bluuebunny/crossref_metadata_2025 huggingface dataset:
Factorization of operators and completely integrable Hamiltonian systems
Authors: Guil Guerrero F.
Published: March 2003

Generalized Miura transformations induced by factorization of an nth-order scalar operator are used to characterize a set of Hamiltonian systems by requiring the conservation of the Gel’fand–Dikii first integrals sequence. The second symplectic structure for the Gel’fand–Dikii equations is obtained in connection with the previous Hamiltonian systems. Bäcklund transformations are also analyzed.
Explicit evaluation of certain Gaussian functional integrals arising in problems of statistical physics
Authors: Adamowski Janusz , Gerlach Bernd , Leschke Hajo
Published: March 2003

An explicit formula is presented for a (conditional) Wiener integral, the integrand of which is an exponential of a general quadratic functional of the path. The functional integrals arising in non-Markovian Gaussian approximations to various problems of statistical physics (e.g., theory of the large polaron, theory of disordered systems) are easily recovered as special cases.
Solution of a Schrödinger inverse scattering problem with a polynomial spectral dependence in the potential
Authors: Jaulent M. , Jean C.
Published: March 2003

The inverse scattering problem for the scalar Schrödinger equation y″+[E−𝒥p = 0n (E1/2n) pup(x)]y = 0, x∈R, is considered. It is solved by reduction to the inverse scattering problem for a matrix Schrödinger equation: Y″+[EI−(U(x)+E 1/2 Q(x))] Y = 0, x∈R.
Electromagnetic energy tensors and the Lorentz equation of motion for fields with electric and magnetic charge distributions
Authors: Nevin J. M.
Published: March 2003

In special or general relativity the electromagnetic energy tensor is usually taken to be ϑab = (1/4π)(FacFbc−(1/4)  gabFcdFcd). This expression may also be used in the generalized theory which allows magnetic as well as electric charge. Rund [J. Math. Phys. 18, 84 and 1312 (1977)] has suggested a new approach to the generalized theory with an alternative form for the energy tensor. We show that in Rund’s theory there are other possible definitions for the energy tensor. However, there is a strong indication that a particular energy tensor gives rise in a definite way to a corresponding Lorentz equation of motion. This equation is derived for each of the energy tensors and it is found that only ϑab gives the Lorentz equation which is usually assumed in the generalized theory. Furthermore, the Lorentz equations arising from the other energy tensors will not give charge quantization.
Two variable relativistic tensor harmonics
Authors: Gmitro M. , Ovchinnikova A. A.
Published: March 2003

Three bases in the Hilbert space of tensor fields on the unit spheres associated with two independent vectors are discussed: the tensor spherical harmonics and the symmetric and unsymmetric tensor helicity harmonics. Under the conditions which we specify they form complete sets of independent Lorentz covariants which may serve the purpose of the analysis of reactions with several particles in the final state.
A 4-vector generalization of the sine–Gordon equation
Authors: Swanson D. G.
Published: March 2003

Using the differential operators from the Dirac equations, an algebra is developed which leads to 4-vector functions and the generalization of many scalar functions. Assuming particles to be described by the potential solutions of the generalized sine–Gordon equation (a set of four coupled nonlinear equations), a single soliton is shown to be localized within a light sphere and have intrinsic properties of group velocity, phase velocity, angular momentum, and wave-particle duality.
Linear response theory revisited III: One-body response formulas and generalized Boltzmann equations
Authors: Charbonneau M. , van Vliet K. M. , Vasilopoulos P.
Published: March 2003

The many-body linear response expressions obtained in previous papers [J. Math. Phys. 19, 1345 (1978); 20, 2573 (1979)] are applied to systems of weakly interacting particles. General expressions for the susceptibility and conductivity in such systems are obtained. The diagonal parts depend on the scattering processes, for which we consider interactions with bosons with mass and electron-phonon interaction. For elastic collisions simple closed forms result. For general two-body collisions, the closed expressions are cumbersome, except when the current is due to collisional current through localized states, such as Landau orbits; in that event a generalized Adams-Holstein result is obtained. The nondiagonal electrical conductivity is shown to be of paramount importance for the quantum mechanical Hall effect. We also derive quantum mechanical Boltzmann equations, both for the diagonal occupancy operator 〈nζ〉t and for the nondiagonal operator 〈c+ζ′ cζ\〉t. The total Boltzmann equation is shown to be fully equivalent with the linear response results. Finally, in the last part we derive the Boltzmann equation for the Wigner function of inhomogeneous systems. In the classical limit this yields the usual Boltzmann transport equation. This equation has therefore been obtained by first principles from the von Neumann equation.
Inverse problems for nonabsorbing media with discontinuous material properties
Authors: Krueger Robert J.
Published: March 2003

One-dimensional electromagnetic and elastic inverse problems are formulated for media with discontinuous material properties. In addition, an impedence mismatch between source and medium is allowed. The measured data for either problem is shown to generate a reflection kernel which is used in the solution of the inverse problem. The solution algorithm itself is a time domain technique which is a special case of previously obtained results for absorbing media.
Theoretical basis for Coulomb matrix elements in the oscillator representation
Authors: Chen Augustine C.
Published: March 2003

