bluuebunny/crossref_metadata_2025 huggingface dataset:
Maximum-entropy calculation of energy distributions
Authors: Poland Douglas
Published: July 2002

We use the maximum-entropy method to calculate molecular energy distributions from the moments of the distribution which in turn can be obtained from the temperature dependence of the heat capacity. If one knows the temperature expansion of the heat capacity through the nth power of the temperature, this then gives the exact first (n+2) energy moments. We illustrate the method for the ideal gas (the Maxwell–Boltzmann distribution of kinetic energy) and then use a model function to show that if one knows four or more moments of the energy distribution this allows one to resolve two or more distinct peaks in this function. We examine argon above the critical pressure, a one-dimensional model, and the protein barnase, all of which exhibit bimodal energy distributions.
Energetics of small n-pentanol clusters from droplet nucleation rate data
Authors: Knott Michael , Vehkamäki Hanna , Ford Ian J.
Published: July 2002

We use nucleation theorems to extract the excess internal energy of small molecular clusters of n-pentanol from experimental droplet nucleation rates. Corrections to the theorems are derived, in order to take into account the nonideality of the vapor phase, but these have only a small effect on our results. Experimental datasets from different groups provide information about clusters of different sizes at a range of temperatures. The analysis shows that there are significant and intriguing deviations from the predictions of the capillarity approximation.
1,2-propanediol and 1,3-propanediol homogeneous nucleation rates and phase transitions in the new phase critical embryos
Authors: Anisimov M. P. , Koropchak J. A. , Nasibulin A. G. , Timoshina L. V.
Published: July 2002

Nucleation rates of supersaturated vapors near the conditions for the critical line for each pair of 1,2- or 1,3-propanediol and carbon dioxide or sulfur hexafluoride at total system pressures of P=0.10, 0.20, and 0.30 MPa have been measured in a flow diffusion chamber. Critical parameters, i.e., temperatures and pressures, of the binary systems versus compositions were semiempirically evaluated. It was found experimentally that there is an area of parameters in the PTx phase diagram, for each pair of vapor and carrier gas investigated in the present research, for which critical embryo phase transitions of the first order take place (where P, T, and x are pressure, temperature, and embryo composition, respectively). The nucleation rate surface singularity and a gap in the number of molecules in critical embryos reflect this area. Shifts of the phase transition temperatures can be initiated by increasing the pressure (or concentration) of the carrier gas. This behavior is peculiar for binary systems. It is well-known that no liquid–liquid phase transitions can exist for a one-component system. At least a binary solution is required for liquid–liquid phase transitions. This means that vapor nucleation of the investigated substances in the carrier gas atmosphere can be considered as nucleation of a binary vapor–gas system. A schematic diagram for the possible metastable vapor conditions is presented. On the basis of our experimental results, one can assume that there exists a surface describing the parameters related with a phase transition of the first order in critical embryos. This surface is located within the volume of the possible vapor metastable conditions.
Surface vibrations of large water clusters by helium atom scattering
Authors: Brudermann Jesko , Lohbrandt Petra , Buck Udo , Buch Victoria
Published: July 2002

The low energy intermolecular vibrational modes of water clusters have been measured by high resolution inelastic helium atom scattering. The water clusters are generated in adiabatic expansions through conical nozzles at the mean sizes n̄=22, 80, and 194. By accompanying semiclassical and classical calculations for n=90 the excited mode near 5.1 meV has been identified as O⋅⋅O⋅⋅O bending motion between adjacent hydrogen bonds, involving 3-coordinated water molecules on the amorphous cluster surface. The energy of this mode increases slightly from 4.3 to 5.5 meV with increasing cluster size from n̄=22 to 194 and approaches the results for the dispersionless surface phonons of ice. The cluster temperature determined from the deexcitation is between 69 and 101 K.
Effective interaction between soft core colloidal particles
Authors: Amokrane S. , Bouaskarne M.
Published: July 2002

The effect of the softness of the repulsive part of the direct solute–solute interaction on the effective interaction in highly asymmetric solute/solvent mixtures is discussed. Its incorporation in the computation of the effective interaction is found necessary for obtaining second virial coefficients compatible with those observed in real suspensions.
On the correlation between photoelectron energy and bending excitation in molecular photoionization
Authors: Miller J. Scott , Poliakoff E. D.
Published: July 2002

We report on excitation of the bending vibration following 3σu−1 photoionization of CO2. Dispersed fluorescence is used to determine the v+=(0,1,0)/v+=(0,0,0) ratio over the range 18⩽hνexc⩽190 eV. The results demonstrate that the bending excitation varies over this wide range, and is influenced by the photoelectron.
Direct vibrational self-consistent field method: Applications to H2O and H2CO
Authors: Yagi Kiyoshi , Taketsugu Tetsuya , Hirao Kimihiko , Gordon Mark S.
Published: July 2002

