bluuebunny/crossref_metadata_2025 huggingface dataset:
Propagation of the fourth-order coherence function in an anisotropic random medium
Authors: Tur Moshe , Beran Mark J.
Published: March 2003

The propagation of the fourth-order coherence function through an anisotropic random medium is investigated for low frequency radiation using the parabolic approximation and perturbation techniques. Theoretical expressions are derived for the intensity fluctuations and correlations of an initial plane wave signal that has propagated a horizontal distance z into the medium. The expressions are valid for anisotropic media in which klH≫1 and kl2v/lH≪1, where k is the radiation wavenumber, lH and lV are, respectively, characteristic correlation lengths parallel and perpendicular to the propagation direction z. The results are compared to those obtained for an isotropic random medium.
Explicit evaluation of the representation functions of IU(n)
Authors: Wong M.K.F. , Yeh Hsin-Yang
Published: March 2003

All representation functions of IU(n) have been found in explicitly closed form. They are obtained through the contraction of U(n+1) or U(n,1). These expressions are closely connected with the generalized beta functions of Gel’fand and Graev.
Existence of localized solutions for certain model field theories
Authors: Strauss Walter A. , Vázquez Luis
Published: March 2003

We study the existence of static solutions of certain model equations. In particular we consider coupled systems of equations and allow the coefficients to be variable, even singular.
Quantum mechanics and stochastic control theory
Authors: Yasue Kunio
Published: March 2003

A time-symmetric stochastic control theory is proposed as one of the representatives of quantum mechanics. The main idea is based on Nelson’s probability theoretical approach to quantum mechanics. His approach is reformulated as a time-symmetric stochastic control problem. Several different control constraints equivalent to Nelson’s are obtained. One of them has a close connection to the Lagrangian formalism of classical mechanics. This suggests to us the use of stochastic calculus of variations. Within the realm of this time-symmetric stochastic control theory it is shown why Schrödinger’s original variational method of quantization was successful. Several advantageous points of the stochastic control theoretical approach to quantum mechanics, including the analysis of the classical limit, are also discussed.
A multidimensional extension of the combinatorics function technique. I. Linear and homogeneous partial difference equations
Authors: Phares Alain J. , Meier Robert J.
Published: March 2003

This paper is aimed at series solutions of physical phenomena that are described by linear homogeneous differential equations, like the Schrödinger differential equation. Series solutions to such equations, when they exist, lead to multidimensional, linear, and homogeneous recurrence relations among the expansion coefficients. The physical constraints imposed on the solutions of an ordinary differential equation (in the case of the Schrödinger equation that would be on the wavefunctions) then lead to a set of ’’initial values’’ on the expansion coefficients. The consistency of the initial values with the recurrence relation or partial difference equation (PDE), is one of the major problems in such cases. Until now, there was no systematic way of obtaining the solution of a PDE in terms of the initial values, and no systematic technique dealing with the consistency check. In this paper, we have been able to solve both of these problems by a natural extension of the combinatorics function technique developed by Antippa and Phares for one-dimensional linear recurrence relations.
Schrödinger operators with l
l/2w(Rl) -potentials
Authors: Kovalenko V. F. , Perelmuter M. A. , Semenov Ya. A.
Published: March 2003

We consider the Schrödinger operators −Δ+V with V in the weak Lq class, with q = 1/2 the underlying dimension, which is the borderline for a definition to be possible. We concentrate first on optimal bounds on how large the weak norm of V can be and then on spectral properties on Lp spaces.
Bound on the diffraction peak for the spin 0–spin 1/2 case
Authors: Sakmar I. A.
Published: March 2003

We apply a recently developed method by the author to the problem of the diffraction peak bound for the spin 0–spin 1/2 particle scattering with the spin taken fully into account. The variational technique is used with the constraints, the total cross section, elastic cross section, and the unitarity of partial waves.
Proof of a Geroch conjecture
Authors: Hauser Isidore , Ernst Frederick J.
Published: March 2003

We prove that any given stationary axisymmetric vacuum space-time (SAV) can be generated from Minkowski space by at least one Kinnersley–Chitre transformation, i.e., by at least one member of the Geroch group K, provided that the metric tensor and the Killing vectors are C3 in a domain which covers at least one point of the axis at which one of the Killing vectors characterizing the space-time is timelike. We find that the set of all Kinnersley–Chitre transformations which map any given SAV into another given SAV is uniquely determined by the initial and final values of the Ernst potential on the axis. An explicit formula for these K-C transformations in terms of the initial and final axis values is given; this formula generalizes an analogous one which Xanthopoulos found for the asymptotically flat SAV’s.
Nonglobal proof of the thin–sandwich conjecture
Authors: Pereira C. Martin
Published: March 2003