Hydrogenic wave functions in the spherical and parabolic bases are shown to correspond, respectively, to a restricted set of wave functions of a four-dimensional harmonic oscillator and its coupled pair of two-dimensional oscillators. This correspondence provides the theoretical basis for algebraic calculations of Coulomb matrix elements in the oscillator representation.
A combinatoric result related to the N-body problem
Authors: Karlsson Bengt R.
Published: March 2003

In the set of complete chains of partitions of N objects, let chains that are related through a permutation of the objects be termed equivalent. The number of equivalence classes μN is shown to equal the Euler number ‖EN−1‖ if N is odd, and 2N(2N−1)‖BN‖/N, where BN is a Bernoulli number, if N is even. The number of elements in each class is also found. In the Yakubovskii-type formulation of the N-body problem in quantum mechanics, μN is the basic number of coupled equations when all particles are identical.
Connection between the infinite sequence of Lie–Bäcklund symmetries of the Korteweg–de Vries and sine-Gordon equations
Authors: Kaliappan P. , Lakshmanan M.
Published: March 2003

From the observation that the infinite sequence of Lie–Bäcklund symmetries of the potential modified Kortweg–deVries (PMK–dV) and the sine–Gordon (s–G) equations are identical, it is shown that there exists a simple connection between the Lie–Bäcklund symmetries (written in the form of evolution equations) of the Korteweg–deVries (K–dV) and s–G equations. Further, this connection is similar to the one obtained by Chodos for the conserved quantities of K–dV and s–G equations. We also point out that the result of Chodos can be realized from the equality of conserved densities of PMK–dV and s–G systems.
Lie-algebraic properties of infinite-dimensional wave equations
Authors: Cant A.
Published: March 2003

To an infinite-dimensional Lorentz-invariant wave equation of the form (αμ∂μ+iκ)ψ(x) = 0 is associated a Lie algebra S over C which contains so(4,C) and αμ. We show by considering a certain class of equations, that in general S is an infinite-dimensional Lie algebra. It has a structure which is quite different from that of known types of infinite-dimensional algebras.
Distorted black holes
Authors: Geroch Robert , Hartle James B.
Published: March 2003

All exact solutions of Einstein’s equation that represent static, axisymmetric black holes distorted by an external matter distribution are obtained. Their structure—local and global—is examined. The Hawking temperature is derived and laws of thermodynamics given for both the total system of black hole and external matter and the black hole considered as a single system. The evolution, induced by Hawking radiation, of distorted black holes is discussed.
Explicit expressions for double Gel’fand states
Authors: Antillón A. , Seligman T. H.
Published: March 2003

Double Gel’fand states are given explicitly as polynomials of boson operators. The coefficients of these polynomials may be expressed in terms of recoupling coefficients of external products of permutation groups or Kronecker products within the unitary group, as well as in terms of multiple Clebsch–Gordan coefficients of the unitary group.
Pseudopotentials and Lie symmetries for the generalized nonlinear Schrödinger equation
Authors: Harnad J. , Winternitz P.
Published: March 2003

The generalized nonlinear Schrödinger equation zxx+izt =  f(z, z*) is analyzed from the point of view of the existence of pseudopotentials, Bäcklund transformations, Lie symmetries, and conservation laws. Applying the Wahlquist–Estabrook method of closed differential ideals we show that eight classes of nontrivial interaction terms  f(z,z*) exist for which the equation allows the existence of pseudopotentials. Five of them simply lead to conservation laws, the remaining three to Bäcklund transformations. The usual ’’cubic’’ nonlinear Schrödinger equation with  f(z,z*) = εz‖z‖2 is obtained as a special case. It is also the only case for which the Bäcklund transformation contains a free parameter. We show that the real and complex parts of this parameter are generated by the dilation and Galilei invariance of the equation.
Regge trajectories in confining potentials
Authors: Datta D. P. , Mukherjee S.
Published: March 2003

The analyticity of the energy level En(l) in the half-plane Re(l)≳− (1)/(2) has been proved for some interesting superpositions of quark-confining potentials.
Melnikov’s method and Arnold diffusion for perturbations of integrable Hamiltonian systems
Authors: Holmes Philip J. , Marsden Jerrold E.
Published: March 2003

We start with an unperturbed system containing a homoclinic orbit and at least two families of periodic orbits associated with action angle coordinates. We use Kolmogorov–Arnold–Moser (KAM) theory to show that some of the resulting tori persist under small perturbations and use a vector of Melnikov integrals to show that, under suitable hypotheses, their stable and unstable manifolds intersect transversely. This transverse intersection is ultimately responsible for Arnold diffusion on each energy surface. The method is applied to a pendulum–oscillator system.
Exact recursion relation for pseudobidimensional arrays of dumbbells
Authors: Mola E. E.
Published: March 2003

Exact relationships are developed that describe the occupation statistics for pseudobidimensional arrays of dumbbells. It is found that E(k,N), the number of ways of arranging k indistinguishable dumbbells on a 3×N diagonal array of compartments is exactly described by the recursion relation E(k,N) = 4E(k−1,N−1)+E(k,N−1)−2E(k−2,N−2). The 3×N diagonal lattice space provides to the central sites of the lattice their full coordination number of nearest-neighboring compartments; therefore the solution of the present system provides a 1×N diagonal (central sites) ’’window’’ to watch the behavior of a true bidimensional array of dumbbells. For large values of N, the dumbbell freedom per lattice site on any given site of the central diagonal is found to be 1.8477⋅⋅⋅, which is only 3% higher than the exact value (1.7916⋅⋅⋅) found for a ’’locked’’ dumbbell on a bidimensional array.
Linear transport in nonhomogeneous media. II
Authors: Larsen Edward W. , Pomraning G. C. , Badham V. C.
Published: March 2003

