u in the coordinates. Their properties are investigated for various cases of wave interactions. The method for analyzing soliton interactions is described in detail. It is first shown that the solutions to the basic equations presented are in agreement with the well-known solutions for two soliton interactions in pure sine–Gordon system. Next, as an example, the analytical method is applied to the extended sine–Gordon system, the behavior of the local distortions produced during the soliton–antisoliton interaction because of existence of the moving singularities is described, and details of the mechanism and properties of them are clarified. It is finally shown that the additional dissipation term proportional to φxxt acts to smooth the distortions resulting from the disappearance of the moving singularities.
Factorization of the dissipative wave equation and inverse scattering
Authors: Weston V. H.
Published: July 2002

A decomposition of the solution of the dissipative wave equation into incoming and outgoing components across a smooth surface in a homogeneous region is presented. (The proof of the decomposition is given only for the plane surface.) This is then applied to the factorization of the dissipative wave equation into incoming and outgoing components in a planar-stratified medium. The Ricatti integral–differential equation for the reflection operator that relates the two components is obtained. It is shown how the zeroth and second moments (with respect to the transverse variable in a planar-stratified medium) of the reflection kernel can be used in the inverse problem to recover the velocity and dissipation coefficient from knowledge of the scattered field.
Gravitational repulsion in sources of the Reissner–Nordström field
Authors: Ponce de Leon J.
Published: July 2002

A number of aspects of the phenomenon of gravitational repulsion in static sources of the Reissner–Nordström field are investigated. It is found that in the case of perfect fluid spheres there exists a close relation between this phenomenon and the Weyl curvature tensor. In fact, it is proved that such a source gives rise to gravitational repulsion only if the pure gravitational field energy inside the sphere is negative. It is also proved that although the gravitational repulsion always takes place in the interior of a perfect fluid charged sphere when its radius r0 is less than the ‘‘classical electron radius’’ re, this is not necessarily so either in the case of anisotropic charged spheres or if the net charge of the body is concentrated at its boundary only. It is shown that the phenomenon can also occur inside charged sources with r0>re. New sources of repulsive gravitation are constructed. They differ from others in the literature, since they neither satisfy the equation of state of ‘‘false vacuum’’ nor are their total gravitational masses entirely of electromagnetic origin. It is found that the charge contributes negatively to the effective gravitational mass MG, in the sense that an increase in the charge causes a decrease in MG. The gravitational repulsion in the new models constructed here is explained as due to this negative contribution rather than due to the strain of vacuum because of vacuum polarization.
General relativistic fluid spheres with nonzero vacuum energy density
Authors: Hiscock William A.
Published: July 2002

Bounds are developed for the ratios M/R and m/R for fluid spheres in asymptotically de Sitter or anti-de Sitter space-times, where M is the mass of the fluid sphere, and m is the total mass interior to R: M plus the interior vacuum energy. This represents a generalization of the work of Buchdahl to the case of a nonvanishing vacuum energy density. In the asymptotically de Sitter case, it is possible to construct models which have m/r→ 1/2 . Further, it is shown that static fluid spheres can exist in an asymptotically de Sitter space with vacuum energy density ρv only if their radius satisfies R≤(8πρv)1/2, a maximum radius smaller by a factor of 3−1/2 than the horizon size of the de Sitter space in the absence of a fluid sphere. If the vacuum energy density is negative, then the ratio m/R is shown to be bounded above by the asymptotically flat limit of (4)/(9), and the radius of a positive total mass (m) sphere is shown to be bounded above by R<(2π‖ρv‖)−1/2.
Exceptional Lie algebras in terms of fermionic creation–annihilation operators
Authors: Sciarrino A.
Published: July 2002

From the embedding E8⊇D4×D4, defining fermionic operators which transform, respectively, as the vectorial and spinorial representations of D4, the algebra of E8 is constructed in terms of a bilinear in the fermionic operators. Then, by embeddings, the adjoint and fundamental representations of the other exceptional algebras are explicitly written.
Lanczos potential
Authors: Ares de Parga Gonzálo , Chavoya A. Oscar , López Bonilla José L.
Published: July 2002

The Lanczos spin tensor [C. Lanczos, Rev. Mod. Phys. 34, 379 (1962)] is obtained for arbitrary space-times type III, N, or o.
Magnetic generalizations of the Carter metrics
Authors: García Díaz Alberto , Bretón Baez Nora
Published: July 2002

Magnetic generalizations of all Carter metrics—Carter A, B(+), B(−), and D solutions—are obtained by applying a Harrison transformation to the Ernst potentials determined from a linear combination of two Killing vectors. The most general magnetized Carter-A metric contains, among other solutions, the magnetized Kerr–Newman metrics and, modulo limiting transitions, the magnetized branches B(+), B(−), and D.
Stochastic field theory at finite temperature and equilibrium states in quantum statistical mechanics
Authors: Bandyopadhyay Pratul , Bhattacharya Brahmananda , Ghosh Pradip
Published: July 2002