A gravitational thin–sandwich conjecture was first proposed by Wheeler and coworkers during the period 1962–4. The present paper contains a proof of the nonglobal form of this gravitational thin–sandwich conjecture. The proof (a) applies for arbitrary choices of the spatial metric and its time derivative; and (b) demonstrates the existence on a spacelike three-surface of solutions which satisfy conditions of continuity known to be sufficient to obtain existence and uniqueness of solutions to Einstein’s equations off the three-surface and existence and uniqueness of geodesics. Riquier’s existence theorem plays an important role in the proof. The relationship of the present results to previous work is discussed. Some global questions associated with the thin–sandwich conjecture are clarified. Some aspects of the relationship of the thin–sandwich conjecture to the problem of the quantization of the gravitational field are noted. Both the vacuum case and the case of a nonviscous fluid are included. The discussion allows for an arbitrary equation of state p = p( ρ).
Inverse scattering connections
Authors: Leon Jérôme JP.
Published: March 2003

We establish and study a transformation which connects the Schroedinger, the Klein-Gordon, and the Dirac operators. This provides an equivalence between their associated direct and inverse spectral transforms.
Symmetries and the Dirac equation
Authors: Steeb W.-H. , Erig W. , Strampp W.
Published: March 2003

A new class of symmetries are given for the Dirac equation without external fields. We consider the two cases of massive and massless particles.
On the substructure of the classical observables xα, pα, and Jαβ
Authors: Nash Patrick L.
Published: March 2003

The position, momentum, and angular momentum (spin + orbital) of a classical massive magnetic dipole particle are constructed from certain pairs of O(3,3) spinors and a scalar σ. These spinor pairs (and also σ) are endowed with a translation transformation law (which is fundamentally different from that of twistors), and are given the name hyperspinors. An action of the covering group of the Poincaré group is defined on hyperspinors and σ. Equations of motion for these hyperspinors and σ are proposed, special cases of which lead to the Lorentz force law for the momentum and the BMT (Bargmann, Michel, and Telegdi) equation for the Pauli–Lubanski pseudovector. A generalization to include SU(N) internal degrees of freedom in this model is suggested.
Geometrical spacetime perturbation theory: Regular higher order structures
Authors: Gowdy Robert H.
Published: March 2003

A coordinate-independent formulation of spacetime perturbation-theory is extended beyond the first-order. Higher-order analogs of the second fundamental form (first metric variation) and corresponding higher-order projection identities lead to higher-order perturbation equations for the spacetime metric fields coupled to spacetime. A deformation-geometrical vertex functional or Frechet derivative is introduced and used to express deformation-covariant perturbation equations in terms of action functionals. The deformation-covariant vertex functionals of the Einstein–Hilbert action functional are computed to fourth order (sufficient for third-order perturbation equations).
Note on Finslerian relativity
Authors: Ishikawa Hirohisa
Published: March 2003

Finslerian structure of spacetime is investigated. For a special type of generalized Finsler metric the explicit expression of Cartan-like metrical connection is derived and it is shown that it resembles the usual one. Causal problems in Finsler-type spacetime are discussed and, based on the arguments, the Einstein-type equations for the Finslerian quantities are derived by using the lifting of a Finsler metric to a tangent bundle. It is shown that a solution of the proposed equations can also be obtained from the complex structure of the tangent bundle. One-form type metrics are used to discuss the geometrical interpretation of isosymmetry. A simple way of obtaining a metrical connection for a general generalized Finsler metric is given.
A family of differential equations arising from multi-ion electrodiffusion
Authors: Leuchtag H. Richard
Published: March 2003

The system of Nernst–Planck equations and Gauss’s law describing an arbitrary mixture of ions in steady-state drift and diffusion is shown to be equivalent to a single ordinary differential equation of order equal to the number of distinct ionic charges in the system.
Some properties of static general relativistic stellar models. II
Authors: Lindblom Lee
Published: March 2003

We expand here the study of the type of identity which has been successfully used to prove the necessity of spherical symmetry in static black holes and uniform density stellar models. We show how the system of partial differential equations, whose solutions correspond to these identities, can be decoupled and partially integrated for fluids with an arbitrary equation of state. The problem of finding such identities is reduced thereby to the problem of finding the solutions to a single ordinary differential equation, plus quadratures.
On the conservation laws in the theory of fields in Finsler spaces
Authors: Ikeda Satoshi
Published: March 2003

Some conservation laws are obtained for the fields in some special Finsler spaces such as scalar curvature space, locally Minkowski space, etc.
On the theory of fields in Finsler spaces
Authors: Ikeda Satoshi
Published: March 2003

Finsler space is a metric space in which the line-element (x, y), instead of the point (x), is chosen as the independent variable, where the vector y is regarded as the internal variable associated with each point x. Therefore, the y-dependence characterizes essentially the theory of fields in Finsler spaces and the Finsler field shows many peculiar features depending on y. So, in this paper, with the aid of the theory of special Finsler spaces such as tangent Riemannian space, locally Minkowski space, etc., some physical aspects carried by y are considered by taking into account the intrinsic behavior of y.
High-energy behavior of phase shifts for scattering from singular potentials
Authors: Brander O.
Published: March 2003

The high-energy behavior of the Jost function in nonrelativistic potential scattering theory is studied for potentials, strongly singular and repulsive at the origin. To be able to give the result in an explicit form, we specialize to the S wave and to pure inverse power potentials. However, the method works for a large class of potentials, and we report briefly on some other cases. We use an asymptotic method, which can be described as a generalization of the JWKB method to arbitrary order, with rigorous error bounds. Some numerical results are given.
Factorization of operators.II
Authors: Fordy Allan P. , Gibbons John
Published: March 2003

