bluuebunny/crossref_metadata_2025 huggingface dataset:
Decay mode solution of the two-dimensional KdV equation and the generalized Bäcklund transformation
Authors: Nakamura Akira
Published: March 2003

We consider the generalization of the customary Bäcklund transform (≡BT) for the two-dimensional (2D) KdV equation, (ut+6uux+uxxx)x +3α2uyy = 0, with α being constant. A nonlinear superposition formula has been obtained and it is shown that the present generalized BT can produce multiple soliton–multiple decay mode solutions.
Evolution equations associated with the discrete analog of the matrix Schrödinger spectral problem solvable by the inverse spectral transform
Authors: Bruschi M. , Ragnisco O. , Levi D.
Published: March 2003

Through the generalized Wronskian technique we derive the whole class of nonlinear differential difference equations associated with the discrete analog of the matrix Schrödinger spectral problem. For such equations we briefly discuss soliton solutions, continuum limit, and Bäcklund transformations.
Some properties of Borel summable functions
Authors: Auberson G. , Mennessier G.
Published: March 2003

Classes of Borel summable functions are defined and studied. Some properties of these functions, which are useful for high-order calculations pertaining to certain physical theories, are proved and discussed. They include reciprocal Watson-like theorems, sufficient conditions for membership in the classes, and asymptotic behaviors of the expansion coefficients after composition of functions.
An expansion of the moments of powers of a Fermi distribution
Authors: Krivine H. , Treiner J.
Published: March 2003

We derive an expansion of the moments of the νth power of a Fermi distribution for any real value of ν in powers of the ratio of the surface thickness to the radius of the distribution. For ν = 1 we recover the Sommerfeld lemma.
Irreducible representations of the complex rotation group in terms of the axis and angles of rotations
Authors: Joshi K. N. , Rajput B. S.
Published: March 2003

The expression for matrix elements corresponding to finite complex rotations have been derived in terms of the complex Euler angles of the complex rotations. Using this expression the values of matrix elements for special cases of eigenvalues of complex angular momentum operator have been computed.
Modified Hamiltonian systems and canonical transformations arising from the relationship between generalized Zakharov–Shabat and energy-dependent Schrödinger operators
Authors: Alonso L. Martínez , Guerrero F. Guil
Published: March 2003

A new family of completely integrable infinite-dimensional Hamiltonian systems is found. Two canonical maps are deduced which transform this family into the families of Hamiltonian systems associated with the generalized Zakharov–Shabat and energy-dependent Schrödinger operators. Through these maps several relevant Hamiltonian structures are connected. In particular, a simple explanation of the second Hamiltonian structure for AKNS equations is given.
Classification scheme for two-dimensional Ermakov-type systems and generalizations
Authors: Sarlet W. , Ray J. R.
Published: March 2003

We describe a classification scheme for certain pairs of coupled, nonlinear second-order ordinary differential equations, having a first integral which can be obtained by an Ermakov-type elimination procedure. The classification produces a hierarchy of systems having different levels of generality. Different cases within the same level are distinguished by the integrability of a certain one-form, which is related to a nonlinear superposition law between the two equations. The study of these one-forms and the classification are made systematic by using the general reduction theorem of Pfaffian forms. The paper contains illustrations of the way previous examples fit into the classification scheme, and a discussion of its generalization to higher dimensions.
Wigner 9j symbols and the product group
Authors: Earp C.
Published: March 2003

The 9 j symbols of a simply reducible Lie group G are related to the 3 j symbols of the product group G×G. It is shown that this relationship leads to certain identities satisfied by the 9 j symbols. Two known identities involving 6 j and 9 j symbols are shown to be reduced forms of a new identity involving 9 j symbols.
Nonscalar extension of shift operator techniques for SU (3) in an O(3) basis. II. Applications
Authors: De Meyer H. E. , Vanden Berghe G. , Hughes J. W. B.
Published: March 2003

In a preceding paper relations have been derived which connect nonscalar quadratic shift operator products. Here, the extreme usefulness of these relations is demonstrated by the example of the O0l -eigenvalue calculation for the cases l = p−i (i = 0,1,2,3, and 4), where ( p,q) is any SU (3) representation. For the first time a case of threefold l-degeneracy is completely solved in a pure analytical way.
Wigner coefficients for a semisimple Lie group and the matrix elements of the O(n) generators
Authors: Gould M. D.
Published: March 2003

A purely algebraic infinitesimal method for obtaining multiplicity-free Wigner coefficients is presented. The method is applied to obtain analytic expressions for the complete matrix elements of all O(n) generators. Moreover the structure of these matrix elements in terms of reduced matrix elements, Wigner coefficients, and reduced Wigner coefficients is made explicit. By comparison with the Wigner–Eckart theorem explicit analytic expressions are obtained for the fundamental Wigner coefficients of O(n). Finally the results are presented in a form which is directly analogous with the corresponding results for U(n).
Classical and quantal systems of imprimitivity
Authors: Giovannini N.
Published: March 2003