Stochastic field theory at finite temperature, when it is formulated from stochastic mechanics, which incorporates Brownian motion in both the external, as well as the internal, space of a particle, and the external and internal fields, and which are written as thermal doublets, gives rise to finite temperature quantum field theory in Minkowski space. The Haag–Hugenholtz–Winnik, (HHW) formalism of modular conjugation and the Tomita–Takesaki theory of modular Hilbert algebra then follow from this finite temperature quantum field theoretical formalism. It is shown that there is an inherent discrete Z2 symmetry among the fields of the doublet, and the equilibrium condition is ensured by this symmetry. When this symmetry is spontaneously broken, thermodynamical equilibrium is destroyed.
Coherent and thermal coherent state
Authors: Mann A. , Revzen M. , Nakamura K. , Umezawa H. , Yamanaka Y.
Published: July 2002

The characterization of coherent states as the quantum states that split into two uncorrelated beams is considered. The characterization leads to the study of coherent states at finite temperature—thermal coherent states (TCS’s). These TCS’s are defined within the formalism of thermo field dynamics (TFD). TFD allows a generalization of the uncertainty relation that accounts for both thermal and quantum fluctuations. The TCS is shown to be a minimal state for the generalized uncertainty relation.
Solution of Dyson equation for elastic membranes
Authors: Kleinert H.
Published: July 2002

The Dyson equation for the renormalization of the curvature stiffness by elastic fluctuations into a simple differential equation is transformed and solved iteratively as well as numerically. If the tension parameter falls below some critical value, the inverse two-point function develops discontinuously a minimum at a nonzero momentum p0. This should be relevant for understanding a transition in elastic membranes.
The four sets of additive quantum numbers of SU(3)
Authors: Patera J.
Published: July 2002

The four maximal sets of additive quantum numbers and related fine gradings of the Lie algebra sl(3,C) are described in detail. The quantum numbers are determined by a grading of the Lie algebra, fine gradings providing maximal sets of them. Two sets of additive quantum numbers are equivalent precisely if the corresponding gradings are equivalent under a transformation from the automorphism group of the Lie algebra.
Microscopic collective nuclear models with horizontal mixture
Authors: Filippov G. F. , Blokhin A. L.
Published: July 2002

By accounting for the difference in the spin and isospin projection among nucleons, the Sp(6,R) dynamical symmetry of the nuclear collective model is amplified in parallel with a horizontal extension of the instrinic shell structure. The generating kernels for the extended symplectic model basis functions are constructed in the form of a shortened coherent state. Analytical expressions for the microscopic Hamiltonian matrix elements, including central and tensor interactions, are obtained between the coherent states indicated.
The theorem of Greenberg and Robinson for two-dimensional quantum field theories
Authors: Baumann Klaus
Published: July 2002

In two space-time dimensions there are quantum fields φ obeying ⧠φ=0, which nevertheless have nonvanishing higher truncated n-point functions. Such fields show up if one wants to adapt the theorem of Greenberg and Robinson to 1+1 space-time dimensions. Using the Jost–Lehmann–Dyson representation we show that if either (a) φ̃(p)=0 for spacelike momenta or (b) W̃φ+φ(p) decreases at least like exp(−p2), then the field φ is the sum of two local fields A and B, where A is a generalized free field and B satisfies ⧠B=0.
On the boson–quasifermion realization of the particle–hole SO(2Ω+1) algebra
Authors: Klein Abraham , Marshalek Eugene R.
Published: July 2002

The shell-model algebra SO(2Ω+1) generated by all bilinear and linear combinations of fermion creation and annihilation operators acting on a Fock space of Ω orbitals may be mapped into an ‘‘ideal space’’ in which particle–hole pairs are described by boson operators, while excess particles or holes are described by fermionlike degrees of freedom called ‘‘quasifermions.’’ After a review of the derivation of the nonunitary generalized Dyson realization, it is shown how this realization can be unitarized in a very simple way with the help of a recently developed technique that utilizes the Casimir invariants of a ‘‘core subalgebra.’’
Radial gauge in Poincaré gauge field theories
Authors: Modanese G. , Toller M.
Published: July 2002

The generalization of the Fock–Schwinger or ‘‘radial’’ gauge condition xiAi =0 to the gauge theories of the Poincaré group, which describe the gravitational field, is treated. It is shown that the choice of a radial gauge is equivalent to the use of normal coordinates and of tetrads parallel transported along autoparallel lines starting at the origin. The formulas that give the fields in the radial gauge starting from an arbitrary gauge and the formulas that give the gauge potentials in terms of the gauge field strengths are derived. The residual gauge freedom, which consists of the arbitrariness in the choice of the origin of the coordinate system and a tetrad of orthonormal vectors at this point is discussed in detail. It is the analog of the usual Poincaré invariance in flat space-time theories. The whole treatment can be extended to gauge theories of the affine and Euclidean groups. As an application, some properties of the homogeneous and isotropic states with random geometric fields are found.
On the Painlevé classification of partial differential equations
Authors: Hlavatý Ladislav
Published: July 2002