We extend the methods of a previous paper [J. Math. Phys. 21, 2508 (1980)], factorizing the general, scalar, third-order differential operator, and obtain a Miura transformation for the Boussinesq equation. We give a general factorized eigenvalue problem. We also give a Hamiltonian structure associated with the factorized eigenvalue problem. We derive several isospectral flows, some of Klein–Gordon type.
Power series expansion for a crossing-symmetric vertex function
Authors: Heiss W. D.
Published: March 2003

Starting from a nonlinear system of coupled integral equations for the vertex parts which are irreducible with respect to the s-, t-, and u-channel, a power series is found for the full vertex function in terms of the vertex part Γ0 which is irreducible with respect to all channels. The problem of finding an expression in closed form remains unresolved, since higher-order products in Γ0 are nonassociative. In a simplified model, the mathematical properties of the series seem to allow successive rational approximations.
Construction of orthonormal vector sets for atoms and molecules by means of recursive variation
Authors: Morikawa Tetsuo , I’Haya Y. J.
Published: March 2003

It is shown using a recursive variation method that the Schmidt orthonormalized vectors are optimal in the sense that the least squared distances are minimized, and that the use of maximal squared overlaps yields a Schmidt canonical orthonormalized vector set which corresponds to the Löwdin canonical vector set. By introducing the Krylov sequence, the method is applied to the derivation of a variational expression for the Lanczos vectors which tridiagonalize any self-adjoint operator. The repeated use of two-step variations is shown to derive a pseudopotential which is useful for the calculations of correlated pair functions.
Comments on ’’Higher order modified potentials for the effective phase integral approximation’’
Authors: Fröman Nanny , Fröman Per Olof
Published: March 2003

It is pointed out that the comparison made in the paper by Floyd, ’’Higher order modified potentials for the effective phase integral approximation,’’ between the expansions introduced by Floyd and by the present authors, respectively, is inadequate as a test of the relative merits of the two expansions. In his comparison Floyd used our unmodified phase-integral approximations, but for the case considered one should instead use our consistently modified phase-integral approximations. The numerical results then obtained are in the present note compared with the numerical results obtained from the expansion derived by Floyd.
Multipole expansion of stationary asymptotically flat vacuum metrics in general relativity
Authors: Kundu P.
Published: March 2003

A multipole expansion scheme is introduced for a wide class of stationary, asymptotically flat, vacuum solutions of Einstein’s equations using the conformal techniques of Geroch and Hansen. An intrinsic choice of the conformal factor and suitable asymptotic flatness conditions enable one to express the rescaled gravitational mass and angular momentum potentials and the rescaled spatial metric as power series in normal coordinates around a point Λ representing the spatial infinity on the conformal manifold. The coefficients of this expansion are certain nonlinear combinations of the Hansen multipole moments. As an example the Schwarzschild metric is discussed in the present framework.
On almost causality
Authors: Akolia G. M. , Joshi P. S. , Vyas U. D.
Published: March 2003

The almost causal precedence concept proposed by Woodhouse and a causality axiom based on it are analyzed. Properties of the almost future are examined and the above causality axiom is shown to be deducible for a causally continuous space–time. It is shown to be coinciding with known causality conditions for a reflecting space–time. Also the equivalence of various causality conditions for a reflecting space–time and a reduction of the causal continuity axiom are obtained. It is next shown that the above causality axiom is not stable under metric perturbations. Then the Seifert future concept has been analyzed and the Woodhouse causality is proved to be strictly weaker than the stable causality condition. It is concluded that as far as the uncertainties in the form of metric perturbations are concerned, the Seifert future is useful but not the almost future.
Null Killing vectors
Authors: Lukács B. , Perjés Z. , Sebestyén Á.
Published: March 2003

Space–times admitting a null Killing vector are studied, using the Newman–Penrose spin coefficient formalism. The properties of the eigenrays (principal null curves of the Killing bivector) are shown to be related to the twist of the null Killing vector. Among the electrovacs, the ones containing a null Maxwell field turn out to belong to the twist-free class. An electrovac solution is obtained for which the null Killing vector is twisting and has geodesic and shear-free eigenrays. This solution is parameterless and appears to be the field of a zero-mass, spinning, and charged source.
Exact composite nearest neighbor degeneracies for one-dimensional lattice spaces
Authors: McQuistan R. B.
Published: March 2003

Expressions are developed which describe exactly the composite, nearest neighbor degeneracy specified by the three kinds of nearest neighbor pairs created when simple indistinguishable particles are distributed on a one-dimensional lattice space.
Asymptotic decay of correlations in the spin- 1/2 Ising model
Authors: Baker George A. , Bessis Daniel
Published: March 2003

We show that in the high-temperature region the spin–spin correlation function decays asymptotically like e−κr/rb, 0⩽b⩽ (1/2) (d−1).
On the reconstruction of the physical Hilbert spaces for quantum field theories with indefinite metric
Authors: Mintchev Mihail , d’Emilio Emilio
Published: March 2003