Elementary continuum and discrete solutions are constructed for transport equations with scattering ratios which are bilinear functions of position. Numerical results are given for some albedo problems.
Remarks on spacetime symmetries and nonabelian gauge fields
Authors: Henneaux Marc
Published: March 2003

Some properties of nonabelian gauge fields invariant under a given group of spacetime transformations are studied and applied to the case of spatial homogeneity and isotropy. All the k = 0 and k = 1 Robertson–Walker models filled with a SO (3) gauge field are derived.
SU(3) wave solutions
Authors: Kovacs Eve
Published: March 2003

An ansatz yielding propagating wave solutions for pure SU(3) gauge theories is exhibited. The solutions are self-dual and have a superposition property like their SU(2) analogs. Possible generalizations of the ansatz which may be used to obtain additional irreducible SU(3) solutions are also suggested.
Dynamical group of microscopic collective states. I. One-dimensional case
Authors: Deenen J. , Quesne C.
Published: March 2003

In the present series of papers it is intended to determine the nature and study various realizations of the dynamical group of microscopic collective states for an A-nucleon system, defined as those A-particle states invariant under the orthogonal group O(n) associated with the n = A−1 Jacobi vectors. The present paper discusses the case of a hypothetical one-dimensional space. Simple invariance considerations show that the dynamical group of collective states is then the group 𝒮𝓅c(2,R), which is the restriction to the collective subspace of the group 𝒮𝓅(2,R) of linear canonical transformations in n dimensions conserving the O(n) symmetry. In addition to the well-known realization of the dynamical group in the Schrödinger representation based upon the Dzublik–Zickendraht transformation, two new realizations are proposed. The first acts in a Barut Hilbert space, which is the subspace of a Bargmann Hilbert space of analytic functions left invariant by O(n). A unitary mapping is established between the ordinary Hilbert space of collective states and the Barut Hilbert space and coherent collective states are defined in the latter. The second is carried out in terms of one boson creation and one boson annihilation operator through a generalized Holstein–Primakoff representation. The generator of a U(1) group, which is the one-dimensional analog of the U(6) group of the interacting boson model (IBM), can then be expressed in terms of the generators of 𝒮𝓅c(2,R). Finally the generalization of the preceding analysis to a d-dimensional space is outlined in the cases where d = 2 or 3. The dynamical group of collective states becomes 𝒮𝓅c(2d,R).
Soliton solutions for self-dual SU(2) gauge fields on Euclidean space
Authors: Letelier Patricio S.
Published: March 2003

Axially symmetric soliton solutions for self-dual SU (2) gauge fields on Euclidean four-dimensional flat space are found using an extension of the Belinsky–Zakharov solution generating technique.
High-energy asymptotic expansion and Regge trajectories for the general even power potential in the Klein–Gordon equation with applications
Authors: Sharma L. K. , Iyer V. P.
Published: March 2003

Large energy asymptotic expansions, wavefunctions, and Regge trajectories of the generalized even power potential V(r) = −g2𝒥∞j = 0N2jr2j in the Klein–Gordon equation are obtained. These general expansions are then used to obtain Regge trajectories for the anharmonic oscillator and Gauss potentials. Finally, the charmonium spectroscopy for an harmonic oscillator is studied.
Bounds for effective conductivity of heterogeneous materials by the finite element method
Authors: Nakamura Mitsunobu , Mizuno Makoto
Published: March 2003

Bounds for the effective conductivity σ* are derived using two standard variational principles established by Beran and the finite element method. We divide a two-dimensional material into triangular finite elements, use a linear local function as a trial function for each element, and apply the function to the variational principles. As a result a very simple method of computing the bounds is derived. As a numerical example, we apply the method to a model for heterogeneous materials and obtain very narrow gaps between bounds for σ*.
Structure and representations of the symmetry group of the four-dimensional cube
Authors: Baake M. , Gemünden B. , Oedingen R.
Published: March 2003

In this paper we give, explicitly, the description of the structure, the characters, and the complete system of irreducible representations of the hyperoctahedral group in four dimensions, which we call W4 (from the German ’’Würfel’’). In a second step, we do the same for the subgroup SW4, which is formed by all pure rotations contained in W4.
A family of sums of products of Legendre functions
Authors: van Haeringen H.
Published: March 2003

We present simple analytic expressions for a few sums of products of Legendre functions, of the type 𝒥∞n = 0(2n+1)Pαn(x)Pβn(y) Pγn(z)Qμn(n).
Asymptotic behavior of the nonlinear diffusion equation n
t = (n−1n
x)x
Authors: Berryman James G. , Holland Charles J.
Published: March 2003