The classification of partial differential equations from the point of view of the singular point analysis is suggested. The general form of the equation for the Painlevé resonances is derived. The Painlevé-type classification of semilinear second-order polynomial partial differential equations in two independent variables is performed.
On continuity of mean values of unbounded observables
Authors: Rusinek Jan
Published: July 2002

An unbounded observable whose mean value at some state changes discontinuously under the action of a *-weakly continuous one-parameter symmetry group is exhibited. Also, a sufficient condition for differentiability of a mean value of a not necessarily bounded observable that evolves under the action of a *-weakly continuous one-parameter automorphism group is given.
On left invariant Brownian motions and heat kernels of nilpotent Lie groups
Authors: Albeverio Sergio , Arede Teresa , Haba Zbigniew
Published: July 2002

Left-invariant Brownian motions on nilpotent Lie groups are studied. Their characterization is given through Ito or Stratonovich stochastic differential equations, their generators are exhibited and the associated heat semigroups are studied. A reduction formula is given for these semigroups and their kernels, as integrals of products of normalized random Gaussian densities.
On bi-Hamiltonian structures
Authors: Frauendiener Jörg , Newman Ezra T.
Published: July 2002

The definition of a bi-Hamiltonian structure is reviewed, and it is shown that for systems of differential equations of the form ẋ=v(x) on even-dimensional manifolds, there always exists locally a bi-Hamiltonian structure. If this structure is ‘‘global,’’ then the system of equations is integrable. Furthermore, the geometry and canonical forms for such structures are discussed.
Electromagnetic and gravitational perturbation of type D space-times
Authors: Fayos F. , Ferrando J. J. , Jaén X.
Published: July 2002

A procedure to solve gauge and tetrad invariant conservation equations coupling electromagnetic and gravitational perturbations of Kerr and Kerr–Newman space-times is presented. This procedure has two steps. In the first place it must be proved that one can use the gauge and tetrad freedom to write the conservation equation as a source-free Maxwell-like equation, and second, the conservation equation has to be solved in this particular gauge.
Exactness of the supersymmetric JWKB quantization formula
Authors: Crescimanno M.
Published: July 2002

A modification of the Fröman and Fröman [JWKB Approximation: Contributions to the Theory (North-Holland, Amsterdam, 1965)] technique is developed in order to study the supersymmetric JWKB formula of Comtet et al. [Phys. Lett. B 150, 159 (1985)]. With this modification, in a direct and nonperturbative manner, it can be proven that this quantization condition is exact for a class of solvable models.
Completely solvable models of the nonlinear Boltzmann equation I. Case of three velocities
Authors: Osland Per , Wu Tai Tsun
Published: July 2002

In one space and one time dimension, a class of models of the nonlinear Boltzmann equation is presented that is exactly solvable for all initial conditions. The models have three velocity components and the following desirable properties: (a) conservation of the number of particles; (b) energy conservation; (c) nonlinearity; (d) positivity of distribution functions; and (e) unique equilibrium state (for any given density), which is approached as t→∞. These models are very rich in structure, and some of their simple properties are studied.
Solutions to higher Hamiltonians in the Toda hierarchies
Authors: Ferreira L. A. , Londe R. M.
Published: July 2002

A method is presented for constructing the general solution to higher Hamiltonians (nonquadratic in the momenta) of the Toda hierarchies of integrable models associated with a simple Lie group G. The method is representation independent and is based on a modified version of the Lax operator. It constitutes a generalization of the method used to construct the solutions of the Toda molecule models. The SL(3) and SL(4) cases are discussed in detail.
Completely positive conjugate-bilinear maps on partial *-algebras
Authors: Ekhaguere G. O. S. , Odiobala P. O.
Published: July 2002

The set of invariant completely positive conjugate-bilinear maps on an arbitrary unital partial ■-algebra is introduced and characterized. By considering a natural order structure on this set, all order intervals in it having the zero map as minorant are characterized and a certain extremal problem is solved. In particular, a Radon–Nikodym theorem for members of the set is deduced. Finally, an extension theorem for completely positive, but not necessarily invariant, conjugate-bilinear maps on unital partial ■-algebras is obtained.
On the monodromy group for the super Schwarzian differential equation
Authors: Uehara Shozo , Yasui Yukinori
Published: July 2002

The first variation of the monodromy group associated with a super Schwarzian differential equation is calculated. The relation between the monodromy period and the Fenchel–Nielsen deformation of a super Riemann surface is presented.
Skyrme-like and topological terms in sigma models
Authors: De Azcárraga J. A. , Rashid M. S. , Zakrzewski W. J.
Published: July 2002

The nature of the terms that can be added to the usual Lagrangian for sigma models is investigated. Some of the new expressions correspond to Skyrme-like terms while others are more topological in character. It is pointed out that for the CP1 case there is only one Skyrme-like term, while for CPN, N>1, more possibilities arise which all become the same if N=1. This suggests the existence of more general Skyrme-like models for N>1.
Properties of the Skyrme soliton configuration
Authors: Ananias Neto Jorge , Galain Ramón Méndez , Ferreira Erasmo
Published: July 2002