It is known that there may exist one or more Hilbert space structures corresponding to an indefinite metric quantum field theory. In this paper we prove that: (a) the existence of a Hilbert space structure is not needed in the construction of the physical Hilbert space(s); (b) different choices of the Hilbert space structure lead to physical Hilbert spaces isomorphic to that (those) mentioned in (a). Consequently, the physical content of the theory can be read off directly from the Wightman functions—in perfect analogy with the positive metric case. In this light we discuss a weaker form of the Wightman–Gårding–Strocchi axioms for indefinite metric quantum field theories.
Bargmann–Wigner equations: Symmetries of multispinors and equations of motion
Authors: Rodriguez M. A. , Lorente M.
Published: March 2003

A study of the Bargmann–Wigner wave equations (BWE) is carried out from the group theoretical point of view. Starting with totally symmetric multispinors of rank n and their expansion in terms of tensor coefficients, the general symmetry properties among them, the equation of motion and the Lorentz content of these tensors are derived for systems of arbitrary spin and nonzero mass. The same procedure is applied to multispinors of mixed symmetry corresponding to any Young diagram. Complete formulas are found for these multispinors, which are necessary in the construction of the first order Lagrangian for the BWE.
Paraxial self-trapped beams in nonlinear optics
Authors: Small Robert D.
Published: March 2003

Self-trapped beam solutions to the equations of nonlinear optics are studied by perturbing the straight ray solutions. In two dimensions, analytic forms for the perturbation solutions are obtained while for the radially symmetric case numerical solutions are produced. In both cases the perturbation amplitude contains an arbitrary function of distance so that a large class of self-trapped beams is produced. The solutions obtained are paraxial, and it is argued that they are the only symmetric paraxial solutions. It is further pointed out that solving the well-known paraxial equations leads to errors unless the solutions obtained are of the form found here since otherwise they violate the paraxial approximation.
1- and 2-topology of reaction networks
Authors: Sinanoğlu Oktay
Published: March 2003

The kinds of reaction networks introduced earlier by this writer are capable of diverse applications in chemical physics, biochemistry, chemical engineering, economics, ecological, and other dynamics. All possible mechanisms or pathways as a function of the numbers of reaction steps ρ or species σ are generated with them. They also give the rate laws, multiplicity of steady states, the nature of their dynamic instabilities, oscillations, etc. These properties are related to a large extent on the 1- and 2-topology of the networks, {𝒩}. The {𝒩} are graphs of two kinds of lines and two kinds of vertices. They can be planar or nonplanar. The genus t and thickness t of any 𝒩 are related to ρ, σ and the numbers of catalytic and autocatalytic cycles. The Betti numbers Bi(p) of 1- and 2-complexes constituted by 𝒩 and other topological invariants of the networks under two kinds of homeomorphisms are given. A number of theorems are stated and proved. The above reaction networks are interesting mathematical objects in that they help classify coupled nonlinear differential equations.
Symmetries of the Schrödinger bundle
Authors: Aldaya V. , de Azcárraga J.A.
Published: March 2003

We exhibit in this paper the invariance of the Schrödinger Lagrangian density under the eleven-parameter group 𝒢(m), central extension of the Galilei group 𝒢. As a result, the quantum mechanical probability ℱρ d3x turns out to be the conserved charge associated with the central generator of 𝒢(m), and the continuity equation is simply the expression of the conservation of the corresponding Noether current.
Formulation of variational principles via Lagrange multipliers
Authors: Kalikstein Kalman
Published: March 2003

Recent work on variational principles in mathematical physics enables one to construct, in a novel and systematic way, stationary expressions for a wide class of functionals P(E), where E is an unknown (vector) function whose defining equation cannot be solved exactly. The method involves the use of Lagrange multipliers, which can be a constant λ, a function F(x,y,z), and a dyadic operator Γ, to account for each of the equations (constraints) that define E. As illustrations, we consider vector and scalar scattering problems, and eigenvalue problems such as the determination of resonant frequencies and propagation constants of waveguides.
Clifford algebras in 2ω dimensions
Authors: Kennedy A. D.
Published: March 2003

We consider the generalization of the Dirac (gamma) algebra to a space-time with dimension 2ω, which is required for the use of the dimensional regularization scheme applied to fermions. In particular we introduce several tricks to facilitate the manipulation of expressions in such algebras, including a polynomial algorithm for taking traces and explicit formulas for Fierz matrices.
Irreducible linear–antilinear representations and internal symmetries
Authors: Garola C. , Solombrino L.
Published: March 2003