We discuss from a group-theoretical point of view, a simple framework in which the classical and the quantal state spaces appear in a unified way. The framework is characterized by the use of (possibly continuous) direct unions of Hilbert spaces. Symmetries are correspondingly represented by families of (anti-) unitary operators. We consider here the associated notions of projective representations as well as the corresponding observables. These observables, classical or quantal, are defined in terms of a slight generalization of the notion of a system of imprimitivity of Mackey.
State spaces for classical and quantal, relativistic and nonrelativistic elementary particles
Authors: Giovannini N.
Published: March 2003

We apply a recently developed mathematical formalism to the kinematical classification of elementary physical systems, more precisely to the derivation of the possible state spaces for single (massive) particles and to their corresponding group theoretical interpretation. We show in particular that in all considered cases, relativistic or not, we find in a unified way two solutions, a quantal one and a classical one.
Noncomplex representations and their relation to antiunitary symmetry
Authors: Kasperkovitz P. , Kahl G.
Published: March 2003

Equivalent eigenvalue problems in real, complex, and quaternionic Hilbert spaces are discussed. In all cases a compact symmetry group is assumed to exist, in the complex case also an antiunitary operator ϑ commuting with both the self-adjoint operator and the elements of the symmetry group and satisfying ϑ2 = ±1. It is shown that the extra degeneracies caused by the existence of ϑ can also be obtained by consideration of an equivalent eigenvalue problem in a noncomplex Hilbert space.
Analytic evaluation of certain zeroth order coulombic hyperangular interaction integrals
Authors: Demiralp Metin , Baykara N. Abdülbaki
Published: March 2003

As has been presented in a previous paper, the use of hyperspherical coordinates in research on a system of electrically charged particles carries mathematical complications into the evaluation of certain kinds of hyperangular interaction integrals. These integrals contain the hyperangular interaction potential and various powers of the inverse of the total angular momentum operator on the space of hyperharmonics, from which the zeroth order hyperharmonic is excluded. In this work the simplest one of these integrals has been taken into consideration. After some intermediate steps, it has been shown that it can be expressed in terms of elementary functions of the cosine of the angle (γ) between the hyperaxes of the potential term for an odd number of particles. In the case of an even number of particles, these integrals can be given in terms of a generalized hypergeometric function of the same argument (γ) and its derivatives.
A note on helicity
Authors: Bialynicki-Birula Iwo , Newman E. T. , Porter J. , Winicour J. , Lukacs B. , Perjes Z. , Sebestyen A.
Published: March 2003

We give a formal definition of the helicity operator for integral spin fields, which does not involve their momentum-space decomposition. We base our discussion upon a representation of the Pauli–Lubanski operator in terms of the action on tensor fields by the Killing vectors associated with the generators of the Poincaré group. This leads to an identification of the helicity operator with the duality operator defined by the space–time alternating tensor. Helicity eigenstates then correspond to self-dual or anti-self-dual fields, in agreement with usage implicit in the literature. In addition, we discuss the relationship between helicity eigenstates, which are intrinsically nonclassical, and states of right or left circular polarization in classical electrodynamics
Bound states of a classical charged nonlinear Dirac field in a Coulomb potential
Authors: Rañada Antonio F. , Uson Juan M.
Published: March 2003

The electromagnetic self-interaction of a bound classical nonlinear Dirac field in a Coulomb potential is studied. It is shown that by a finite renormalization procedure the radiative corrections can be eliminated at order α2, after which the energy levels coincide with those of the hydrogen atom.
A model of a quantum mechanical treatment of measurement with a physical interpretation
Authors: Schroeck Franklin E.
Published: March 2003

Projections onto minimum uncertainty states for Weyl systems are interpreted as being associated with elementary particles. This identification yields physically motivated definitions of measurements, instruments, and observables, which, in turn, lead to a quantum mechanical treatment of instruments, a divergence from the von Neumann collapse scheme of measurement, a framework for simultaneous measurement of position and momentum, and a derivation of action-at-a-distance—all consequences of the uncertainty relations.
All nontwisting N’s with cosmological constant
Authors: Díaz A. García , Plebański J. F.
Published: March 2003

The set of all essentially different nontwisting type-N solutions with cosmological constant is presented in such a tetrad gauge and coordinatization that the metric depends linearly on an arbitrary structural function. The special branches of the solutions of this type are shown to amount to the contractions of the most general branch.
On the existence of simultaneous synchronous coordinates in spacetimes with spacelike singularities
Authors: Wald Robert M. , Yip Ping
Published: March 2003

We investigate the issue of when a synchronous coordinate system exists which entirely covers a singularity simultaneously. For a spacetime with a spacelike singularity (or, more precisely, with a spacelike causal boundary) we prove that such coordinates exist if and only if the ’’maximum lifetime function’’ satisfies certain boundedness, differentiability, and limit properties. Our results lend plausibility to the validity of the use of simultaneous synchronous coordinates to analyze physically realistic spacelike singularities. Nevertheless, we construct a number of examples which do not satisfy our conditions and thus do not admit such coordinates.
Transformation modified singular spherical integrals for an arbitrarily time-dependent charged particle in a crystal
Authors: Chee-Seng Lim
Published: March 2003