The vibrational self-consistent field (VSCF) and virtual configuration interaction (VCI) methods are directly combined with ab initio electronic structure calculations for evaluations of the potential energy at VSCF quadrature points. Referred to as direct VSCF and direct VCI, respectively, these methods have been applied to evaluations of anharmonic vibrational energy levels of H2O and H2CO at the second-order Mo/ller–Plesset MP2/aug-cc-pVTZ and MP2/cc-pVTZ computational levels, respectively. The purpose of the present study is to develop a direct methodology for vibrational state calculations by examining the accuracy of the results, as well as their computational costs. In addition, the accuracy and applicability of two approximate potential energy surfaces (PES), a quartic force field (QFF), and the PES determined by the modified-Shepard interpolation method (Int-PES), are investigated via comparisons of calculated energy levels of vibrational states with those derived by the direct methods. The results are analyzed in terms of three considerations: (i) truncations of higher-order intercoordinate couplings in the PES; (ii) mode–mode coupling effects; (iii) approximations in ab initio electronic structure methods. In the direct VCI calculations, the average absolute deviations in fundamental frequencies relative to the experimental values are 9.3 cm−1(H2O) and 34.7 cm−1(H2CO). The corresponding values evaluated with approximate PESs relative to those derived by the direct method are 35.0 cm−1 (QFF) and 15.3 cm−1 (Int-PES) for H2O, and 6.3 cm−1 (QFF) and 10.3 cm−1 (Int-PES) for H2CO.
Solution of the associative mean spherical approximation for a multicomponent dimerizing hard-sphere multi-Yukawa fluid
Authors: Kalyuzhnyi Yu. V. , Blum L. , Reščič J. , Stell G.
Published: July 2002

The analytical solution of the associative mean spherical approximation (AMSA) for a Yukawa dimerizing multicomponent hard-sphere fluid is derived. The general multi-Yukawa case is discussed. The simpler one-Yukawa case with factorizable coefficients is explicitly solved. As in the previously discussed electrolyte case the solution of the AMSA reduces to the solution of only one nonlinear algebraic equation for the scaling parameter ΓB. The analytical results for the AMSA closure is illustrated by numerical examples and computer simulation for the one-component one-Yukawa dimerizing fluid. Good agreement between theoretical and computer simulation results was found for both the thermodynamic properties and the structure of the system.
Remarks about the nilpotent symmetries of quantum gauge field theories
Authors: Kaempffer F. A.
Published: July 2002

A conjugation symmetric representation of Becchi–Rouet–Stora (BRS) and anti-BRS operations is presented which differs from the usual versions by terms cubic in the ghost fields. Some consequences of requiring quantum gauge field theories to be invariant under both BRS and anti-BRS transformations are examined.
Finite hard rod systems and their thermodynamic limit. III. Collision frequency, no-collision probability, and velocity autocorrelation function
Authors: Kasperkovitz P. , Reisenberger J.
Published: July 2002

We use the methods developed for the one-dimensional hard rod gas in the preceding papers to derive exact expressions for the average number of collisions per unit time, the probability that a tagged particle does not collide with other ones within a given time interval, and the velocity autocorrelation function. It is discussed how these expectation values, obtained for finite systems and three kinds of ensembles (smallest stationary, microcanonical, and canonical), behave as the size of the system increases (thermodynamic limit).
Hopf bifurcation in Yang–Mills mechanics
Authors: Kursawe Ulrich , Malec Edward
Published: July 2002

The periodic non-Abelian space-independent solutions to Yang–Mills SU(2) equations are studied. Hopf bifurcation is shown to appear. New analytic solutions generating a simple Abelian source are found and their stability is discussed. The source can be produced by a fermion field; a self-consistent solution of Yang–Mills–Dirac equations is presented.
On the axial gauge: Ward identities and the separation of infrared and ultraviolet singularities by analytic regularization
Authors: Lee Hoong-Chien , Milgram Michael S.
Published: July 2002

It is shown that the method of analytically regulating Yang–Mills theories in the axial gauge preserves gauge invariance. Two- and three-point Ward identities are computed and verified at the one-loop level. The method also permits a convenient and gauge-invariant separation of infrared and ultraviolet singularities in the axial gauge. In the axial gauge the renormalization constants Z3=Z1=1+11g2C2/(48πε2), leading to a β function which is identical to that computed in the covariant ξ gauges.
A projection-based solution to the SP(2N) state labeling problem
Authors: Gould M. D. , Kalnins E. G.
Published: July 2002

A projection-based solution to the symplectic group state labeling problem is presented. The approach yields a nonorthogonal Gel’fand–Tsetlin basis for the irreducible representations of Sp(2n). A method for evaluating the corresponding overlap coefficients is discussed. The action of the Sp(2n) generators, in the basis obtained, is determined and some matrix element formulas are derived. The results obtained are comparable to the matrix element formulas for O(n) and U(n).
Conformal transformations and viscous fluids in general relativity
Authors: Carot J. , Mas Ll.
Published: July 2002

It is shown that viscous fluid solutions can be obtained by performing conformal transformations of vacuum solutions of Einstein’s field equations. The solutions obtained by such a procedure can be matched, under certain conditions, to their respective original vacuum metrics.
Systematics of strongly self-dominant higher-order differential equations based on the Painlevé analysis of their singularities
Authors: King R. B.
Published: July 2002