We reconsider a well-known classification, due to Wigner, of the unitary–antiunitary finite-dimensional irreducible group representations within a somewhat generalized mathematical framework, where, in particular, any algebraically closed field K with an involutory automorphism j is considered in place of the complex field C. We show that each case of the classification can be characterized by the set 𝒰′l of the linear mappings that commute with the given set 𝒰, which is now assumed to be an irreducible semigroup of linear and antilinear (i.e., j-semilinear) mappings, and explicitly exhibit 𝒰′l. Then, this classification is crossed with the classification of the sets of linear and antilinear mappings that has been obtained in some previous work and that generalizes the old classification of the unitary representations introduced by Frobenius and Schur. We obtain a new classification in which every case can be characterized by the group 𝒰c of the invertible linear and antilinear mappings which commute with the semigroup 𝒰. Whenever 𝒰 represents the symmetry group of some physical system, 𝒰c may represent ’’internal’’ symmetries, so that the problem of finding these symmetries is now related to some natural classification of 𝒰. In particular, it turns out that in four cases 𝒰c reduces to its linear part 𝒰cl = 𝒰′l\{0}, whereas in the remaining nine cases 𝒰c is an extension of 𝒰cl through G2, which reduces to a semidirect product, but not to a direct one, in three cases and to a direct product in three cases.
Universal formats for nonlinear ordinary differential systems
Authors: Kerner Edward H.
Published: March 2003

It is shown that very general nonlinear ordinary differential systems (embracing all that arise in practice) may, first, be brought down to polynomial systems (where the nonlinearities occur only as polynomials in the dependent variables) by introducing suitable new variables into the original system; second, that polynomial systems are reducible to ’’Riccati systems,’’ where the nonlinearities are quadratic at most; third, that Riccati systems may be brought to elemental universal formats containing purely quadratic terms with simple arrays of coefficients that are all zero or unity. The elemental systems have representations as novel types of matrix Riccati equations. Different starting systems and their associated Riccati systems differ from one another, at the final elemental level, in order and in initial data, but not in format.
Treatment of some singular potentials by change of variables in Wiener integrals
Authors: Blanchard Ph. , Sirugue M.
Published: March 2003

Using a regularization of the classical Kepler problem, we show that a change of process and a change of time in stochastic differential equations allow a treatment of singular potentials in Wiener integrals.
Jump conditions for fields that have infinite, integrable singularities at an interface
Authors: Costen Robert C.
Published: March 2003

Jump conditions are derived for a basic set of first order partial differential equations whose fields have infinite, integrable singularities, as well as finite discontinuities, at a moving and deforming interface. These basic formulas are then applied to Maxwell’s electrodynamic equations and yield the jump conditions that hold when the electric and magnetic fields have such singularities. These jump conditions are shown to be generalizations of formulas previously derived for double charge layers in electrostatics and for an interface with surface magnetization density in magnetostatics. The basic formulas are also used to obtain jump conditions for the wave equation and other second order partial differential equations whose fields have finite discontinuities at an interface. A similar application to second order vector identities yields a new set of jump identities. These identities show that the normal and tangential components of the jump in a vector field are kinematically interdependent; e.g., shock waves and vortex sheets are kinematically linked—a fact that may be significant for shock-slip flows in aerodynamics. The jump identities also indicate the fields that must be measured at an epoch in order to calculate the instantaneous growth/decay rate of a propagating discontinuity, such as an atmospheric front. A feature of the derivation is that the field jumps and surface densities are mathematically defined as continuous and differentiable functions of three-dimensional space and time that assume physical values on the physical interface. This approach is simpler and more general than previous approaches that define jumps and surface densities only on the physical interface because the brackets (jumps) now commute with all derivatives, instead of with only the tangential and displacement derivatives. Boundary value problems with propagating infinite singularities in the electrodynamic fields are presented as examples.
Distributionlike representations of *-algebras
Authors: Mathot Françoise
Published: March 2003

Non-self-adjoint representations of *-algebras in a Hilbert space give rise by an extension and transposition procedure to representations in larger spaces, such as distribution spaces. Those new representations provide examples of operators of nested Hilbert spaces which would be very singular operators when considered in the Hilbert space only.
A class of solutions of Calapso–Guichard equations
Authors: Ray Dipankar
Published: March 2003

A class of solutions is indicated for Calapso–Guichard equations of surface theory.
Integrated rotational parameter as a constraint for the variational lower bound of the diffraction peak
Authors: Sakmar I. A.
Published: March 2003

The contributions of the imaginary parts of the partial waves to an angle integral of the rotation parameter R is taken as a third constraint in addition to the total cross section σT and σel,im, in the variational calculation of the lower bound for the diffraction peak.
Entropy in classical and quantum physics
Authors: Cyranski John F.
Published: March 2003

The enigma of ’’entropy’’ is reconsidered from the viewpoint of generalized information theory on a lattice generated from measurements that define the system. A small (incomplete) set of natural axioms for a global information measure is developed sufficiently to deduce as a special case a generalization of Segal’s entropy on a W*-algebra (classical and quantum). A simple relationship between monotonicity of entropy and a semigroup on [0,∞] (representing composibility of information) is presented. Various extensions of information-theoretic results are incidentally proven, including relations between regular composible informations (on an orthocomplemented complete lattice) and measures (on σ—ideals of the lattice).
Fermionic coherent states in a Fock superspace
Authors: Valle J. W. F.
Published: March 2003

Fermionic coherent states (FCS) are constructed via the Weyl supergroup of isometries of a Fock superspace. Their properties are derived and the connection with the pseudomechanics formalism is pointed out.
Canonical transformations relating the oscillator and Coulomb problems and their relevance for collective motions
Authors: Moshinsky M. , Seligman T. H.
Published: March 2003