A charged particle activates inside a crystalline medium and, thereafter, acts with an arbitrary time-dependent amplitude factor. Both electric and magnetic anisotropies coexist. Corresponding sets of permittivity and permeability principal axes are unaligned. A scalar field is subsequently formulated as the difference between two quadruple Fourier integrals. Each of these is first subjected to a separate transformation of the wavevector variable. It is then reduced to a singular spherical integral. This leads to the establishment of (i) a deactivation by-product of a dark core, (ii) induction of in-phase modes. Other, more general, singular spherical integrals are next deduced. Applications are then made to the compounded uniaxial medium; results are physically and geometrically interpreted.
Three-dimensional relativistic scattering of electromagnetic waves by an object in uniform translational motion
Authors: Michielsen B. L. , Herman G. C. , de Hoop A. T. , de Zutter D.
Published: March 2003

A general, relativistic formalism is developed for the three-dimensional scattering of electromagnetic waves by an object that is in uniform translational motion with respect to a source of electromagnetic radiation. The theory applies to objects of arbitrary size, shape, and physical composition. In particular, the temporal frequency spectrum of the field detected by a receiver that is stationary with respect to the source is determined. Numerical results pertaining to the scattering of a time-harmonic plane wave by a small, uniformly moving particle are presented.
The uniqueness of gravity as a Poincaré or Lorentz gauge theory
Authors: McKellar R. J.
Published: March 2003

The uniqueness of the Einstein–Cartan–Sciama–Kibble theory is examined using a concomitant approach. The demand that the Lagrangian be a scalar density under coordinate transformations and a scalar under Poincaré or Lorentz gauge transformations as well as be degenerate in the order of the Euler–Lagrange expressions determines a class of Lagrangians whose Euler–Lagrange equations reduce essentially to the Einstein vacuum field equations with cosmological term.
A statistical approach to perturbation theory and inverse-energy-weighted sum rules
Authors: Halemane Thirumala Raya
Published: March 2003

A distribution function formalism is developed for perturbation theory and inverse-energy-weighted sum-rules (IEWSR). The second-order perturbation is linear in the CLT (central limit theorem) limit. A polynomial expansion is also developed for the same. Finally, some applications are indicated.
A calculation of the Casimir force on a circular boundary
Authors: Sen Siddhartha
Published: March 2003

The zero point energy of a three-dimensional scalar field in the presence of a circular boundary of radius R is calculated using a Green’s function method. It is found that the energy is cutoff-dependent. The cutoff-dependent terms are explicitly calculated in terms of the geometry of the problem. It is found that E(ω0) = + 0.045/2R + (S/4π) ω20 −[(1/256)] ℱc2(s) ds] lnω0R, where S is the length of circular boundary (S = 2πR), c(s) the curvature of the boundary [c(s) = 1/R], and ω0 is the cutoff frequency.
Application of a stochastic waveguide propagation model to ocean acoustics
Authors: Sutton G. R.
Published: March 2003

The problem of interest is the long-range (low-frequency) propagation of acoustic signals through the ocean. The loss of spatial coherence of the signal as a result of scattering by large scale internal waves leads to a limitation on the resolution of the direction of the source of the signal. The applicability of a stochastic waveguide propagation model to this problem in ocean acoustics is investigated.
Inequalities in isotropic homogeneous turbulence theory
Authors: Rosen Gerald
Published: March 2003

It is postulated that the energy spectrum function is the Laplace transform of a nonnegative distribution φ. The principal physical parameters in the longitudinal correlation function are then expressed in terms of φ integrals and interrelated by Hölder inequalities, to yield experimentally confirmed results like Lp⩾1.825λ.
Electrostatic structural transitions in a Gaussian Wigner solid
Authors: Hall George L.
Published: March 2003

A derivation is supplied for a functional relation between the Fuchs energy ε and the Madelung energy S for a Gaussian Wigner solid (GWS) in which the usual uniform background of a Wigner solid (WS) is replaced by a periodic array of Gaussians with variable ’’ripple’’ parameter p allowing the WS and the empty lattice in the limits of small p and large p, respectively. It is the zeros of Δε, and not of ΔS, that are relevant for structural transitions between two lattices. Much can be determined about the transitions with minimal computations by utilizing a modest amount of information about order relations on certain theta functions. With increasing p, the sequence of lowest-energy structures restricted to the cubics is bcc, fcc, and sc. A later report will treat the Yukawa WS (YWS) in which the Gaussians are replaced with Yukawa distributions. The functional relation is again derivable, and it is not given by Medeiros and Mokross’s recent assumption that 2εYWS = SYWS.
The Peierls–Griffiths argument for disordered Ising systems
Authors: Roepstorff Gert
Published: March 2003

We study Ising systems with random competing ferromagnetic and antiferromagnetic nearest neighbor interaction on a simple cubic lattice of arbitrary dimension. We use a version of the Peierls–Griffiths argument to prove the existence of a ferromagnetic phase and derive lower bounds for the critical concentration of antiferromagnetic bonds.
An axiomatic system for Minkowski space–time
Authors: Schutz John W.
Published: March 2003