The asymptotic behavior of the equation nt = (ln n)xx is studied on the finite interval 0⩽x⩽1 with the boundary conditions n(0,t) = n(1,t) = n0 and initial data n(x,0)⩽n0. We prove that asymptotically ln[n(x,t)/n0]→A exp(−π2t/n0)21/2 sin πx and also provide rigorous upper and lower bounds on the asymptotic amplitude A in terms of integrals of nonlinear functions of the initial data. The rigorous bounds are compared to values of A obtained from computer experiments. The lower bound L = (23/2/π)exp[li(1+Q)−γ], where li is the logarithmic integral, γ is Euler’s constant, and Q = (π/2)ℱ[n(x,0)/n0−1]sin πx dx, is found to be the best known estimate of A.
Variational principles for resonances. II
Authors: Ramm A. G.
Published: March 2003

Variational principles for calculating the complex poles of Green’s function are given. Convergence of the numerical procedure is proved.
Convergence of the T-matrix approach to scattering theory
Authors: Ramm A. G.
Published: March 2003

The T-matrix numerical scheme is widely used in practice. Convergence of this scheme was not proved. A proof of convergence is given in this paper.
Killing vectors in self-dual, Euclidean Einstein spaces
Authors: Boyer C. P. , Finley J. D.
Published: March 2003

Using the formalism of complex ℋ-spaces, we show that all real, Euclidean self-dual spaces that admit (at least) one Killing vector may be gauged so that only two distinct types of Killing vectors appear; in Kähler coordinates these are the generators of a translational or a rotational symmetry. We give explicit forms both for the Killing vectors and for the constraint on the Kähler potential function Ω which allows for such a Killing vector. In the translational case we show how all such spaces are determined by the general solution of the three-dimensional, flat Laplace’s equation and how these are related to the multi-Taub–NUT metrics of Gibbons and Hawking. In the rotational case we simplify the equation determining Ω, but this is not sufficient to obtain the general solution.
Properties of three-dimensional Cartesian tensors. II. Arbitrarily oriented tensors expressed in generalized spherical functions. Ranks through 4
Authors: Russ Muchere C. , Hollingsworth C. A.
Published: March 2003

Explicit expressions for the rotation of Cartesian tensors of ranks through 4 are obtained. These are given in terms of the irreducible components and the generalized spherical functions. They can be obtained in terms of the reducible components by the use of results which were obtained previously. As a simple illustration of an application of the results, an expression is obtained for the energy of an octupole as a function of the orientation of the octupole in an inhomogeneous field.
An ℰ6⊗𝒰(1) invariant quantum mechanics for a Jordan pair
Authors: Truini P. , Biedenharn L. C.
Published: March 2003

Quantum mechanical spaces associated with geometries based on exceptional groups are of interest as models for internal (quark) symmetries. Using the concept of a Jordan pair, two copies of complex 3×3 octonionic Jordan algebras (ℳ83) are shown to define a quantum mechanics over the complex octonionic plane having ℰ6⊗𝒰(1) as automorphism group. The unusual features of this new quantal structure (neither a projective geometry, nor a lattice) are discussed.
The investigation of some self-similar solutions of Einstein’s equations
Authors: Bogoyavlensky O. I. , Moschetti G.
Published: March 2003

New application of self-similar generalizations of homogeneous cosmological models is shown in the problem of nonstationary nonspherically-symmetric accretion of self-gravitating gas on the center. For self-similar Bianchi types II and III, solutions of the system of Einstein equations are reduced to some dynamical system of small order. A number of exact solutions in empty space and for the stiff equation of state of matter is found.
Twistor bundles and gauge action principles of gravitation
Authors: Luehr C. P. , Rosenbaum P. M.
Published: March 2003

A gauge theory of gravitation is constructed with a twistor bundle as the starting point. Each fiber is a twistor space, acted upon by the Poincaré group, which forms an internal symmetry group. The formalism leads to a twistor action principle which overcomes difficulties encountered in previous attempts in the literature to formulate a true spinorial variational principle.
Continuity of sample paths and weak compactness of measures in Euclidean field theory
Authors: Haba Z.
Published: March 2003

Under an assumption on the asymptotic u→∞ behavior of the generating functional ℱ exp[uφ( g)] dμ(φ), an estimate is obtained on ‖χ(x)−χ(x′)‖, where χ(x) = φg(x) ≡φ( g(⋅−x)), showing Hölder continuity of φg(x) for a class of g. It is proved that the family of measures vγ, with dvγ(χ) = dμγ(φg) and ℱ expχ(x) dvγ(χ) bounded in γ, is weakly conditionally compact. In application to the infinite volume cutoff μκ measures in P(φ)d , these results imply the continuity of μκ(C) when κ→∞ for a class of sets C. Such a property allows distinguishing the interacting measures from the free ones.
Structure results for the Segal quantization of Fermi systems
Authors: Gallone Franco , Sparzani Antonio
Published: March 2003

In Segal’s approach to linear Fermi quantum systems, a one particle picture with linear symmetries (e.g., with a linear dynamics) can be quantized very straightforwardly when a complexification is given for the (real linear) one particle picture. We examine how the symmetries that are embodied in the one particle picture can determine the structure of the family of the possible complexifications. Among other results, we prove that if the symmetries can be represented in a suitably irreducible way then the complexification is essentially unique. Also, when the one particle space is a generalization of the one defined by the Dirac equation, we prove that there are many complexifications, and inequivalent too, as they generate inequivalent representations of the canonical anticommutation relations; however, we find two criteria that single out the ’’physical’’ complexification. We use the general results we prove to discuss a few familiar models.
Time-dependent embeddings for Schwarzschild-like solutions to the gravitational field equations
Authors: Chyba Christopher F.
Published: March 2003