The present paper can be viewed from two standpoints. The first is that it derives the canonical transformation that takes the Hamiltonian of the Coulomb problem (in the Fock–Bargmann formulation) into that of the harmonic oscillator, while transforming the angular momenta of both problems into each other. The second is the one in which the solution of the previous problem is required if we wish to find the canonical transformation relating microscopic and macroscopic collective models, where the former is derived from a system of A particles moving in two dimensions and interacting through harmonic oscillator forces. The canonical transformation shows the existence of a U(3) symmetry group in the microscopic collective model corresponding to that of the three-dimensional oscillator which is the Hamiltonian of the macroscopic collective model. The importance of this result rests on the fact that had the motion of the particles taken place in the physical three-dimensional space, rather than the hypothetical two-dimensional one discussed here, the symmetry group would have been U(6) rather than U(3). Thus, the group theoretical structure of an s-d boson picture or, equivalently, of a generalized Bohr–Mottelson approach, is present implicitly in an A-body system interacting through harmonic oscillator forces.
Semiunitary projective representations of the complete Galilei group
Authors: Cariñena José F. , Santander Mariano
Published: March 2003

A systematic study of the semiunitary projective representations of the Galilei group including reflections is presented. They are found by means of the semiunitary representations of a representation group.
A unified treatment of the representation functions of SO(n,1), SO(n+1), and ISO(n)
Authors: Wong M. K. F. , Yeh Hsin-Yang
Published: March 2003

An explicit expression is obtained for all the representation functions of SO(n,1), SO(n+1), and ISO(n). It is found that the representation functions of SO(n,1) and SO(n+1) are basically expressible as hypergeometric functions 2F1 with arguments 1-e−2ζ and 1-e2iδ, respectively, for n≳2, multiplied by Weyl coefficients of SO(p), p = 3, 4, ..., n. The representation functions of ISO(n) are then obtained from those of SO(n,1) or SO(n+1) by contraction. They are expressible as sums over a confluent hypergeometric function with argument 2iγξ, multiplied by Weyl coefficients of SO(p), p = 3, 4, ..., n. This provides an interesting alternate form for the representation functions of ISO(n) obtained previously by Wong and Yeh as a sum over Bessel functions.
Convergence of Berryman’s iterative method for some Emden–Fowler equations
Authors: Luning C. D. , Perry W. L.
Published: March 2003

The equation y′′+λa(x)yα(x) = 0, 0<x<1, y(0) = y(1) = 0, α≳0, arises in the study of nonlinear diffusion equations connected with crossfield diffusion in plasmas. We show that for a particular choice of starting iterate, the computational method which Berryman developed for this equation does converge, and furnishes upper and lower bounds for y(x).
A direct study of a Marchenko fundamental equation with centripetal potential
Authors: Coz Marcel
Published: March 2003

A direct study of a class of singular (ℓ≠0) fundamental equations is shown to be possible. The method used for this proof follows Marchenko’s nonsingular (ℓ = 0) approach, step by step. Throughout the paper the interest of a simultaneous study of the ’’Marchenko associated equation’’ is stressed. Also it will be shown why the Marchenko approach does not extend to complex interactions. In order to treat a complex interaction one must therefore resort to a new set of ideas.
On reduction of the four-dimensional harmonic oscillator
Authors: Iwai Toshihiro
Published: March 2003

This paper deals with reduction of the four-dimensional harmonic oscillator by use of a one-parameter subgroup U(1) of the symmetry group SU(4), U(1) being the symmetry subgroup generated by an ’’angular momentum.’’ The angular momentum determines in the energy surface S7 an ’’energy-momentum’’ manifold S3×S3 on which a subgroup SU(2)×SU(2) of SU(4) acts. The reduction process yields a manifold S3×S2 = S3×S3/U(1) on which SO(4) acts effectively.
Classification of orbits of Fokker’s time-asymmetric relativistic two-body problem
Authors: Fahnline Donald E.
Published: March 2003

The requirements that the proper velocities of the particles in Fokker’s time-asymmetric relativistic two-body problem be timelike and future pointing restrict the variables ρ1 and ρ2 associated with the distances between the particles as measured in their rest frames. Employing these restrictions in an algebraic equation relating ρ1 and ρ2 to the total angular momentum and the total four-momentum, assumed timelike and future pointing, classifies the physical orbits of the system. The results include orbits similar to those of the nonrelativistic Kepler problem and several new types in which the angular velocity is opposite to the total angular momentum. This information is required for the integration of the equations of motion to determine the orbits in four-space.
Inverse scattering inverse source theory
Authors: Bojarski Norbert N.
Published: March 2003