Properties of the Euler–Lagrange differential equation for cos F, where F is the chiral angle of the classical Skyrme soliton in the hedgehog ansatz, are investigated. The power series solution for y=cos F, is obtained that presents the behavior of an almost geometric series, and the existence of single poles located at imaginary values of the radial variable r is shown. Padé approximants are built to the series expansion about the origin, and its terms are modified in order to incorporate the main features of the asymptotic behavior of the field configuration. Thus rational fractions are constructed which provide very good and practical analytical representations of the Skyrme soliton profile function.
Effective Hamiltonian within the microscopic unitary nuclear model. II: The study of s
d nuclei with two valence particles
Authors: Avramenko V. I. , Blokhin A. L.
Published: July 2002

Within the microscopic version of the unitary collective model with horizontal mixing the effective Hamiltonian for 18O and 18Ne nuclei is constructed. The algebraic structure of the considered Hamiltonian corresponds to the familiar phenomenological ones with the SU(3)-mixing terms that describe the transitional spectra. The Hamiltonian, including both the central nuclear and Coulomb interactions, is diagonalized on the basis of three SU(3) irreducible representations with two orbital symmetries.
An alternative explicit construction of N-soliton solutions in 1+1 dimensions
Authors: Chau Ling-Lie , Shaw J. C. , Yen H. C.
Published: July 2002

Using the special Riemann-problem technique of Zakharov et al. [Sov. Phys. JETP 47, 1017 (1978)], an explicit N-step Bäcklund transformation is derived for a class of 1+1-dimensional nonlinear evolution equations, thus providing an alternative explicit expression of their N-soliton solutions which no longer involves computations of the intermediate solutions, nor leaves any expansion of N×N determinants (and their differentiation) to be done.
Classical mechanics of special relativity in a Riemannian space-time
Authors: Zerzion Daniel , Horwitz L. P. , Arshansky R. I.
Published: July 2002

It is shown that the two-body problem with action-at-a-distance interaction potential in the framework of a canonical manifestly covariant mechanics, for which there exists a consistent and well-developed quantum version, can be embedded in a Riemannian manifold (with conformal metric) where the curvature replaces the explicit appearance of the potential. The geodesic motion in the conformal space coincides with the solutions of the Hamilton equations of motion in the corresponding flat space problem. The reparametrization invariant form of the action principle which leads to the geodesic equation is shown to be equivalent to the underlying canonical mechanics with a particular choice of parameter. This program realizes the possibility of describing a class of nongravitational interactions in space-time by essentially geometrical means. A relation is proposed between the Einstein tensor in the conformal space and the (nonconserved) energy momentum tensor associated with relative motion, with the help of a Brans–Dicke type field. The structure of the result suggests a generalization of the principle of equivalence, for dealing, at least, with the two-body problem, which treats a manifold of relative space-time as the globally defined coordinates for which there exists, at every point, a local frame in which the metric is conformal (in the absence of nongravitational forces, this procedure reduces to the usual one). In this way, one can treat gravitational and a certain class of nongravitational forces in a unified way.
Generalized expression for the numbers of perfect matching of cylindrical m×n graphs
Authors: Narumi Hideyuki , Hosoya Haruo , Murakami Hiroshi
Published: July 2002

The analytical expression for the numbers of perfect matching for the cylindrical m×n lattice graphs was derived by diagonalizing the skew-symmetric matrix after Kasteleyn but with a little modification. The results are compared with the recursion relations obtained earlier by the present authors.
Effective Hamiltonian within the microscopic unitary nuclear model. I: Coherent-state restriction technique for microscopic Hamiltonian
Authors: Filippov G. F. , Blokhin A. L.
Published: July 2002

A technique of projecting the microscopic nuclear Hamiltonian on the SU(3) group enveloping algebra is developed. The proposed approach is based on the effective Hamiltonian restoring from the matrix elements between the coherent states of the SU(3) irreducible representations. The technique is displayed for almost magic nuclei within the mixed representation basis, and for arbitrary nuclei within the single representation.
Unitary lowest weight representations of the noncompact supergroup OSp(2m*/2n)
Authors: Günaydin M. , Scalise R. J.
Published: July 2002

The oscillator construction of the unitary lowest weight representations of the noncompact supergroup OSp(2m*/2n) with the even subgroup SO*(2m)×USp(2n) is given. Simple rules for determining the SO*(2m)×USp(2n) decomposition of the lowest weight representations of OSp(2m*/2n) are derived. The particular examples of OSp(4*/2) with the even subgroup SU(1,1)×SU(2)×SU(2) and OSp(4*/6) with the even subgroup SU(1,1)×SU(2)×Usp(6) are studied in greater detail.
Including spin in the Raychaudhuri equation
Authors: Fennelly A. J. , Krisch Jean P. , Ray John R. , Smalley Larry L.
Published: July 2002