This paper presents a simple way of classifying higher-order differential equations based on the requirements of the Painlevé property, i.e., the presence of no movable critical points. The fundamental building blocks for such equations may be generated by strongly self-dominant differential equations of the type (∂/∂x)nu =(∂/∂xm)[u(m−n+p)/p] in which m and n are positive integers and p is a negative integer. Such differential equations having both a constant degree d and a constant value of the difference n−m form a Painlevé chain; however, only three of the many possible Painlevé chains can have the Painlevé property. Among the three Painlevé chains that can have the Painlevé property, one contains the Burgers’ equation; another contains the dominant terms of the first Painlevé transcendent, the isospectral Korteweg–de Vries equation, and the isospectral Boussinesq equation; and the third contains the dominant terms of the second Painlevé transcendent and the isospectral modified (cubic) Korteweg–de Vries equation. Differential equations of the same order and having the same value of the quotient (n−m)/(d−1) can be mixed to generate a new hybrid differential equation. In such cases a hybrid can have the Painlevé property even if only one of its components has the Painlevé property. Such hybridization processes can be used to generate the various fifth-order evolution equations of interest, namely the Caudrey–Dodd–Gibbon, Kuperschmidt, and Morris equations.
Time-dependent invariants and quantum mechanics in two dimensions
Authors: Dhara A. K. , Lawande S. V.
Published: July 2002

A class of time-dependent problems in two space dimensions possessing time-dependent invariants, bilinear in momenta, is considered. Explicit expression of the potentials and the corresponding invariants are derived. Quantum mechanics is introduced in these time-dependent problems directly through a Feynman propagator defined as a path integral involving the classical action. The propagators are shown to admit expansions in terms of the eigenfunctions of the corresponding invariant operators. Equivalence of the present theory to that of Lewis and Riesenfeld [H. R. Lewis, Jr. and W. B. Riesenfeld, J. Math. Phys. 10, 1458 (1969)] is discussed.
On the generalized Gibbs formula and the thermodynamic solution of the Boltzmann equation
Authors: Chen M.
Published: July 2002

The purpose of this paper is to examine the relationship between the entropy balance equation, the Gibbs formula, and the Boltzmann equation. Consider a system of a mixture of gases contained in an arbitrary region Ω with volume V, where no chemical reactions take place. Let fi be the one-particle distribution function of species i. First, suppose there exist some fi, such that the entropy density ρS, the entropy flux Js, the entropy production σ, and the Boltzmann H-function, H(t), satisfy, respectively, the entropy balance equation and the Boltzmann H-equation under appropriate boundary conditions on the surface ∂Ω of Ω. Then fi can be shown to satisfy the Boltzmann equation. Under the functional hypothesis, where fi depends on time t and the spatial coordinates r only in terms of the thermodynamic variables—particle density of species i, ρi, hydrodynamic velocity v, energy density E, stress tensor π̄i, heat flux Q′i, and mass flux Ji, and possibly the spatial derivatives of { ρi, v, E, π̄i, Qi, Ji}, the entropy balance equation together with the semipositive definiteness of the entropy production, σ≥0, then provides an alternative method of solving the Boltzmann equation. The thermodynamic variables, in turn, are governed by their corresponding evolution equations with appropriate boundary conditions.

Second, to the linear order of the spatial gradients of the temperature T, the hydrodynamic velocity v, and the ratio of the particle number ni /n, the entropy balance equation then yields a generalized Gibbs formula and a nonlinear solution of fi in terms of the thermodynamic variables, such that σ≥0. The generalized Gibbs formula is an exact one-form of the thermodynamic variables that contains the equilibrium Gibbs formula. Furthermore, if fi is linearized, it is identical to the expression given by Grad’s 13-moment method. Finally, we consider the stability problem of the evolution equations for π̄i, Q′i, and Ji.
A unified treatment of SU(N) inner and outer multiplicities
Authors: Schmidt Jeffrey R.
Published: July 2002

A combinatorial approach is developed for calculation of weight multiplicities at or near the center of a weight diagram. The result may be used to determine the inner multiplicity of such a weight, or to decompose the product of several representations into irreducible summands.
Remarks on the Yang–Mills equations in four dimensions: CP2
Authors: Nash C.
Published: July 2002

This paper examines properties of solutions to the Yang–Mills equations in four dimensions and in particular on the manifold CP2: Two solutions are found: one is neither self-dual nor anti-self-dual but is a solution of the full Yang–Mills equations, the other is a self-dual solution.
Uniqueness of the metric from the Weyl and energy-momentum tensors
Authors: Hall G. S. , Rendall A. D.
Published: July 2002

It is shown that for a general space-time in Einstein’s theory (with the term ‘‘general’’ being precisely defined) the Weyl tensor and energy-momentum tensor determine the metric up to a constant conformal factor. One of the conclusions may be interpreted as a generalization of the well-known Brinkmann theorem characterizing pp waves in vacuo.
Rational functions of momentum as invariants for one-dimensional, time-dependent potentials: Basic theory
Authors: Goedert João , Lewis H. Ralph
Published: July 2002

A framework for the momentum-resonance formulation of Lewis and Leach [Ann. Phys. (NY) 164, 47 (1985)] that casts new light into the nature of exact, explicitly time-dependent invariants for one-dimensional, time-dependent potentials and produces additional examples of such invariants is presented. The momentum-resonance formulation postulates that the invariant be a rational function of momentum with simple poles, which are called momentum resonances. It is shown that an invariant of resonance type can be written as a functional of the potential in terms of the solution of a system of linear algebraic equations; and a single necessary and sufficient condition for a potential to admit an invariant of resonance type is obtained. These results are obtained by reformulating the problem in terms of a set of discrete moments that satisfy two separate recursion formulas. Invariants for new time-dependent potentials can be obtained and previously known invariants are recovered.
Representations of N=2 extended supergravity and unitarity conditions in Osp (N,4)
Authors: Van der Jeugt Joris
Published: July 2002