Minkowski space–time is developed in terms of a set of undefined primitive elements called events, certain subsets of events called paths which correspond to the worldlines of free particles, and a temporal order relation on each path. Nine axioms describe the existence and uniqueness of paths, temporal order, connectedness, causality, collinearity, continuity, isotropy, and dimension.
The spreading of free wave packets and the entropy of position
Authors: Grabowski Marian
Published: March 2003

The spreading of free wave packets is expressed by means of the entropy of position for a certain class of states. Connection between such formulation and the usual treatment is discussed.
Source equivalency based on the energy specification of order l
Authors: Dolzycki Stanislaw J.
Published: March 2003

It is shown that the multipole expansion of electrostatic energy can be expressed in the form of energy specification S{We} =〈[P]l,∇(l)φ〉, where ∇(l) is a differential operator, whereas φ and [P]l represent an arbitrary test potential and equivalent reduced volume multipole density, respectively. Two electrostatic sources are l-equivalent if their energy specifications are identical. The formalism by means of which electrostatic multipole sources can be effectively handled is developed.
Space-time algebra approach to curvature
Authors: Sobczyk G.
Published: March 2003

Introducing the notions of vector and bivector differentiation into the Dirac algebra, considered as a Clifford algebra, makes possible an extremely concise and geometrically transparent treatment of the curvature tensor and its properties, and of related topics such as Lorentz invariants, characteristic equations, Petrov types, and principal null directions by explicit construction.
Statistical mechanics and the gravothermal catastrophe
Authors: Cally P. , Monaghan J. J.
Published: March 2003

Jensen’s inequality is applied to the canonical partition function of a self-gravitating system to determine the best independent particle potential. The inequality allows the stability to be analyzed very easily. We recover the results of Lynden-Bell and Wood for the onset of an instability in an isothermal sphere in a heat bath. Our eigenvalue analysis leads to results very similar to those of Horwitz and Katz, but we differ in the description of the l=1 perturbation.
A decomposition theorem for finite-dimensional Hermitian projections
Authors: Giannoni M. J.
Published: March 2003

We investigate conditions for the existence of a decomposition of a Hermitian projector ρ into two Hermitian and time-reversal invariant operators ρ0 and χ under the form ρ=eiχ ρ0 e−iχ. Sufficient conditions are given and an explicit construction of a decomposition is performed when they are fulfilled. A stronger theorem of existence and uniqueness is studied.
Reduction of the CP
N nonlinear sigma model
Authors: Eichenherr H. , Honerkamp J.
Published: March 2003

Using the concept of gauge equivalence of two-dimensional classical field theories, we reduce the cPN nonlinear σ model to a system of 2N−1 independent real fields obeying relativistic field equations.
Gaussian states on the algebra of the infinite classical system
Authors: Naudts J.
Published: March 2003

A class of states on the algebra of the infinite classical system is characterized by the vanishing of the higher order (n≳2) truncated correlation functions. The states are called Gaussian. It is shown how liquids and crystals can be described by Gaussian states.
Realization, extension, and classification of certain physically important groups and algebras
Authors: Salingaros Nikos
Published: March 2003

An associative algebra of differential forms with division has been constructed. The algebra of forms in each different space provides a practical realization of the universal Clifford algebra of that space. A classification of all such algebras is given in terms of two distinct types of algebras Nk and Sk. The former include the dihedral, quaternion, and Majorana algebras; the latter include the complex, spinor, and Dirac algebras. The associative product expresses Hodge duality as multiplication by a basis element. This makes possible the realization of higher order algebras in a calculationally useful algebraic setting. The fact that the associative algebras, as well as the enveloped Lie algebras, are precisely those arising in physics suggests that this formalism may be a convenient setting for the formulation of basic physical laws.
The Racah algebra for groups with time reversal symmetry
Authors: Newmarch J. D. , Golding R. M.
Published: March 2003

The elements of the Racah algebra for a general compact group with time reversal symmetry are developed. As time reversal is antilinear it is not possible to treat these groups by representation theory but we may instead use Wigner’s theory of corepresentations. The results we obtain often parallel those for linear groups but there are some important divergences. We illustrate these with the grey double point groups.
Subgroups of Lie groups and separation of variables
Authors: Miller W. , Patera J. , Winternitz P.
Published: March 2003

Separable systems of coordinates for the Helmholtz equation ΔdΨ =EΨ in pseudo-Riemannian spaces of dimension d have previously been characterized algebraically in terms of sets of commuting second order symmetry operators for the operator Δd. They have also been characterized geometrically by the form that the metric ds2=gik(x)dxidxk can take. We complement these characterizations by a group theoretical one in which the second order operators are related to continuous and discrete subgroups of G, the symmetry group of Δd. For d=3 we study all separable coordinates that can be characterized in terms of the Lie algebra L of G and show that they are of eight types, seven of which are related to the subgroup structure of G. Our method clearly generalizes to the case d≳3. Although each separable system corresponds to a pair of commuting symmetry operators, there do exist pairs of commuting symmetries S1,S2 that are not associated with separable coordinates. For subgroup related operators we show in detail just which symmetries S1,S2 fail to define separation and why this failure occurs.
Generating functions for SU(2) plethysms with fixed exchange symmetry
Authors: Patera J. , Sharp R. T.
Published: March 2003