An explicit formula for embedding the Schwarzschild solution in a three-dimensional flat space with indefinite metric for arbitrary Kruskal timelike coordinate v is presented. The time development of the Schwarzschild solution can then be represented by a succession of spacelike surfaces, each corresponding to a different value of v. It is seen that the standard representation of the Schwarzschild metric, the Flamm paraboloid, is in fact the v = 0 special case of a similar time-dependent embedding in a three-dimensional Euclidean space with positive definite metric. However, this embedding is inadequate in that it is not defined for most values of v. Thus, the embedding in a space with indefinite metric is to be preferred. The results for the Schwarzschild case are found to be readily extended to all metrics of a certain class, and a general embedding formula for arbitrary v results. Embeddings for the Schwarzschild, de Sitter, and Reissner–Nordström metrics are then special cases of this general form. It is seen that all such solutions behave similarly as v gets large. This suggests an alternate interpretation of the oscillatory character of the Reissner–Nordström ’’wormhole.’’
Lattice dynamics, random walks, and nonintegral effective dimensionality
Authors: Hughes Barry D. , Shlesinger Michael F.
Published: March 2003

Definitions of the nonintegral effective dimensionality of recursively defined lattices (fractal lattices) may be based on scaling properties of the lattices, or on the qualitative behavior of cooperative phenomena supported by the lattices. We examine analogs of these definitions for regular (i.e., periodic) lattices supporting long-range interactions. In particular, we show how to calculate a harmonic oscillator effective dimension, a scaling dimension, and a random walk effective dimension for simple cubic lattices with a class of long-range interactions. We examine the relationship between these three dimensions for regular lattices, and conjecture a constraint on the analogs of these dimensions for fractal lattices.
Lorentz invariance of the extended object
Authors: Jacquot J. L. , Umezawa M.
Published: March 2003

It has been known for a few years that the Heisenberg field of the extended object can be obtained in expanded form as a power series of quantum operators and creation and annihilation operators by solving the Yang–Feldman equation. Such an expression is called a dynamical map (mapping of the infield into the Heisenberg field). We will show that the Heisenberg field thus expressed (the dynamical map) is Lorentz covariant if it satisfies the equal time canonical commutation relation. In this paper we limit ourselves to the invariance of the first order term. Also, our Heisenberg field is (1+1) dimensional and is of the tree approximation. In the course of the calculation, we find that the quantum mechanical operator and the quantized field may be mixed by the Lorentz transformation if the space derivative of the classical field soliton solution is assumed to decrease not faster than 1/x2. It indicates that the Hilbert space may not be the direct product of two sub-Hilbert spaces, even though it is a product of two subspaces, one of which is a Fock space of the quantized field and the other is of the quantum mechanical operator.
The pattern space factor and quality factor of cylindrical source antennas
Authors: Jarem John M.
Published: March 2003

For the first time the quality factor of cylindrical source antennas is derived by a plane wave expansion. The evanescent energy (and therefore the quality factor) as defined by a plane wave expansion is shown to be different from Collin and Rothschild’s [IEEE Trans. Antennas Propagation AP-12, 23 (1964)] quality factor.
On the phase transition of the one-dimensional Percus–Yevick equation for an arbitrary potential of finite range
Authors: Chen M.
Published: March 2003

A qualitative investigation of the one-dimensional Percus–Yevick integral equation by perturbation method is discussed for an arbitrary potential of finite range l. When the particle density ρ is restricted to the interval (0,1) it is proved that every order of perturbation has a unique continuous and bounded solution, which can be expressed as a convergent generalized Fourier series. The perturbation series is absolutely and uniformly convergent if the supremum norm of the nth order solution is less than or equal to n!. Under the assumptions (i), 0<ρ<1 and (ii), the absolute and uniform convergence of the perturbation series, it can be proved that the Percus–Yevick equation cannot exhibit a phase transition.
On approximating the solutions of the Chandrasekhar H-equation
Authors: Vatsya S. R.
Published: March 2003

Method of moment and the Newton approximants to the Chandrasekhar H-function are shown to converge to the physical solution uniformly. The latter also converge monotonically faster than the iterative approximations obtained previously.
Generalized SU(2) spherical harmonics
Authors: Bystricky J. , Gaskell R. , Patera J. , Sharp R. T.
Published: March 2003

The generating functions for polynomial tensors based on each SU(2) tensor of rank from 7 to 13 (angular momentum 7/2 to 13/2) are given in a ’’positive’’ form suitable for interpretation in terms of an integrity basis. An iterative procedure for extending the results to higher rank tensors is indicated.
On a certain class of two-sided continuous local semimartingales: Toward a sample-wise characterization of the Nelson process
Authors: Yasue Kunio
Published: March 2003

Working with the extended framework of stochastic integrals recently discovered by Itô, a complex of stochastic processes inherent in quantum mechanics, the Nelson process, is characterized in terms of sample paths. It is shown that the Nelson process belongs to a certain class of two-sided continuous local semimartingales. Several basics of stochastic calculus in this class are presented. Stochastic calculus of variations is applied in this class to construct the Nelson process and to further illustrate some details of its sample paths. Examples are the bound states, the two-slit interference, and the gravity in quantum mechanics.
On Jacobi’s decomposition of the motion of a heavy symmetrical top into the motions of two free triaxial tops
Authors: Yamada K. , Shieh S.
Published: March 2003