The structure of unitary irreducible representations of the Lie superalgebra Osp (2,4), the algebra of N=2 extended supergravity, is investigated in detail. In particular, four new classes of shortened multiplets are found, and the complete unitarity conditions are given. The shortened multiplets are shown to correspond to atypical infinite-dimensional representations. Finally, unitarity conditions for Osp(N,4), 3≤N≤8, are constructed.
Comment on a paper by Alain J. Phares and Francis J. Wunderlich [J. Math. Phys. 2
6, 2491 (1985)]
Authors: Wheeler John C.
Published: July 2002

The claim of Phares and Wunderlich [J. Math. Phys. 26, 2491 (1985)] to have obtained the exact closed form analytic solution to the problem of dimers on infinite two- and three-dimensional lattices is shown to be incorrect. Their expressions do not agree with exact expansions obtained by virial and lattice counting methods.
The sum rule for spectroscopic factors in the seniority scheme of identical particles
Authors: Nomura Masao
Published: July 2002

Spectroscopic factors partitioning an identical-particle state into a couple of substates with definite seniorities are summed into a simple form. This sum rule is an extension of the reduction relation for the fixed-seniority average of a many-body operator. The seniority projection operator is utilized throughout the present formulation
Asymptotically flat space-times have no conformal Killing fields
Authors: Garfinkle David
Published: July 2002

It is shown that asymptotically flat space-times with certain properties do not admit conformal Killing fields which are not Killing fields. The space-times must be vacuum, asymptotically Minkowskian, and have positive Bondi energy.
The Φ4 equations of motion. I. A new constructive method: The Φ iteration
Authors: Manolessou Marietta M.
Published: July 2002

A new method for the construction of a nontrivial Φ44 model consistent with the general principles of a Wightman quantum field theory is proposed. The renormalized equations of motion for the connected Green’s functions in the Euclidean momentum space are considered. Using a fixed-point method in an appropriate Banach space, the existence of a unique nontrivial solution of these equations is proved when the coupling constant Λ is fixed positive and smaller than a finite value. As a first step that avoids the difficulties of the renormalization operation, the corresponding problem in two dimensions is solved first. Also, in order to deal with all technical complexities that stem from the purely combinatorial nature of the equations, the corresponding zero-dimensional problem was studied previously. In all cases, it has been proved that the nontrivial solution exists inside particular subsets of the corresponding Banach space, characterized by the alternating signs and the factorization (or ‘‘splitting’’) properties of the Green’s functions at zero external momenta. These properties first appeared ‘‘experimentally’’ by the iteration of the two-dimensional system of equations called ‘‘Φ iteration’’ in the paper, and have been crucial for the conservation of the norms and for the contractivity of the nonlinear mappings.
Exact scalar and spinor solutions in some rotating universes
Authors: Krori K. D. , Borgohain P. , Kar P. K. , Das (Kar) Dipali
Published: July 2002

In this paper exact solutions of the Klein–Gordon and Weyl equations in some rotating universes are presented.
Representation theory of superconformal quantum mechanics
Authors: Bohm A. , Kmiecik M. , Boya L. J.
Published: July 2002

The analogy between the representations of SU(1,1/1) and SU(2,2/1) is explained and used to suggest the latter as a spectrum supergroup of superconformal relativistic quantum mechanics for systems with rotational degrees of freedom.
Nonstatic charged spheres admitting a conformal Killing vector
Authors: Rago H.
Published: July 2002

Exact, nonstatic, spherically symmetric solutions of the Einstein–Maxwell equations are found for self-gravitating charged spheres under the assumption of the existence of a conformal Killing vector. Solutions are matched to the Reissner–Nordstrom metric and it is found that as a consequence of the junction conditions, the material must be anisotropic. The radius of the sphere for static distributions corresponds to the radius of the unstable null circular orbit of the Reissner–Nordstrom geometry.
On chains of orthosymplectic Lie superalgebras and the n-dimensional quantum harmonic oscillator
Authors: Beckers J. , Cornwell J. F.
Published: July 2002

Triplets of embedded orthosymplectic Lie superalgebras are singled out and analyzed in terms of their respective even and odd root systems. The corresponding chains of embeddings are considered for arbitrary integers m and n (for both m≠n and m=n). It is shown that the second member inside each triplet is always in a one-to-one correspondence with the semidirect sum of the third member and the associated Heisenberg superalgebra that is characterized by the same entries m and n. For arbitrary m=n, invariance superalgebras of the n-dimensional harmonic oscillator are recovered and their one-to-one correspondence associated with a recent ‘‘character reversal’’ phenomenon linking these invariance superstructures is rigorously explained. Specific and general cases as well as conclusions are presented.
The asymptotic behavior of nonlinear waves near a cosmological Cauchy horizon
Authors: Moncrief Vincent
Published: July 2002