The inverse scattering inverse source problem associated with the inhomogeneous Helmholtz wave equation, the (special case) Sturm–Liouville (acoustic wave) equation, and the time-independent Schrödinger equation is treated . To this end, the concepts of a reference wave velocity and an associated free reference space Green’s function spectrum are introduced. A modified Kirchhoff surface integral, containing only the gradient of the real part of this free reference space Green’s function spectrum and the fields on a measurement surface is formulated, yielding an integral equation for the unknown fields and sources in the interior of the closed piecewise smooth surface on which the (remotely sensed) fields are known. A well-posed, analytic closed form solution of this integral equation for the unknown fields and their Laplacians is obtained with the aid of a (modified) spatial Fourier transform in which the reference velocity is continually varied in such a fashion that the Ewald sphere shell sweeps to fill the entire transform space. The unknown potential or medium properties and the unknown sources are then determined algebraically for the inverse scattering and inverse source problems, respectively. The effects of finite sampling density and incomplete observation domain are discussed briefly.
Hypervirial calculation of energy eigenvalues of a bounded centrally located harmonic oscillator
Authors: Fernández Francisco M. , Castro Eduardo A.
Published: March 2003

The diagonal hypervirial equations for enclosed quantum systems which obey boundary conditions φ(a) = φ(b) = 0 are applied to calculate energy eigenvalues of a bounded centrally located harmonic oscillator. Hypervirial equations were previously derived by us [F. M. Fernández and E. A. Castro, Int. J. Quantum Chem. (in press)], and recurrence rules are easier to deal with than previous formulas based on the roots of the hypergeometric series. The comparison of numerical results with those given by Vawter [R. Vawter, J. Math. Phys. 14, 1864 (1973)] shows the greater accuracy of the hypervirial method.
Strange solutions to field theories in one spatial dimension
Authors: Mattis Daniel C. , Sutherland Bill
Published: March 2003

Many models of interacting particles rely heavily for their solution on restriction to one-dimensional motion and a linearized kinetic energy. We examine this in detail, and find that the linearization can lead to patently strange and possible spurious solutions in first quantization. The usual, correct solutions are obtained only in second quantization. The strange solutions do not reduce to the usual plane wave determinantal solutions, even when the interactions are extinguished, and have the character of a condensed phase — a sort of Wigner lattice—for arbitrary interactions.
Hamiltonian formulation for the gauge theory of the gravitational coupling
Authors: Giachetti Riccardo , Ricci Riccardo , Sorace Emanuele
Published: March 2003

This paper studies the Hamiltonian mechanics of a relativistic particle interacting with a gravitational field considered as a gauge field of the Poincaré group. We follow a general method developed by Sternberg for the case of internal symmetries, that describes the interaction by a suitable modification of the symplectic form. This approach is reviewed and the explicit examples of the electromagnetic and Yang–Mills gauge interactions are widely explained in local coordinates. The peculiar features of a gauge theory of the Poincaré group are then discussed and the geometrical picture that emerges suggests the way of modifying the symplectic form for a correct description of the gravitational coupling.
On the application of energy conditions and algebraic classification in general relativity
Authors: Moody Michael C. , Ray John R.
Published: March 2003

The application of the ideas of the symmetry classification of space-time, the algebraic classification of the energy-momentum tensor, and the dominant energy conditions for macroscopic matter to the problem of searching for solutions to the field equations of general relativity is discussed. These ideas are then specifically applied to certain space-times of G4 symmetry to demonstrate the ability of this approach to obtain both new and general solutions. For macroscopic matter, G4I1 symmetry is shown to have only one general solution; symmetries G4V, G4VII1, and G4VII2 are shown to allow no solutions whatever; and the method is used to discover a new solution for G4VIII1 symmetry. A similar solution would be expected for G4VIII2 symmetry.
On the dynamics of infinite anharmonic systems
Authors: Marchioro C. , Pellegrinotti A. , Pulvirenti M.
Published: March 2003

The nonequilibrium dynamics of a large class of classical systems of anharmonic oscillators is studied. An existence theorem for the solution of the hierarchical equations describing the evolution of the states is given.
Pair site occupation probability for one-dimensional array of dumbbells
Authors: Maltz A. , Mola E. E.
Published: March 2003

We present two different approaches to evaluating the probability of finding in a particular state two neighboring lattice sites on a one-dimensional array of dumbbells. The results we find are exact and the same with either the first or the second procedure.
Distributional and regulator limits for circuit breaker regularized Feynman amplitudes
Authors: Hampton Richard R.
Published: March 2003

This paper continues an investigation of circuit breaker (sometimes called point split) regularized Feynman amplitudes and Taylor (BPHZ) subtraction terms. A circuit breaker regularized amplitude is essentially a Fourier transform with respect to internal (loop) momenta of the Feynman integrand. It is shown that the regularization produces tempered distributions in the external momenta in the limit as the propagator epsilon is taken to zero. It is also shown that for renormalized amplitudes the regularization may be removed interchangeably before or after the propagator epsilon is taken to zero. The regularization should be useful for studying time ordered functions and may lead to a more direct proof of the unitarity property of BPHZ renormalized perturbative field theory. A final incidental result in this paper is a new proof that the Feynman amplitudes produced by the forest formula of BPHZ are tempered distributions.
Geometrical structure of Faddeev–Popov fields and invariance properties of gauge theories
Authors: Quirós M. , de Urries F. J. , Hoyos J. , Mazón M. L. , Rodriguez E.
Published: March 2003