The Raychaudhuri equation for a spin fluid matter content is developed. The equation is applied to the behavior of an irrotational, unaccelerated fluid. The development of singularities in the expansion is studied for constant spin densities.
The electromagnetic scattering problem in the time domain for a dissipative slab and a point source using invariant imbedding
Authors: He Sailing , Ström Staffan
Published: July 2002

A vertical magnetic dipole source above an inhomogeneous slab is considered where the permittivity ε=ε(z) and conductivity σ=σ(z) vary with the depth z. Using the axial symmetry of the problem, a Hankel transform is introduced. Besides physical scattering kernels, ‘‘nonphysical’’ scattering kernels are introduced and the direct and inverse transformed problem is solved by means of wave splitting in an invariant imbedding approach. The imbedding equations for the nonphysical scattering kernels are simpler than the corresponding equations for the physical kernels and they are solved using existing techniques for the imbedding equations for normally incident plane waves. The solution for the physical kernels is obtained by establishing relations between the two sets of kernels. These relations are given by Volterra equations of the second kind and thus are very easy to solve numerically. Some applications and extensions of the results derived in the paper are discussed.
On the action of the Pauli–Lubanski Casimir operator in a relativistic supersymmetric quantum field theory
Authors: Lopuszański Jan
Published: July 2002

The properties of the states Q(L1)1...Q(Ln)u( j,j), n≤N are investigated in a Lorentz rest frame; u(j,j) describes a massive one-particle state of a maximal spin value j and a maximal spin projection j in a given field theoretical model; Q(L)A, A=1,2 stands for the Lth spinor charge, L=1,...,N, and N is the number of spinor charges appearing in the model. In particular, the concentration of this paper is on exploring the behavior of the before-mentioned states under the action of the Pauli–Lubanski Casimir operator for the Poincaré group and a discussion of the results so obtained is given.
Bernstein processes and spin-1/2 particles
Authors: Djehiche Boualem
Published: July 2002

A pure jump Bernstein process whose probability density is the product of the solution of the (imaginary time) Schrödinger equation and its adjoint equation, associated to a class of time dependent Hamiltonians describing spin-1/2 particles, is constructed. A path integral representation of these solutions, in terms of this process, is obtained as well as a calculus over path space for the associated Euclidean quantum observables.
D-dimensional torus as compact manifold and Kaluza–Klein cosmological model
Authors: Srivastava S. K.
Published: July 2002

Singularity-free solutions of higher-dimensional Einstein field equations are obtained in the background of M4×TD manifold (M4 is a usual four-dimensional Friedmann– Robertson–Walker model and TD is a D-dimensional torus). Moreover, through dimensional reduction and one-loop quantum correction to scalar field, time-dependent cosmological constant Λ, effective gravitational constant Geff, and a fine-structure constant e/4π are derived in the effective four-dimensional theory using solutions of Einstein’s equations. It is found that at late times Λ≂0.
Stokes constants for a certain class of second-order ordinary differential equations
Authors: Zhu Chaoyuan , Nakamura Hiroki
Published: July 2002

By generalizing the coupled wave integral equations method devised by Hinton, the Stokes phenomena of the standard second-order ordinary differential equations with the following coefficient functions q(z) are analyzed: (i) q(z)=a2Nz2N+∑j=−∞N−1ajzj; (ii) q(z)=a2N−1z2N−1+∑j= −∞N−2ajz j; (iii) q(z)=∑j=04ajz j, with a3=0; and (iv) q(z)=∑j=03ajz j, with a2=0. First the relations are derived among the Stokes constants, which enable the expression of all Stokes constants in terms of only one. Furthermore, this one Stokes constant is shown to be expressed in the analytical form of a convergent infinite series as a function of the coefficients of q(z). This was done for all four cases listed above.
Modular invariance of the propagator of an extended particle
Authors: Finkelstein Robert J.
Published: July 2002

By generalizing from systems characterized by finite Lie algebras the propagator of an extended particle that appears in a gauge theory based on an affine algebra is discussed.
Algebraic structures of the quantum projective [sl(2,C)-invariant] field theory: Local projective field algebra DSCR [sl(2,C)]
Authors: Juriev D.
Published: July 2002

Based on the renormalized pointwise product version of the operator formalism, the new examples of the quantum projective [sl(2,C)-invariant] field theory, connected with the vertex operators of the discrete spectrum in the model of the Verma modules over the Lie algebra sl(2,C), are constructed.
On a variational principle for the Nambu dynamics
Authors: Fecko Marián
Published: July 2002

A variational principle for the Nambu dynamics is analyzed. Since the equations of motion single out a distinguished two-form rather then a one-form, the usual construction of the action S[γ] as an integral of a one-form along the curve γ on the extended phase space has to be modified.
Factorization of a dissipative wave equation and the Green functions technique for axially symmetric fields in a stratified slab
Authors: He Sailing
Published: July 2002