A number of fixed-plethysm generating are given for SU(2); a fixed -plethysm generating function gives the content of the component with definite exchange symmetry of the direct product of a given number of copies of an irreducible representation Rl, with l running through all values. New symmetries are found relating antisymmetric to symmetric products, and relating plethysms in which the number of factors is interchanged with the factor representation label l. Expressions for two-box plethysm generating function for SU(3) and for fixed-plethysm generating functions for SU(2) based on reducible representations are also given.
General U(N) raising and lowering operators
Authors: Gould M. D.
Published: March 2003

It is the aim of this paper to obtain the general form of U(n) raising and lowering operators. The raising and lowering operators constructed previously by several authors are then compared. The Hermiticity properties of these operators are also investigated. The methods presented extend, with trivial modifications, to the orthogonal groups.
Expansion of a function about a displaced center
Authors: Rashid M. A.
Published: March 2003

An extremely simple closed expression is obtained for the coefficients which appear in the expansion of a function of a special type about a displaced center. A conjecture about the vanishing of a certain coefficient which appear in the expansion of a Slater-type orbital about a displaced center is also proved.
On some properties of solutions of Helmholtz equation
Authors: Ramm A. G.
Published: March 2003

We give a new method to prove results of the following type. Let: (∇2 + k2)u=0 in DR={x‖x‖?R}, k2≳0. (1) If u∈L2(DR), then u≡0 in DR. (2) If ‖x‖mu(x)→0 as ‖x‖→∞, x21+⋅⋅⋅+x2N−1?cx−2pN ,p≳0, m=1, 2, 3,..., ‖x‖[(∂u/∂‖x‖)−iku‖x‖→∞]→0, then u≡0 in DR.
Gauge equivalence of exactly integrable field theoretic models
Authors: Honerkamp J.
Published: March 2003

Exactly integrable field theoretic models are constructed which are gauge equivalent to the n-component or m⋅n component nonlinear Schrödinger equations and to the O(n) nonlinear σ-model. We obtain the CPn- Heisenberg model or the Grassmann–Heisenberg model and the generalized sine-Gordon model respectively. Consequences for the conserved quantities are discussed.
A new expression for the high-energy upper bound on the scattering amplitude
Authors: Chaichian Masud , Fischer Jan , Molodensky S. M. , Nelipa N. F. , Vrkoč Ivo
Published: March 2003

The two Froissart–Martin high-energy upper bounds for forward and nonforward scattering are combined into one formula under the additional assumption that the scattering amplitude is polynomially bounded in energy for all scattering angles inside the Lehmann–Martin ellipse. The method used presents a modification of that of Kinoshita, Loeffel, and Martin. The analogous bound for the scattering of particles with spin is obtained as well. Using the same method, a bound for the case of complex scattering angles is also derived and ways leading to its improvement by using the solution of the Dirichlet problem are suggested.
Integrals over the Fermi function
Authors: Rockmore R.
Published: March 2003

A method for evaluating integrals over the Fermi distribution function using results from Mellin–transform theory is presented. The connection of this approach with the operational result of Blankenbecler is explicated. The method is used to calculate the profile function for a Fermi distribution.
Perturbation methods for the (almost) zero modes and the Green’s function in an instanton gas background
Authors: Hietarinta Jarmo , Nemeschansky Dennis
Published: March 2003

We formulate an approximation method which can be used to compute the almost zero modes and the generalized Green function in the background of an approximate instanton gas solution. The main problem of choosing the starting point is solved by requiring that the zeroth-order operator H0 annihilates the original isolated single-instanton zero modes. The zeroth-order approximation to H−10, on the other hand, is constructed from the free Green’s function with local bumps provided by the one-instanton Green’s function.
On decoupling of finite singularities in the scattering theory for the Schrödinger operator with a magnetic field
Authors: Perelmuter M. A. , Semenov Ya. A.
Published: March 2003

In this paper, the authors extend the theory of the effect of local singularities on scattering theory to include magnetic fields.
Self-adjointness and spectrum of Hamiltonians in nonrelativistic quantum electrodynamics
Authors: Arai Asao
Published: March 2003

The nonrelativistic quantum electrodynamics is formulated in a mathematically rigorous way. The self-adjointness and the basic spectral property of the Hamiltonians are proved.
Contacts of space–times
Authors: Maia M. D.
Published: March 2003

The concept of contact between manifolds is applied to space–times of general relativity. For a given background space–time a contact approximation of second order is defined and interpreted both from the point of view of a metric pertubation and of a higher order tangent manifold. In the first case, an application to the high frequency gravitational wave hypothesis is suggested. In the second case, a constant curvature tangent bundle is constructed and suggested as a means to define a ten parameter local space–time symmetry.
Intrinsic isometry groups in general relativity
Authors: Szafron D. A.
Published: March 2003

We derive necessary and sufficient tensor conditions for the existence of a four-parameter isometry group G4 which acts multiply transitively on a Riemannian V3. We then apply these results to determine which spatially homogeneous cosmological models have induced 3-metrics which are invariant under such a four-parameter group.
Conserved densities for nonlinear evolution equations. II. Odd order case
Authors: Abellanas L. , Galindo A.
Published: March 2003