Let 𝒫n be the trivial principal bundle with structural group G and base space 𝒫n−1, 𝒫1 being the usual fiber bundle of gauge theories. In order to give a geometrical interpretation to the Faddeev–Popov fields, as well as to the Becchi, Rouet, and Stora transformations, we need to use the fiber bundle 𝒫3. The gauge fields and the Faddeev–Popov ghost and antighost fields appear as part of certain 1-forms defined on the base space 𝒫2. The anticommuting character of the ghost and antighost fields is essentially due to their identification with 1-forms. The Becchi, Rouet, and Stora transformations are identified with generalized infinitesimal gauge transformations on 𝒫3 of parameters related to the ghost fields. We obtain a further invariance of the action given by a similar generalized infinitesimal gauge transformation on 𝒫3 related to the antighost fields.
Field equations invariant under indecomposable representations of the Lorentz group
Authors: Hlavatý L. , Niederle J.
Published: March 2003

Relativistic equations in which the fields cotransform under the direct sum of indecomposable representations of the Lorentz group are derived and discussed.
On the existence of neutrino ’’zero-modes’’ in vacuum spacetimes
Authors: Sen Amitabha
Published: March 2003

Neutrino ’’zero modes’’ in curved spacetime, the analog of static solutions of the neutrino equation in flat space, are defined as the kernel of an elliptic operator obtained from a ’’3+1’’ decomposition of the neutrino equation relative to a spacelike hypersurface. In this paper, vacuum, globally hyperbolic spacetimes that admit ’’zero modes’’ are characterized.
Incompressible fluid turbulence at large Reynolds numbers: Theoretical basis for the t−1 decay law and the form of the longitudinal correlation function
Authors: Rosen Gerald
Published: March 2003

Approximately valid for large values of the time t, a formal solution to the Hopf Φ equation is obtained here as an asymptotic power series in t−1. This approximate solution is directly applicable to grid-generated isotropic homogeneous turbulence at large Reynolds numbers during the initial (inertial-force dominated) period of decay; thus, the solution accounts for the observed t−1 decay law and the fact that the longitudinal correlation function f is independent of t. It is observed that the longitudinal correlation function measured by Frenkiel, Klebanoff, and Huang is consistent with the theoretical asymptotic behavior f = (const)r−3 as r→∞ and fitted by the expression f = [1+0.770(r/M)]−3, where M is the grid mesh length and the separation distance r is greater than the Taylor microscale (10νt)1/2. Interestingly enough, this form for the longitudinal correlation function is shown to be derivable from a variational principle.
Restrictions on relativistically rotating fluids
Authors: Schendel J. , Winicour J.
Published: March 2003

We develop an extensive set of inequalities which apply to the surface of a relativistically rotating fluid with asymptotically flat exterior. We explore the physical content of these inequalities by examining the restrictions they impose on the existence of rotating fluid models with Kerr exteriors. In that case, the dominant set of inequalities can be expressed in a simple analytic form. We find for all models with Kerr parameter a≳m that there is a finite maximum redshift between observers at the fluid surface and at infinity. However, for all models with 0<a/m?1 there is no upper bound to the redshift. In the static limit, as a/m→0, a finite redshift maximum emerges in a discontinuous manner. The value of this maximum depends upon the moment of inertia of the static background fluid. We discuss the implications toward the possibility of a high redshift quasar model.
Generalized Schrödinger representation and its application to gauge field theories
Authors: Arisue Hiroaki , Fujiwara Toshiaki , Inoue Takuo , Ogawa Kaku
Published: March 2003

A generalization of the Schrödinger representation is presented and applied to theories with indefinite metric as well as those with positive definite metric. It enables us to construct the wavefunctional formalism of the quantum electromagnetic field equivalent to the operator formalism in covariant gauges. The theoretical foundation of the Wick rotation of the dynamical variable A0(x) is established.
Higgs multiplets in the adjoint representation of SU(N)
Authors: Mitra P.
Published: March 2003

The general pattern of symmetry breaking due to two Higgs multiplets in the adjoint representation of SU(N) is studied. It is shown that when N≳2, the requirement of renormalizability raises the minimum number of multiplets required for a complete breakdown from two to three.
Propagation in a tropospheric duct with a single-step discontinuity in the refractive index in the direction of propagation
Authors: Ott R. H.
Published: March 2003

A Green’s function approach is used to derive an expression for the field inside a laterally inhomogeneous duct. The laterally inhomogeneous duct is assumed to have a single step, and convergence criteria for the step size and number of modes are discussed.
A Hamiltonian structure of the interacting gravitational and matter fields
Authors: Szczyrba Wiktor
Published: March 2003

We present a Hamiltonian formulation for classical field theories. In a general case we write the Hamilton equation by means of the energy–momentum function E and the symplectic 2-form Ω. We investigate thoroughly an important example, the gravitational field coupled to a matter tensor field. It will be shown that the energy-momentum differential 3-form yields a generalization of the Komar energy formula. We prove that the energy–momentum function E, the symplectic 2-form Ω, the Hamilton equation, and four constraint equations for initial values of canonical variables give rise to the system which is equivalent to the Euler–Lagrange variational equations. We also discuss relations between the Hamilton equation of evolution, the degeneracy of the symplectic 2-form Ω, and the action of the diffeomorphism group of spacetime in the set of solutions.