The time domain scattering problem for axially symmetric fields and a dissipative stratified slab is considered. Explicit representations are derived for the wave splitting operators that factorize the dissipative Hankel transformed wave equation. The Green functions approach associated with this splitting is developed. Partial differential equations (PDEs) for the Green functions are derived and used to derive the imbedding equations for the reflection and transmission kernels. Numerical results for the internal fields are given in the direct problem, and the phase velocity is reconstructed in the inverse problem.
Fractional statistics, Z
p spin system, and XY model
Authors: Goswami Gautam , Bandyopadhyay Pratul
Published: July 2002

The Zp spin system in two dimensions from the point of view of fractional statistics is studied herein. It is found that, for p≤4, the system represents a gas of particles having a specific fermion number when p=2 corresponds to fermion number 1 and p=3 and 4 corresponds to a fractional fermion number. However, for p≥5, the corresponding system does not represent particles having any specific statistics; rather, it represents a hedgehog behavior. The XY model represented by a Zp spin system at p→∞ limit corresponds to bosonic kinks composed of vortex–antivortex pairs below a certain temperature. The two massive phases observed in a Zp system for 2≤p≤4 is related to their intrinsic fermionic character, and the three phases observed for p≥5 when a massless phase occurs in between two massive phases is related to the hedgehog behavior of the corresponding particles so far as their statistics is concerned. The XY model corresponding to a Zp spin system at p→∞ represents massive bosonic kinks as bound states of vortex–antivortex pairs below a certain temperature when the spin waves are massless and, as the temperature goes up, the bound states dissociate and massless kinks and massive spin waves appear. The nonexistence of an ordered phase for a continuous symmetry model is related to the inherent bosonic character of the corresponding particles.
New reductions of the Kadomtsev–Petviashvili and two-dimensional Toda lattice hierarchies via symmetry constraints
Authors: Konopelchenko Boris , Strampp Walter
Published: July 2002

New types of reductions of the Kadomtsev–Petviashvili (KP) hierarchy and the two-dimensional Toda lattice (2DTL) hierarchy are considered on the basis of Sato’s approach. Within this approach these hierarchies are represented by infinite sets of equations for potentials u1,u2,u3,..., of pseudodifferential operators and their eigenfunctions ψ and adjoint eigenfunctions ψ*. The KP and the 2DTL hierarchies are studied under constraints of the following type: ∑n=1N αnSn(u1,u2,u3,...)=Ωx, where Sn are symmetries for these hierarchies, αn are arbitrary constants, and Ω is an arbitrary linear functional of the quantity ψ(λ)ψ*(μ). It is shown that for the KP hierarchy these constraints give rise to hierarchies of 1+1-dimensional commuting flows for the variables u2,u3,...,uN,ψ,ψ*. Many known systems and several new ones are among them. Symmetry reductions for the 2DTL hierarchy give rise both to finite-dimensional dynamical systems and 1+1-dimensional discrete systems. Some few results for the modified KP hierarchy are also presented.
On symmetries of radially symmetric nonlinear diffusion equations
Authors: Sophocleous Christodoulos
Published: July 2002

In this paper symmetries are sought for radially symmetric nonlinear diffusion equations of the type ut=r1−N[rN−1f(u)ur]r. The nonlinear forms of this equation which admit Lie classical symmetries are completely classified and are shown to exist when f=un, eu. Also, a trivial symmetry exists for arbitrary f. Lie–Bäcklund symmetries are also considered when f=un and shown to exist when n=0 (linear case) and when n=−2 and N=1.
Bi-Hamiltonian systems and Maslov indices
Authors: Scherer W.
Published: July 2002

It is shown that any Lagrangian distribution on a 2n-dimensional symplectic manifold Γ is equivalent to a principal O(n) bundle obtained as a reduction of the frame bundle. Bisymplectic manifolds with Nijenhuis recursion operators are studied and it is shown that the set of all bi-Lagrangian distributions is a trivial bundle the structure group being the homogeneous space U(1)n/O(1)n. Various formulas for Maslov indices of closed curves are given including one using only data from the recursion operator.
The Fermi and Bose congruences for free semigroups on two generators
Authors: Parks A. D.
Published: July 2002

Using a free semigroup and a free monoid generated by two symbols, two congruences are introduced. These congruences provide natural equivalence classifications of all finite composite creation and annihilation operators for fermions and bosons such that equivalent operators act identically (to within a nonnegative integer multiple) upon the associated basis states. The resulting quotient structures are shown to be isomorphic to two elementary inverse semigroups and their algebras are used to construct generalized commutation forms. These provide for the easy evaluation of any fermion anticommutator and any reduced word boson commutator.
Addendum to a dynamical formalism of singular Lagrangian system with higher derivatives
Authors: Saito Yoshihiko , Sugano Reiji , Ohta Tadayuki , Kimura Toshiei
Published: July 2002