The asymptotic behavior of solutions of the nonlinear wave equation (with cubic nonlinearity) is studied on background vacuum space-times containing compact Cauchy horizons at the boundaries of their maximal Cauchy developments. The analytic form of the general solution of the linearized equations and that of the nth-order perturbation equations for arbitrarily large n are derived. It is shown how to sum the leading-order terms of the full perturbation series to derive what is presumably the asymptotic form of the general solution of the original nonlinear wave equation near the Cauchy horizon of the background space-time. It is also shown how the indicated asymptotic behavior leads to a natural classification of solutions in terms of ‘‘Lagrangian submanifolds’’ of an associated phase space.
An infinite number of hidden variables in hyper-Kähler metrics
Authors: Takasaki K.
Published: July 2002

Three types of hidden variables, both independent and dependent, are shown to underlie the hyper-Kähler geometry in a complexified setting. The variables satisfy an infinite set of differential equations (‘‘hierarchy’’), just as in the case of most nonlinear integrable systems. The notion of the Plebanski key functions [J. Math. Phys. 16, 2395 (1975)] is extended to this hierarchy to give an analog of the notion of the ‘‘τ function.’’ Two examples of special solutions, which are reminiscent of several solution techniques in the theory of nonlinear integrable systems, are presented for illustration.
A new unitary operator for a pair of coupled oscillators
Authors: Fan Hong-yi
Published: July 2002

Using the IWOP (integration within ordered product) technique, a new unitary operator is found that is useful in diagonizing the Hamiltonian of a pair of coupled harmonic oscillators. The coordinate representation of the unitary operator is presented, and is well applied to obtain the wave function of energy eigenstate of the coupled oscillator.
Explicitly time-dependent constants/symmetries of the higher-order KP equations
Authors: Case K. M. , Monge A.
Published: July 2002

For higher-order Kadomtsev–Petviashvili (KP) equations, the existence of explicitly time-dependent constants of motion is discussed. Generalizing the results for the ordinary KP equation, constants T(m)n,l polynomial in t are constructed for each lth order KP equation, for all n≥m (l−1)−1.
Viscous fluid spheres in general relativity
Authors: Banerjee A. , Dutta Choudhury S. B.
Published: July 2002

The spherically symmetric distribution of a dissipative fluid with nonvanishing bulk as well as shear viscosity is discussed. The cosmological constant is included in the field equations for more generality. The junction conditions are applied at the boundary of the sphere to match with the exterior Schwarzschild metric to yield the condition T11=0. In the presence of the bulk viscosity alone spatial homogeneity demands the vanishing of shear as well as the conformal flatness of the space-time. On the other hand, nonzero shear viscosity along with the uniform density assumption result in a unique temporal behavior of the matter density increasing always in the course of time.
On the Cauchy problem for the theory of gravitation with nonlinear Lagrangian
Authors: Jakubiec Andrzej , Kijowski Jerzy
Published: July 2002

For a theory of gravitation with nonlinear Lagrangian it is shown that the Cauchy problem is well posed.
Disproof of a conjectured inequality arising in the theory of magnetic flux diffusion
Authors: Book David L. , Brun Todd A.
Published: July 2002

The conjecture that the magnetic field energy introduced into an imperfectly conducting medium by diffusion is less than the thermal energy produced by the associated Joule heating is shown to imply the positivity of a certain integral operator with an indefinite kernel. Counterexamples are found by means of a variational calculation.
Angular reduction in multiparticle matrix elements
Authors: Lehman D. R. , Parke W. C.
Published: July 2002

A general method for reduction of coupled spherical harmonic products is presented. When the total angular coupling is zero, the reduction leads to an explicitly real expression in the scalar products of the unit vector arguments of the spherical harmonics. For nonscalar couplings, the reduction gives Cartesian tensor forms for the spherical harmonic products; tensors built from the physical vectors in the original expression. The reduction for arbitrary couplings is given in closed form, making it amenable to symbolic manipulation on a computer. The final expressions do not depend on a special choice of coordinate axes, nor do they contain azimuthal quantum number summations, or do they have complex tensor terms for couplings to a scalar; consequently, they are easily interpretable from the properties of the physical vectors they contain.
Factor structure of the Tomimatsu–Sato metrics
Authors: Perjés Zoltán
Published: July 2002

It is shown that the factoring property of the Tomimatsu–Sato metrics follows from the structure of special Hankel determinants. A set of linear algebraic equations determining the factors is found. The factors of the first five Tomimatsu–Sato metrics are tabulated.
Character calculations for semisimple Lie algebras
Authors: Vretare L.
Published: July 2002

A recursive method for calculation of characters of semisimple Lie algebras is outlined. By slight modifications algorithms are obtained for the computation of weight multiplicities, Kronecker products, and branching rules, as well as symmetrized Kronecker powers.
Green’s functions of the edh operators
Authors: Ivancovich J. , Kozameh C. , Newman E. T.
Published: July 2002

The spin-weight s Green’s functions for the operator ð and powers of ð are obtained. The extension of these Green’s functions to negative values of s and to the ð̄n operators, as well as a procedure for obtaining the Green’s function for any combination of products of ðn and ð̄n, is also given.
Characteristic classes of super vector bundles
Authors: Bruzzo Ugo , Ruipérez Daniel Hernández
Published: July 2002