Jacobi discovered that the motion of a heavy symmetrical top can be decomposed into the motions of two torque-free triaxial tops. In this paper we investigate the connection between the three sets of the dynamical constants in the three top motions. The formulas connecting these constants are found to be projective transformations (fractional linear transformations).
Vector fields generating analysis for classical dissipative systems
Authors: Cantrijn F.
Published: March 2003

A class of vector fiels is identified which (locally) generate first integrals of a dissipative system. The structure of these vector fields and of the corresponding invariants is studied. The relationship with a previously proposed generalization of Noether’s theorem for nonconservative systems, is pointed out.
Root parities and phase behavior in the slow-fluctuation technique
Authors: Augusteijn Marijke F. , Breitenberger Ernst
Published: March 2003

The slow-fluctuation technique for integrating autonomous, conservative, nonlinear, near-resonant oscillatory systems of many degrees of freedom requires ultimately no more than the study of a certain polynomial. It is shown that a paritylike property can be attributed to the roots of this polynomial, which proves helpful in even the most complex situations. It aids to classify the solutions of the equations of motion in terms of ’’representatives’’ which involve only one-half of the integration constants, the other half being rather unimportant physically, and it allows one to start up the representative motions from representative initial conditions. It also leads to a characterization of phase behavior which in particular describes not only the constant-amplitude motions but also their dynamical neighborhoods, and in many cases it explains gross features of the motion such as the occurrence of Lissajous-like patterns and orbit reversals.
Irreducible representations of SU(m/n)
Authors: Hurni J.-P. , Morel B.
Published: March 2003

Typical and atypical representations of SU(m/n) are worked out in an explicit and pedestrian way. Examples are given.
A constructive approach to bundles of geometric objects on a differentiable manifold
Authors: Ferraris M. , Francaviglia M. , Reina C.
Published: March 2003

A constructive approach to bundles of geometric objects of finite rank on a differentiable manifold is proposed, whereby the standard techniques of fiber bundle theory are extensively used. Both the point of view of transition functions (here directly constructed from the jets of local diffeomorphisms of the basis manifold) and that of principal fiber bundles are developed in detail. These, together with the absence of any reference to the current functorial approach, provide a natural clue from the point of view of physical applications. Several examples are discussed. In the last section the functorial approach is also presented in a constructive way, and the Lie derivative of a field of geometric objects is defined.
Gödel-type universe with a perfect fluid and a scalar field
Authors: Chakraborty S. K. , Bandyopadhyay N.
Published: March 2003

The paper contains, along with a brief review of solutions of general relativistic field equations when the metric is of a particular cylindrically symmetric stationary form, a new solution of the same general category when the energy-momentum tensor is due to a perfect fluid plus a scalar field. It turns out that under these constraints, the space-time is completely homogeneous and contains closed timelike lines. There is, however, a nonuniqueness in the interpretation as one can introduce a Maxwellian electromagnetic field of arbitrary strength along with the perfect fluid and the scalar field.
Existence of solutions of integral equations in the thermodynamics of one-dimensional fermions with repulsive delta function potential
Authors: Lai C. K.
Published: March 2003

We prove by an iteration scheme that the solutions of coupled integral equations in the thermodynamics of the fermions in one dimension with delta function potential exist.
Oscillatory magnetohydrodynamic flow and heat transfer between conducting plates
Authors: Soundalgekar V. M. , Bhat J. P.
Published: March 2003

An approximate solution of the oscillatory flow of an electrically conducting fluid, between two parallel and electrically conducting plates and under transversely applied magnetic field, is given for the transient velocity, the transient magnetic field, amplitude and the phase of the skin friction and the rate of heat transfer. It is observed that the transient flow, amplitude, and the phase of the skin-friction and the rate of heat transfer are affected by the individual electrical conductance ratios of the plates, which is not so in the case of steady magnetohydrodynamic (MHD) channel flow between conducting plates.
Direct approach to the periodic solutions of the multidimensional sine–Gordon equation
Authors: Zagrodziński J.
Published: March 2003

A number of identities for multidimensional theta functions and their derivatives are derived. Application to the nonlinear partial differential equations is exemplified for the sine–Gordon equation. In consequence, the multidimensional sine–Gordon equation can be reduced to a functional equation, and then to a set of algebraic equations. Several particular cases are also discussed.
On the stability problem of a pair of adjoint operators
Authors: Löwdin Per-Olov
Published: March 2003