A formulation for singular Lagrangians with higher derivatives in a previous paper is supplemented and a complete formulation of canonical theory for the systems is presented. It is shown that our previous formulation reproduces all constraints included in the Ostrogradski transformations, by using stationarity conditions of primary constraints. Secondarily, on the effect of adding a total time derivative term to a nonsingular Lagrangian with higher derivatives, the previous paper is revised so as to give a correct formulation for counting the numbers of first and second class constraints. It is concluded that the main part of our previous formulation needs no essential change.
Study of quommutators of quantum variables and generalized derivatives
Authors: Fairlie David , Nuyts Jean
Published: July 2002

A general deformation of the Heisenberg algebra is introduced with two deformed operators instead of just one. This is generalized to many variables, and permits the simultaneous existence of coherent states, and the transposition of creation operators.
Tensor products of representations of C(SUq(2))
Authors: Lesniewski Andrzej , Rinaldi Maurizio
Published: July 2002

The tensor products of the irreducible representations of the algebra of continuous functions on the quantum group SUq(2) were studied. Using the methods of q-calculus it was proven that the tensor product of two infinite dimensional irreducible representations may be decomposed into a direct integral of irreducible representations.
Two parameter deformation of Virasoro algebra
Authors: Chung Won-Sang
Published: July 2002

In this paper the two parameter deformation of Virasoro algebra is derived. Two parameter deformation of central charge is also obtained. The operator product expansion for (p,q)-deformed Virasoro algebra is derived.
The (N,M)th Korteweg–de Vries hierarchy and the associated W-algebra
Authors: Bonora L. , Xiong C. S.
Published: July 2002

A differential integrable hierarchy, which is called the (N,M)th Korteweg–de Vries (KdV) hierarchy, whose Lax operator is obtained by properly adding M pseudo- differential terms to the Lax operator of the Nth KdV hierarchy is discussed herein. This new hierarchy contains both the higher KdV hierarchy and multifield representation of the Kadomtsev–Petviashvili (KP) hierarchy as subsystems and naturally appears in multimatrix models. The N+2M−1 coordinates or fields of this hierarchy satisfy two algebras of compatible Poisson brackets which are local and polynomial. Each Poisson structure generates an extended W1+∞- and W∞-algebras, respectively. W(N,M) is called the generating algebra of the extended W∞-algebra. This algebra, which corresponds with the second Poisson structure, shares many features of the usual WN-algebra. It is shown that there exist M distinct reductions of the (N,M)th KdV hierarchy, which are obtained by imposing suitable second class constraints. The most drastic reduction corresponds to the (N+M)th KdV hierarchy. Correspondingly the W(N,M)-algebra is reduced to the WN+M-algebra. The dispersionless limit of this hierarchy and the relevant reductions are studied in detail.
The patchwork divergence theorem
Authors: Dray Tevian , Hellaby Charles
Published: July 2002

The divergence theorem in its usual form applies only to suitably smooth vector fields. For vector fields which are merely piecewise smooth, as is natural at a boundary between regions with different physical properties, one must patch together the divergence theorem applied separately in each region. We give an elegant derivation of the resulting patchwork divergence theorem which is independent of the metric signature in either region, and which is thus valid if the signature changes.
Compact homogeneous universes
Authors: Koike Tatsuhiko , Tanimoto Masayuki , Hosoya Akio
Published: July 2002

A thorough classification of the topologies of compact homogeneous universes is given except for the hyperbolic spaces, and their global degrees of freedom are completely worked out. To obtain compact universes, spatial points are identified by discrete subgroups of the isometry group of the generalized Thurston geometries, which are related to the Bianchi and the Kantowski–Sachs–Nariai universes. Corresponding to this procedure their total degrees of freedom are shown to be categorized into those of the universal covering space and the Teichmüller parameters. The former are given by constructing homogeneous metrics on a simply connected manifold. The Teichmüller spaces are also given by explicitly constructing expressions for the discrete subgroups of the isometry group.
Harmonic analysis on tube-type affine homogeneous phase spaces
Authors: Fan Qihong
Published: July 2002

In this paper, the coherent states and the POV measures on tube-type affine homogeneous phase spaces are studied. The results extend the continuous wavelet analysis of the affine group ′ax+b′ and the phase space analysis of the Galilei and Poincaré groups to the general affine groups.
Boson–fermion correspondence for Hall–Littlewood polynomials
Authors: Jing Naihuan
Published: July 2002

The boson–fermion correspondence is given for the case of the Hall–Littlewood polynomials, which is a t-deformation of the correspondence realizing the Schur polynomials.
Statistical mechanics of the deformable droplets on flat surfaces
Authors: Kholodenko Arkady L.
Published: July 2002

A comprehensive statistical mechanics treatment of (non)interacting deformable planar droplets of arbitrary rigidity is developed. Closed form exact analytic results are obtained for the area statistics of a single droplet and for the decay rates of metastable states characteristic of the first-order phase transitions for an assembly of such droplets. To select the correct form of the interaction between the droplets, the reparametrization invariance is taken into account. Most of the known two-dimensional lattice models are obtained as the limiting cases of the interacting droplet model discussed in the text.
The absolute rigidity of the Neveu–Schwarz and Ramond superalgebras
Authors: van den Hijligenberg N. W. , Kotchetkov Yu. Yu.
Published: July 2002