A theory of characteristic classes for complex super vector bundles over supermanifolds is developed. Such characteristic classes are proved to fulfill the usual properties, and it is shown that, under suitable conditions, they can be represented in terms of supersmooth curvature forms.
Parabose algebras and subgraph polynomials
Authors: Graudenz Dirk
Published: July 2002

A graph theoretical method is proposed for the calculation of inner products in the Fock spaces of parabose algebras. For this purpose, a new class of polynomials associated with finite graphs is introduced. The obtained results can be generalized to the parafermi case.
Deformations of some infinite-dimensional Lie algebras
Authors: Fialowski Alice
Published: July 2002

The concept of a versal deformation of a Lie algebra is investigated and obstructions to extending an infinitesimal deformation to a higher-order one are described. The rigidity of the Witt algebra and the Virasoro algebra is deduced from cohomology computations for certain Lie algebras of vector fields on the real line. The Lie algebra of vector fields on the line that vanish at the origin also turns out to be rigid. All the affine Lie algebras are rigid; this is derived from the cohomology of their maximal nilpotent subalgebra. On the other hand, the maximal nilpotent subalgebras in both the Virasoro and affine cases are not rigid and have interesting nontrivial deformations (in fact, most vector field Lie algebras are not rigid).
The problem of gravity-gyroscopic waves, which are excited by the oscillations of a curve
Authors: Kharik V. M. , Pletner U. D.
Published: July 2002

The problem of the oscillations of an ideal stratified rotating fluid, which are excited by a curve in the case when the distribution of pressure on both sides of curve is prescribed, is considered. The solution to the problem, as well as results about symmetry properties of the potentials used for the solution of such problems, is obtained. The question of the uniqueness of the solution is also considered.
Separation of variables and exact solution to Dirac and Weyl equations in Robertson–Walker space-times
Authors: Villalba V. M. , Percoco U.
Published: July 2002

In this paper the separation of variables is presented in the Dirac equation in open, flat, and closed expanding cosmological Robertson–Walker universes. The equations governing the radial variable and the evolution of the time-dependent factor are obtained. An exact solution to the Weyl equation is derived for an arbitrary expansion factor of the Robertson–Walker metrics. An exact solution to Dirac equation in a universe filled with radiation is also presented.
A supersymmetric Benney hierarchy: A semiintegrable system
Authors: Kupershmidt B. A.
Published: July 2002

It is shown that supersymmetry can weaken integrability: A supersymmetric extension of the quasiclassical limit of the KP hierarchy has flows that no longer commute between themselves but still have an infinite common set of conserved densities. This extension has, thus, no Hamiltonian structure.
Kronecker products, minuscule representations, and polynomial identities
Authors: Iosifescu Mircea , Scutaru Horia
Published: July 2002

The special role of the highest long and highest short roots in the derivation of extremum properties of the weights of irreducible representations of semisimple Lie algebras is pointed out. These properties are used to give an intrinsic and unifying reformulation, as well as a new proof of Klimyk’s theorem on Kronecker products [Ukrain. Mat. Z. 18, 19 (1966)]. This new form of Klimyk’s theorem reveals the special position of the minuscule representations in Kronecker products; as an immediate consequence, the explicit formula for the Kronecker product of an arbitrary representation with a minuscule representation is obtained. Explicit expressions for the weights of the minuscule representations are given. New derivations of theorems of Dynkin [Trudy Mosk. Obsch. 1, 39 (1952)] and Feingold [Proc. Am. Math. Soc. 70, 109 (1978)] on Kronecker products, as well as the necessary condition for a Kronecker product to decompose in two irreducible components are obtained. The proofs are based on a theorem of Parthasarathy, Ranga Rao, and Varadarajan [Ann. Math. 85, 383 (1967)].
On the convergence of the Magnus expansion in the Schrödinger representation
Authors: Fernández Francisco M. , Echave Julián , Castro Eduardo A.
Published: July 2002

The convergence properties of the Magnus expansion in the Schrödinger representation are investigated. A quite general result is rigorously derived from first-order perturbation theory. A finite matrix representation is presented for obtaining the exponential time-evolution operator more easily. Two time-dependent models, an oscillator and a spin system, are considered as illustrative examples.
Equations of state and plane-autonomous systems in Bianchi V imperfect fluid cosmology
Authors: Coley Alan A.
Published: July 2002

A new general approach for investigating imperfect fluid cosmological models is introduced in which the equations of state are completely ‘‘dimensionless.’’ Such equations of state are then utilized to reduce the Einstein field equations governing Bianchi V imperfect fluid cosmologies to a plane-autonomous system of equations, thus enabling the qualitative behavior of these cosmological models to be analyzed in a straightforward manner. The resulting plane-autonomous system is investigated. Finally, exact solutions of the Bianchi V imperfect fluid field equations in the case when the equations of state take on a particularly simple form are discussed.
Dynamics of solitons in a damped sine-Hilbert equation
Authors: Matsuno Y.
Published: July 2002

A damped sine-Hilbert (sH) equation is proposed. It can be linearized by a dependent variable transformation which enables one to solve an initial value problem of the equation. The N-soliton solution is obtained explicitly and its properties are investigated in comparison with those of the N-soliton solution of the sH equation. In particular the interaction of the two solitons is explored in detail with the aid of the pole representation. It is found that the interaction process is classified into the two types according to the initial amplitudes and positions of both solitons. In the general N-soliton case the long-time behavior of the solution is shown to be characterized by the positive N zeros of the Hermite polynomial of degree 2N. Finally, a linearized version of the damped sH equation is briefly discussed.
Essential singularities of spherically symmetric space-times
Authors: Qadir Asghar
Published: July 2002