This paper extends to nonlinear evolution equations of odd order the analysis of existence and structure of the polynomial conserved densities. The results for low order densities are similar to the case of even order. The situation for densities with high order derivatives is now radically different. An asymptotic algorithm is presented for the search of such densities, which are shown to be quadratic in the highest derivatives. The very existence of just one high order conserved density is shown to severely restrict the evolution equation, and in the third order case it leads, with some minor additional hypothesis, to the KdV family.
Moment problem approximants to the Chandrasekhar H-equation
Authors: Masson D.
Published: March 2003

Approximate solutions to the Chandrasekhar H-equation are obtained by considering a truncated moment problem. Convergence to the physical solution is proved and a numerical example is outlined.
Measurement in stochastic mechanics
Authors: Shucker David S.
Published: March 2003

Stochastic mechanics is an explanation of nonrelativistic quantum phenomena in terms of stochastic differential equations. In this note a simple example of a measurement is constructed and the behavior of the sample paths of the corresponding stochastic differential equation is examined. The sample demonstrates that stochastic mechanics provides a natural explanation of the ’’reduction of the wave packet.’’
Quantum mechanical Hamiltonian models of discrete processes
Authors: Benioff Paul
Published: March 2003

Here the results of other work on quantum mechanical Hamiltonian models of Turing machines are extended to include any discrete process T on a countably infinite set A. The models are constructed here by use of scattering phase shifts from successive scatterers to turn on successive step interactions. Also a locality requirement is imposed. The construction is done by first associating with each process T a model quantum system M with associated Hilbert space ℋM and step operator UT. Since UT is not unitary in general, M, ℋM, and UT are extended into a (continuous time) Hamiltonian model on a larger space which satisfies the locality requirement. The construction is compared with the minimal unitary dilation of UT. It is seen that the model constructed here is larger than the minimal one. However, the minimal one does not satisfy the locality requirement.
Self-graviting anisotropic fluids with plane symmetry
Authors: Letelier P. S. , Machado R.
Published: March 2003

The general solution to Einstein’s equations coupled to an anisotropic fluid described by two perfect-fluid components is obtained in the case that (1) the space–time is plane-symmetric, (2) each fluid component is irrotational, and (3) each one obeys the equation of state pressure = energy density. The method used consists of solving the equivalent problem of the Einstein’s equations coupled to a complex massless-scalar field. The space-time singularities are studied using the concept of velocity-dominated singularity. Comoving systems of coordinates are also studied.
Homothetic solutions of Einstein’s equations and shock waves
Authors: Moschetti Gaetano
Published: March 2003

The problem of joining two homothetic solutions of Einstein’s field equations with a perfect fluid is considered in general, without any symmetry requirements.
Local gauge field theory formalism
Authors: McKellar R. J.
Published: March 2003

In this paper we develop a local gauge field theory formalism which is designed for use in a concomitant approach to motivate the field equations of gauge field theories. Several interesting identities are derived which enable us to gain further insight into these theories and into previously used formalisms and techniques.
The role of noncompact Lie algebras in relativistic wave equations. II
Authors: Cant A.
Published: March 2003

This paper continues the study, begun in a previous paper, of the role of real Lie algebras in the theory of finite-dimensional Lorentz invariant wave equations of the form (αμ∂μ+iκ)ψ(x) = 0. The connection with the discrete transformations of space reflection and charge conjugation is established. The consequences for the formation of infinite-dimensional wave equations are briefly discussed.
Converging lower bounds to atomic binding energies
Authors: Singh S. R.
Published: March 2003

A method is proposed to obtain approximations converging from below to a finite number of the nonrelativistic binding energies of atomic systems. The method requires that the Hamiltonian be decomposable as a sum of an unperturbed part and a non-negative perturbation. The eigenvalues of the unperturbed part are assumed to be known. For computational purposes, one needs the matrix elements of the square of the Hamiltonian, in addition to those of the Hamiltonian itself. These elements are used to construct a matrix valued function whose eigenvalues have the bounds as their fixed points. The elements of the matrix are obtained by solving a system of linear equations typical of variational methods. An iterative procedure is shown to yield converging lower bounds to the fixed points and thus to the binding energies.
Thermal blooming calculations with analytical diffraction approximated expressions
Authors: Hillion P. , Quinnez S.
Published: March 2003

Using the analytical results obtained in a forthcoming paper, we discuss here the thermal blooming of collimated and focused laser beams in some simple steady state and transient cases where an approximation of hydrodynamic equations is available. We still obtain tractable expressions which make it possible to plot the isointensity curves.
Analysis of a nonlinear integral equation arising in the study of the magnetic field in the critical state model of superconductivity
Authors: Beyer W. A. , Wing G. M. , Migliori A.
Published: March 2003

In the critical state theory of superconductors the magnetic field can be given as the solution of a nonlinear integral equation of Uryson type. It is shown that for sufficiently small values of physical and geometric parameters the equation always has a unique solution. A sufficient condition for the nonvanishing of the B-field is derived and application is made to several models, two of which result from experiments with NbTi and Nb3Sn. The investigation seems to cast doubt on the validity of some aspects of the critical state theory.
Energy density and spatial curvature in general relativity
Authors: Frankel Theodore , Galloway Gregory J.
Published: March 2003