We prove that the second cohomology group with coefficients in the adjoint module of both the infinite-dimensional Lie superalgebras k(1) and k+(1), as well as their unique central extensions, which are known as the Neveu–Schwarz and the Ramond superalgebras, respectively, is equal to zero. This particularly implies that all these Lie superalgebras are rigid, i.e. they can only be deformed in a trivial manner.
On the consistent effect histories approach to quantum mechanics
Authors: Rudolph Oliver
Published: July 2002

A formulation of the consistent histories approach to quantum mechanics in terms of generalized observables (POV measures) and effect operators is provided. The usual notion of ‘‘history’’ is generalized to the notion of ‘‘effect history.’’ The space of effect histories carries the structure of a D-poset. Recent results of J. D. Maitland Wright imply that every decoherence functional defined for ordinary histories can be uniquely extended to a bi-additive decoherence functional on the space of effect histories. Omnès’ logical interpretation is generalized to the present context. The result of this work considerably generalizes and simplifies the earlier formulation of the consistent effect histories approach to quantum mechanics communicated in a previous work of this author.
Exact results on a Dirac-like Lee model
Authors: Wang Y. , Pu Fu-Cho
Published: July 2002

A one-dimensional massive Lee model is studied via the Bethe ansatz method. The exact engenstates and the energy spectrum are obtained. The general picture of the excitations is discussed.
Criteria for inverted temperatures in evaporation–condensation processes
Authors: Cornille H. , d’Almeida A.
Published: July 2002

A recent criterion for shock waves which predicts the behaviors of the internal energy across the shock is extended to a vapor between two interfaces. We look at the predictions of monotonic or not behavior and at the possible inversion of the internal energy inside the gas. We consider different discrete Boltzmann models, construct new classes of exact solutions (models with a rest particle and models leading to 3×3 Riccati systems), and verify the criteria predictions.
Integration of the Einstein–Dirac equations
Authors: Bagrov V. G. , Obukhov V. V. , Sakhapov A. G.
Published: July 2002

The problem of exact integration of the Einstein–Dirac equation is studied. To solve this set of equations metrics admitting complete separation of variables in the Dirac equation are considered. At the first stage Stäckel spaces of types (3.1) and (3.0) are studied. For the first case obtained solutions contain arbitrary functions depending on one variable only (five real functions for the Einstein–Weyl equations and four real functions for the Einstein–Dirac ones). For the second one all solutions belonging to the diagonal metrics of Bianchi type 1 are found.
Fock space representation of differential calculus on the noncommutative quantum space
Authors: Mishra A. K. , Rajasekaran G.
Published: July 2002

A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of the new algebra for the statistics of quanta are analyzed and discussed. The concept of statistical transmutation between bosons and fermions is introduced.
Nonlinear dynamical systems and classical orthogonal polynomials
Authors: Kowalski K.
Published: July 2002

It is demonstrated that nonlinear dynamical systems with analytic nonlinearities can be brought down to the abstract Schrödinger equation in Hilbert space with boson Hamiltonian. The Fourier coefficients of the expansion of solutions to the Schrödinger equation in the particular occupation number representation are expressed by means of the classical orthogonal polynomials. The introduced formalism amounts to a generalization of the classical methods for linearization of nonlinear differential equations such as the Carleman embedding technique and Koopman approach.
The doublet representation of non-Hilbert eigenstates of the Hamiltonian. II
Authors: Castagnino M. , Domenech G. , Levinas M. , Umérez N.
Published: July 2002

Applying the doublet representation we analyze the solutions of a Hamiltonian system which has eigenstates with complex eigenvalues. The example of the Friedrichs model allows us to show how the appearance of solutions with non-Hilbert initial conditions is linked to the energy degeneration of the Hamiltonian spectrum. We discuss the difficulties of giving a physical meaning to the growing or decaying non-Hilbert solutions. We also suggest a way to circumvent the problem of the anomalous probabilities related to both complex energy eigenvalues and degeneration of the spectrum.
Advection–diffusion around a curved obstacle
Authors: Ahluwalia Daljit S. , Keller Joseph B. , Knessl Charles
Published: July 2002

Advection and diffusion of a substance around a curved obstacle is analyzed when the advection velocity is large compared to the diffusion velocity, i.e., when the Peclet number is large. Asymptotic expressions for the concentration are obtained by the use of boundary layer theory, matched asymptotic expansions, etc. The results supplement and extend previous ones for straight obstacles. They apply to electrophoresis, the flow of ground water, chromatography, sedimentation, etc.
N
-extended superelliptic integrable systems
Authors: Felipe Raúl , Ongay Fausto
Published: July 2002

A supersymmetric extension for an arbitrary number of odd parameters of the stationary KdV equation is studied; we call this an N-extended super KdV. It is shown that it is related to superelliptic curves, and thereafter the complete ring of superdifferential operators commuting with the associated Schrödinger operator is constructed.