As an introduction, the eigenvalue problem for a linear operator T having a discrete point spectrum and a complete set of eigenfunctions is studied. The bivariational principle for T and its adjoint operator T° is derived, and the biorthogonal properties of their eigenfunctions are discussed. The main part of the paper is then concerned with the problem whether these features can be extended also to a general pair of adjoint operators, T and T°, in which case the eigenvalue problem is replaced by the more general stability problem. The stability problem for a pair of adjoint operators—T and T°—is first formulated in terms of nonorthogonal projectors—O and O°—which decompose these operators and satisfy the commutation relations TO=OT and T°O°=O°T°. In the case of a finite space, these skew-projectors may be explicitly expressed in product forms derived from the reduced Cayley–Hamilton equation for the operator T. It is shown that, if the stable subspaces defined by these projectors are properly classified by their Segre characteristics, one may explicitly derive the form of the projectors for the irreducible stable subspaces associated with the individual Jordan blocks of the so-called classical canonical forms of the matrix representations of T and T°. It is further shown that, in such a case, the biorthonormality property of the generalized eigenfunctions is still valid, and that a bivariational principle may be derived. The extension of these results to infinite spaces is finally briefly discussed.
On the binary collision expansion and resummations of it
Authors: Royer Antoine
Published: March 2003

It is pointed out that when there are only two interaction terms in the Hamiltonian, the binary collision expansion (BCE) for the scattering operator can be resummed into a closed form. When there are more than two interaction terms, one can resum the BCE into a continued-fraction-like form by using repeatedly the two interactions resummation. Concise derivations of the BCE are first given, the time-dependent BCE being obtained in a form applicable to both quantum evolution operators and classical frequency modulated oscillators.
A class of finite-dimensional Lie algebras, the Casimir operators of which are not of finite type
Authors: Berdjis F.
Published: March 2003

A class of complex finite-dimensional Lie algebras is constructed, the center of the universal enveloping algebra of each element of which is not finitely generated. For the construction of these Lie algebras, we use the counterexample of Nagata answering Hilbert’s 14th problem in the negative.
Transient fields in dispersive media
Authors: Marx Egon
Published: March 2003

The problem addressed in this paper is the determination of transmitted and scattered fields produced by a transient electromagnetic field incident on a three-dimensional body when the body and the surrounding medium are allowed to be dispersive. Instead of decomposing the pulse into its Fourier components, the solution is carried out in the time domain to take advantage of marching-in-time procedures. Maxwell’s equations are suitably modified, and the reduction of the problem to the solution of an integral equation for a single tangential vector field is adapted to dispersive media. A simple conductor and a collisionless plasma are studied as examples.
Generalized two-dimensional O(3) sigma model
Authors: Arik M. , Neyzi F.
Published: March 2003

We generalize the two-dimensional O(3) nonlinear σ-model while preserving its conformal invariance. The integrability condition of this model encompasses the sine-Gordon equation in addition to some special cases which are found to be of the same form. The time-independent solutions exhibit solitonlike behavior.
First-order equations of motion for classical mechanics
Authors: Skinner Ray
Published: March 2003

A global canonical first-order equation of motion is derived for any mechanical system obeying Newton’s second law. The existence of a Lagrangian is not assumed, but the properties of the canonical equation are similar to those of the Hamiltonian formulation. The choice of map F from velocity space to phase space is not determined by the condition that the first-order equation of motion be equivalent to a second-order equation on configuration space and therefore is left open to be selected on the basis of other considerations. The canonical equation is a covector or 1-form equation on the Whitney sum T*Q⊕TQ and contains the second-order equation condition, restriction to the graph of the map F, and Newton’s equation of motion in first-order form. The last is related to Newton’s second-order equations by the consistency condition that the motions not lead off graph F in T*Q⊕TQ. The first-order equation of motion can be projected onto phase space if the map F can be inverted.
A one-fixed-point Killing parameter transform
Authors: Krisch J. P.
Published: March 2003

A single fixed-point transformation which generates solutions to the field equations is discussed. The method is applied to several examples.
A dense set of cyclic vectors for quantum field polynomial algebras
Authors: Driessler Wulf , Summers Stephen J.
Published: March 2003

It is shown that in the Hilbert space of a quantum field theory with a nonzero mass gap there exists a dense set of vectors, each entire analytic for the energy–momentum operators, that are cyclic for the polynomial algebra 𝒫(Rd) [and for the local polynomial algebras 𝒫(𝒪), for any nonempty 𝒪 ⊆ Rd]. It is proven that for every vector Φ from this dense set there exists an element Q ∈ 𝒫(Rd) such that QΦ=Ω, where Ω is the vacuum, and QΩ=0. A similar, stronger result is proven for free field theories (including mass zero).
Galilean field theories and nonlocal S-matrix symmetries
Authors: Garber Wolf-Dieter
Published: March 2003

Any operator that commutes with the S matrix and is additive, i.e., transforms an asymptotic incoming n-particle state as a sum of its constituent one-particle states, is called a symmetry of the S matrix. The structure of local S-matrix symmetries in Galilean field theories is known. In this paper, S-matrix symmetries that are nonlocal, i.e., may transform asymptotic fields into nonlocal operators, are investigated under the assumption that there is a finite number of such symmetries in the theory.
Unitary representations of the (4+1)-de Sitter group on irreducible representation spaces of the Poincaré group
Authors: Moylan P.
Published: March 2003

The construction of the principal continuous series of unitary representations of the simply-connected covering group of the (4+1)-de Sitter group on unitary irreducible representation spaces of the Poincaré group is presented. A unitary irreducible representation space of this covering group of the de Sitter group is realized as the direct sum of two irreducible representation spaces of the Poincaré group. Possible physical implications are indicated. In particular, an interpretation of the instantaneous velocity operator in the Dirac theory as the spin part of the de Sitter boosts is given. We obtain a simple method of computing the matrix elements of the generators of the de Sitter group in an SO(4) basis using the matrix elements of the generators of the four-dimensional Euclidean group. Also we obtain explicit expressions for certain matrix elements between the spinor and SO(4) basis of the representation space as functions on the coset space SO(4)/SO(3).
General indices of simple Lie algebras and symmetrized product representations
Authors: Okubo S. , Patera J.
Published: March 2003