Positive energy density tends to limit the size of space. This effect is studied within several contexts. We obtain sufficient conditions (which involve the energy density in a crucial way) for the compactness of spatial hypersurfaces in space-time. We then obtain some results concerning static or, more generally, stationary space-times. The Schwarzchild solution puts an upper bound on the size of a static spherically symmetric fluid with density bounded from below. We derive a result of roughly the same nature which, however, requires no symmetry and allows for rotation. Also, we show that static or rotating universes with Λ = 0 require that the density along some spatial geodesic must fall off rapidly with distance from a point.
A new set of coherent states for the isotropic harmonic oscillator: Coherent angular momentum states
Authors: Bracken A. J. , Leemon H. I.
Published: March 2003

The Hamiltonian for the oscillator has earlier been written in the form where ν† and ν are raising and lowering operators for ν†ν, which has eigenvalues k (the ’’radial’’ quantum number), and λ† and λ are raising and lowering 3-vector operators for λ†⋅λ, which has eigenvalues l (the total angular momentum quantum number). A new set of coherent states for the oscillator is now defined by diagonalizing ν and λ. These states bear a similar relation to the commuting operators H, L2, and L3 (where L is the angular momentum of the system) as the usual coherent states do to the commuting number operators N1, N2, and N3. It is proposed to call them coherent angular momentum states. They are shown to be minimum-uncertainty states for the variables ν, ν† , λ, and λ†, and to provide a new quasiclassical description of the oscillator. This description coincides with that provided by the usual coherent states only in the special case that the corresponding classical motion is circular, rather than elliptical; and, in general, the uncertainty in the angular momentum of the system is smaller in the new description. The probabilities of obtaining particular values for k and l in one of the new states follow independent Poisson distributions. The new states are overcomplete, and lead to a new representation of the Hilbert space for the oscillator, in terms of analytic functions on C×K3, where K3 is the three-dimensional complex cone. This space is related to one introduced recently by Bargmann and Todorov, and carries a very simple realization of all the representations of the rotation group.
Young–tableau methods for Kronecker products of representations of the classical groups
Authors: Fischler Mark
Published: March 2003

Diagrammatic methods for decomposing Kronecker products of arbitrary representations of any of the classical groups are presented. For convenience, efficient ways of computing the dimensions and quadratic Casimir’s C2(R) are also given. These methods seem more useful for hand calculations than the method of Schur functions (or characteristic polynomials). An appendix presents the Kronecker products for any two representations of dimension ⩽100.
Analytical approach to initial-value problems in nonlinear systems
Authors: Brenig L. , Fairén V.
Published: March 2003

A method based on the equivalence between finite-dimensional nonlinear and infinite-dimensional linear systems of ordinary differential equations is presented in order to calculate the time-dependent solutions of nonlinear physico-chemical systems. The solution is cast in the form of power series whose general term is known analytically.
Laplace transforms and asymptotic expansions of orthogonal polynomials
Authors: Glasser M. L.
Published: March 2003

New integral representations for orthogonal polynomials which possess a generating function are obtained by considering their Laplace transforms with respect to order. The method is used to derive some uniform asymptotic estimates for the associated Laguerre polynomials and to test an approximation scheme used in electron gas theory.
Further comments on the behavior of acceleration waves of arbitrary shape
Authors: Sharma V. D. , Menon V. V.
Published: March 2003

Converging waves with nonzero initial critical amplitude are completely characterized. It is shown that for a converging wave a necessary and sufficient condition for the initial critical amplitude to be zero is that the converging wave is spherical.
The maximality of Lorentz spaces and their importance with respect to classical and quantum electrodynamics
Authors: Gessner W.
Published: March 2003

The indefinite metric state space 𝒮M of the covariant form of the quantized Maxwell field M contains, as is known, a family of continuously many, isomorphic, isometric pre-Hilbert spaces ℒq, called Lorentz spaces, each of which corresponds to one square-integrable, prescribed, classical, spatial distribution q(x) of the total charge Q = 0. The quotient spaces ℒq/𝒩q modulo the subspace 𝒩q⊆ℒq of all elements with norm 0 are indeed Hilbert spaces in 𝒮M and it appears that any QED which has to do with 𝒮M has to be formulated not on 𝒮M as a whole but on the family of these Lorentz spaces. To support this assumption we embed any ℒq/𝒩q in ℒq in an isomorphic-isometric way and thus get Hilbert spaces ℓ q in 𝒮M, but not in a unique way; we will show that the different possibilities of this embedding correspond exactly with the different gauges. The main results about any embedding space ℓ q are, however, that it is a maximal Hilbert space in 𝒮M (under a premise referring to the expectation values of charge distribution), and that any Hilbert space of 𝒮M which is ’’physically important’’ in some sense is necessarily one of these ℓ q. In this way the family {ℓ q‖q∈Q} of Lorentz spaces (defined by the index set Q) has some outstanding properties so that the ℓ q are now characterized by these qualities (and no longer in the heuristical way via generalization of the classical Lorentz condition). Starting now with the prominent role of the ℓ q we get not only a deeper understanding of the Lorentz condition of classical electrodynamics—the properties of the ℓ q lead us automatically to the definition of a positive-definite state space of QED with the use only of these ℓ q. (Our considerations refer not to full but to some restricted QED; the restriction is primarily given by the above-mentioned index set Q so that extensions to full QED seem possible.) We show that our definition of a state space is consistent with time evolution, given by the Hamiltonian H, and that the QED on the basis of this state space is a constraint-free theory because the otherwise-necessary selection rules of Lorentz condition and charge conservation are now superfluous (and not present in a hidden form either). Furthermore, the properties of Lorentz spaces lead us automatically to a new concept of observables, all of which commute from the beginning with the operator of charge distribution. As a special observable we discuss the number operator N(k) of photons by showing that this, in general, cannot be of the form a+μaμ. A modified form of N(k) and with it a reformulation of the Hamiltonian H of QED is given. All these considerations go back to the properties of the Lorentz spaces and thus, basically, to the canonical quantization of the Maxwell field.
A semiclassical treatment of path integrals for the spin system
Authors: Kuratsuji Hiroshi , Mizobuchi Yutaka
Published: March 2003