The essential singularities of four-dimensional spherically symmetric space-times with some additional symmetries are discussed. The significance of the results is considered.
Real representations of Clifford algebras
Authors: Brihaye Y. , Maslanka P. , Giler S. , Kosinski P.
Published: July 2002

Simple proof of classification theorem of all real irreducible representations of Clifford algebras is given.
Some soliton solutions for the quadratic bundle
Authors: Vaklev Y. S.
Published: July 2002

An explicit form of the N-soliton solutions related to the auxiliary linear problem of the quadratic bundle of a special kind is obtained. A recipe to find their gauge equivalent solutions is given. It is shown that the additional reduction of the potential is sufficient but not necessary. The asymptotic behavior of the investigated solutions is studied. Some examples are given in the end.
Natural bundles. III. Resolving the singularities in the space of immersed submanifolds
Authors: Swift S. Timothy
Published: July 2002

This is the third of a sequence of articles dealing with the geometry and applications to field theories of natural infinite dimensional bundles. In this paper, a method for resolving the singularities in the space of immersed submanifolds Imm(M,N)/Diff(M) is described. This desingularization is completely natural, emerging as it does from a consideration of principal bundles associated with the manifold pair (M,N). Geometrical aspects of the bundles involved in our construction are discussed, and the potential rôle of this geometry in physical theories is outlined. In the final section, a brief description of the action of the codomain diffeomorphism group Diff(N) on the manifold of immersions Imm(M,N) is provided.
Geometrization of classical mechanics
Authors: Ghaboussi F.
Published: July 2002

In this paper, it is shown that the symplectic description of the Hamiltonian mechanics contains a gauge structure, where the symplectic form acts as connection form.
Equivalence between the Nielsen and the scaling transformations in one-dimensional quasiperiodic systems
Authors: Iguchi Kazumoto
Published: July 2002

An equivalence between the Nielsen transformations in mathematics and the scaling transformations in quasiperiodic physics in one dimension is shown herein. By recognizing this equivalence one becomes able to obtain the trace map for the quasiperiodic lattices constructed by an arbitrary number of atoms in the chain, where the atoms are symbolized by letters. In this approach the scaling transformations are regarded as the automorphisms of the set of letters, which induce the trace map as the inner automorphisms.
A generalized Birkhoff theorem for the Einstein–Yang–Mills system
Authors: Brodbeck Othmar , Straumann Norbert
Published: July 2002

Some results of a systematic study of the coupled Einstein–Yang–Mills (EYM) equations for arbitrary gauge groups are presented herein. In a first step a group theoretical analysis of spherically symmetric EYM fields is given. This will lead to a concise description of a large class of principal bundles for which the spherically symmetric solutions of the EYM equations have to be static (generalized Birkhoff theorem) and the metric must be of the Reissner–Nordstro/m-type.
On the regularization of Schrödinger operators with Coulombic singularities
Authors: Chantelau Klaus
Published: July 2002

A regularization method will be investigated for the Coulomb problem in three dimensions, which has been mostly applied to classical systems, namely, the Kustaanheimo–Stiefel transform. The regularization is developed within the context of self-adjoint extensions of differential operators and may be used for the semiclassical analysis of low-lying eigenvalues of the Schrödinger operator for one electron in the field of a finite number of fixed nuclei.
Two classes of dynamical systems all of whose bounded trajectories are closed
Authors: Iwai Toshihiro , Katayama Noriaki
Published: July 2002

According to the Bertrand theorem, the Kepler problem and the harmonic oscillator are the only central force dynamical systems that have closed orbits for all bounded motions. In this article, other dynamical systems having such a closed orbit property are found on T*(R3−{0}). Consider a natural dynamical system on T*(R4−{0}) whose Hamiltonian function is composed of kinetic and potential energies, and invariant under a SO(2) action. Then one can reduce the system to a Hamiltonian system on T*(R3−{0}) by the use of the Kustaanheimo–Stiefel transformation. If the original potential on R4−{0} is a central one, Bertrand’s method is applicable to the reduced system for determining the potential so that any bounded motions may be periodic. As a result, two types of potential functions will be found; one is linear in the radial variable and the other proportional to the inverse square root of that. The dynamical systems obtained are capable of physical interpretation. In particular, the dynamical system with the inverse square root potential may be called the twofold Kepler system, whose bounded trajectories have a self-intersection point.
Duality in long-range Ising ferromagnets
Authors: Meurice Yannick
Published: July 2002

It is proved that for a system of spins σi=±1 having an interaction energy −∑Kijσiσj with all the Kij strictly positive, one can construct a dual formulation by associating a dual spin Sijk=±1 to each triplet of distinct sites i, j, and k. The dual interaction energy reads −∑(ij)DijΠ k≠i,jSijk with tanh(Kij)=exp(−2Dij), and it is invariant under local symmetries. The gauge-fixing procedure, identities relating averages of order and disorder variables, and representations of various quantities as integrals over Grassmann variables are discussed. The relevance of these results for Polyakov’s approach of the 3-D Ising model is briefly discussed.
Supermultiplets coupling in complex manifolds. Exterior canonical formalism
Authors: Foussats A. , Repetto C. , Zandron O. P. , Zandron O. S.
Published: July 2002