In many branches of physics, it is important to know the decomposition of a product representation ρ⊗ρ⊗⋅⋅⋅⊗ ρ (n times) of identical representations ρ of a simple Lie algebra into irreducible components with a given Young tableau symmetry. We show that the notion of representation indices introduced elsewhere is a very useful tool in dealing with this problem. We calculate explicit formula for general pth order indices D( p) ( ρ) for all classical simple Lie algebras. Sixth-order indices for exceptional Lie algebras are also discussed.
Some properties of the eigenfunctions of the dilated model Hamiltonians with complex potentials
Authors: Froelich Piotr
Published: March 2003

A pair of operators H(θ) and H(θ*) obtained by dilation into opposite directions of a model Hamiltonian with nonreal potential is considered. Relations between the resonant eigenfunctions of H(θ) and H(θ*) are studied.
Rational von Neumann lattices
Authors: Boon M. , Zak J. , Zucker I. J.
Published: March 2003

A rational von Neumann lattice is defined as a lattice in phase space with the constants a and b in the x and p directions given by a ratio of integers. Zeros of harmonic oscillator functions in the kq representation on such lattices are found. It is shown that the number of zeros of the kq function determines the number of states by which a set on a von Neumann lattice is overcomplete. Interesting relations between theta functions are derived on the basis of their connection with the harmonic oscillator states in the kq representation.
Verification of the global Markov property in some class of strongly coupled exponential interactions
Authors: Gielerak Roman
Published: March 2003

We verify the global Markov property in some class of strongly coupled exponential interactions in two-dimensional space-time. To obtain this result we apply the Albeverio and Ho/egh-Krohn strategy. The basic ingredients we use in order to employ this strategy are the Fortuin–Kastelyn–Ginibre correlation inequalities.
Normalization of the three-body Bethe–Salpeter wavefunction for protons
Authors: Tomozawa Yukio
Published: March 2003

We discuss the normalization condition for a three-body Bethe–Salpeter amplitude and apply the result to the relativistic wave function for protons.
Recursive formulas for Morse-oscillator matrix elements of arbitrary powers of 1−exp[−a(r−r
e)]
Authors: Tran Loc Binh , Huffaker J. N.
Published: March 2003

The variable y=1−exp[−a(r−re)] is a natural one to use in connection with a Morse oscillator. A simple formula is derived via the factorization method relating the Morse matrix element 〈0‖ yn ‖0〉 to 〈0‖yn−1 ‖0〉 and 〈0‖yn−2‖ 0〉. Another simple formula is derived, with which all matrix elements 〈v′‖yn ‖v〉 can be calculated recursively, starting from values of 〈0‖yn‖ 0〉.
Path integral approach to multiple scattering
Authors: Gross Eugene P.
Published: March 2003

Multiple scattering of a wave in a system of scatterers with random, uncorrelated positions is studied with path integrals. The Edwards–Gulyaev expression for the position averaged Green’s function is used to find the density expansion of the complex optical potential. The expansion is in terms of exact medium propagators and scattering matrices in the medium. The first term is the coherent potential approximation. A source dependent generalization of the path integral is used to derive a functional equation for the optical potential. This leads to a hierarchy for correlation functions that involves exact medium propagators and scattering matrices. The simplest truncations yield new integral equations that are generalizations of the coherent potential approximation and are compatible with the density expansion.
Reduction of inner-product representations of unitary groups
Authors: Nikam R. S. , Dinesha K. V. , Sarma C. R.
Published: March 2003

A direct method for the reduction of inner products of irreducible representations (irreps) of unitary groups has been proposed using the duality between the permutation and unitary groups. A canonical tensor basis set has been used to obtain a closed expression for the Clebsch–Gordan coefficients of U(n). This expression involves the subduction coefficients arising in the outer-product reduction of SN1⊗SN2→SN1+N2 of the permutation groups, the symmetrization coefficients of U(n), and matrix elements of the standard representation of SN. The expression holds good for an inner-product reduction of irreps of U(n), and is independent of n. The method has been illustrated with examples.
Practical use of the Hamilton–Jacobi equation
Authors: Chodos Alan , Sommerfield Charles M.
Published: March 2003

We show by means of several examples how the Hamilton–Jacobi equation can be used to solve nonlinear ordinary differential equations whose direct integration is otherwise difficult.
Extended test particles in geometric fields
Authors: Toller M.
Published: March 2003

We treat the motion of an extended spinning test particle interacting with external fields belonging to a large class, which includes curvature, torsion, Maxwell, and Yang–Mills fields. We use a unified geometric description of all these fields based on a multidimensional space which generalizes the principal fiber bundle of the Lorentz frames. Guided by the work of Dixon, we give suitable definitions of the energy, the momentum, the angular momentum, the charge, and the isotopic spin of the extended particle, and we derive exact equations for the derivatives of these quantities. We discuss the pole–dipole approximation, and we compare our results with the special cases treated by other authors.