Starting with path integrals in the SU(2) coherent state representation, the semiclassical approximation of the propagator for the spin system is investigated. By extending the idea of the semiclassical expansion method, which was developed in the usual phase-space path integrals, to the path integrals in the curved phase space, which is characteristic of the SU(2) coherent states, we obtain a closed form for the semiclassical propagator. As an application, we discuss the semiclassical quantization condition for the spin system.
Semiclassical approximations at positive temperatures in stochastic physics
Authors: Moore Steven M.
Published: March 2003

Semiclassical approximations are developed for stochastic mechanics and stochastic field theory at positive temperatures. The tunneling phenomena of Euclidean quantum mechanics is seen to have a statistical interpretation. A semiclassical algorithm for calculating the generating functional of the moments of the positive-temperature process is developed. Positive-temperature fluctuations around a scalar soliton and in the pure SU(2) Yang–Mills theory are also briefly considered.
Interior dynamics in the unified connected reaction theory of Polyzou and Redish
Authors: Polyzou Wayne
Published: March 2003

We discuss the unified reaction theory of Polyzou and Redish [Ann. Phys. (N.Y.) 119, 1(1979)] with regard to the freedom to perturb the approximate Hamiltonian by a connected operator. A proper treatment of this freedom is crucial for a good treatment of the dynamics. We show how to construct an effective N-body force so the approximate Hamiltonian is a projection of the exact Hamiltonian on an appropriate infinite dimensional subspace. Because this operator is connected it should not alter the unitarity considerations in the above paper. The methods used in constructing this effective interaction can also be used to reformulate the scattering integral equations as equivalent equations with noncompact contractive kennels. This reduces the scattering problem to uniformly convergent perturbation theory.
Statistical mechanics of an exactly integrable system
Authors: Creamer Dennis B. , Thacker H.B. , Wilkinson David
Published: March 2003

The equilibrium thermodynamics of the nonlinear Schrödinger model at finite temperature is calculated by means of the quantum inverse method. Working directly in an infinite volume we derive the equation of state and the integral equation which determines the excitation spectrum. This integral equation is found to be closely related to the Gelfand–Levitan expression for the charge density operator.
Quantum field theory of singletons. The Rac
Authors: Flato M. , Fronsdal C.
Published: March 2003

Dirac singletons are the most elementary physical objects on de Sitter space; massless particles are two-singleton states. Singleton field theory is characterized by a gauge structure that is strikingly similar to that of massless particles. The Rac and the Di are described by a scalar field and a spinor field, respectively, so the appearance of a fully developed gauge structure is remarkable. In this paper Rac field theory is quantized by using an indefinite metric, in close analogy with the Gupta–Bleuler method of electrodynamics. A Lagrangian theory of interacting Rac fields is also given, including the unique invariant local-interaction between Racs.
Quasicontinual approach to a field theory on a lattice: General theory
Authors: Garczyński Wl/odzimierz , Stelmach Jerzy
Published: March 2003

A general theory is systematically presented for handling sets of discrete quantities like values of a field on a lattice, with use of special functions of continuous variables. Those functions, which interpolate their discrete lattice values, form a so-called quasicontinuum. The multiplication rule for interpolating functions, corresponding to the multiplication of lattice sites values of those functions, turns out to be a nonlocal operation. Moreover, the Leibnitz rule for differentiation of a product is invalid here and its defect is found explicitly. The derivatives of interpolating functions at lattice sites may be readily calculated and yield results found earlier by the SLAC (Stanford Linear Accelerator Center) group.
The n-bubble diagram contribution to g-2
Authors: Laursen M. L. , Samuel M. A.
Published: March 2003

We obtain an exact integrated expression for the contribution of the mass-independent n-bubble diagram to the leptonic g-2. Furthermore, we find an interesting pattern of zeros among the coefficients of the zeta functions which occur in the result. This pattern also occurs when we generalize to integrals of the same type as the one occurring in the n-bubble diagram. We explain this pattern in a theorem which we rigorously prove.