The coupling of N=1 supergravity to n scalar multiplets on a Kähler manifold from the exterior canonical point of view is treated. This constrained system is analyzed by using the first and second order Hamiltonian formalism. The constraints, the extended Hamiltonian, and the equation of motion are obtained. The first class constraints which determine all the gauge symmetries are also given.
A geometric criterion for adiabatic chaos
Authors: Kaper Tasso J. , Kovačič Gregor
Published: July 2002

Chaos in adiabatic Hamiltonian systems is a recent discovery and a pervasive phenomenon in physics. In this work, a geometric criterion is discussed based on the theory of action from classical mechanics to detect the existence of Smale horseshoe chaos in adiabatic systems. It is used to show that generic adiabatic planar Hamiltonian systems exhibit stochastic dynamics in large regions of phase space. To illustrate the method, results are obtained for three problems concerning relativistic particle dynamics, fluid mechanics, and passage through resonance, results which either could not be obtained with existing methods, or which were difficult and analytically impractical to obtain with them.
An analytical solution of the two-dimensional exciton–phonon matrix element
Authors: Kaushik Sumanth
Published: July 2002

This article presents an analytical solution to an integral that is fundamental in the calculation of the phonon ionization cross sections of two-dimensional excitons. This integral, which is a Bessel transform of a confluent hypergeometric function, is encountered in the calculation of the matrix element between the ground state and an excited state of a two-dimensional hydrogen atom due to exciton–phonon interaction. This integral is shown to be expressible in terms of a sum of two associated Legendre functions.
Finite dimensional irreducible representations of the quantum algebra Uq(C2)
Authors: Yang Yaping , Yu Zurong
Published: July 2002

In this article, the communtation relations of the generators of quantum algebra Uq(C2) are analyzed and irreducible q-tensor operators of rank (1/2) of quantum algebra SUq(2) are constructed. By means of the property of a q-tensor operator, finite irreducible representations of Uq(C2) can be easily obtained. Some low dimensional representations are tabulated.
Nonlinear theories of spin-2 field in terms of Fierz variables
Authors: de Freitas Luciane R. , Novello M. , Pinto-Neto N.
Published: July 2002

Exceptional nonlinear Lagrangians for a spin-2 field in terms of Fierz variables are obtained using the method proposed by Lax. They are equivalent to the Born–Infeld Lagrangian for a spin-1 field theory and are free from unbounded growth of wave velocities.
The reduction of five dimensional Chern–Simons theories
Authors: Temple-Raston M.
Published: July 2002

The effects of gauge symmetries on Lagrangian gauge theories which include the Chern–Simons term are studied herein. It is found that the Chern–Simons term appended to a five dimensional Yang–Mills theory makes nontrivial contributions to the classical field equations in four and two dimensions depending on the gauge group, but makes no contribution to the field equations in three dimensions, regardless of the gauge group. In addition to the reduction of Yang–Mills–Chern–Simons, the pure Chern-Simons theory is reduced in five dimensions—a topological field theory—to two and three dimensions. The potential physical observability of solutions to the resulting field equations is examined by determining if a nontrivial spontaneous symmetry breaking is permitted.
W*-KMS structure from multi-time Euclidean Green functions
Authors: Gielerak R. , Jakóbczyk L. , Olkiewicz R.
Published: July 2002

An axiomatic approach to the problem of reconstruction of a dynamics from the Euclidean multi-time Green functions is proposed. The existence of a W*-algebra on which the reconstructed dynamics acts as the canonical group of modular automorphisms is shown. A condition under which the reconstruction from the one-time and multi-time Green functions are equivalent is formulated.
q-Euclidean space and quantum Wick rotation by twisting
Authors: Majid S.
Published: July 2002

The quantum matrix algebra R21x1x2=x2x1R is studied and proposed for the standard 2×2 case as the coordinates of q-deformed Euclidean space. The algebra in this simplest case is isomorphic to the usual quantum matrices Mq(2) but in a form which is naturally covariant under the Euclidean rotations SUq(2)⊗SUq(2). A quantum Wick rotation is introduced that twists this system precisely into the approach to q-Minkowski space based on braided matrices and their associated spinorial q-Lorentz group.
Coherent states, path integral, and semiclassical approximation
Authors: Funahashi Kunio , Kashiwa Taro , Sakoda Seiji , Fujii Kazuyuki
Published: July 2002

Using the generalized coherent states it is shown that the path integral formulas for SU(2) and SU(1,1) (in the discrete series) are WKB exact, if it is started from the trace of e−iTĤ, where Ĥ is given by a linear combination of generators. In this case, the WKB approximation is achieved by taking a large ‘‘spin’’ limit: J,K→∞, under which it is found that each coefficient vanishes except the leading term which indeed gives the exact result. It is further pointed out that the discretized form of path integral is indispensable, in other words, the continuum path integral expression sometimes leads to a wrong result. Therefore great care must be taken when some geometrical action would be adopted, even if it is so beautiful as the starting ingredient of path integral. Discussions on generalized coherent states are also presented both from geometrical and simple oscillator (Schwinger boson) points of view.