bluuebunny/crossref_metadata_2025 huggingface dataset:
Asymptotic approximations, with error estimates, of the scattering matrix for quantal Coulomb excitation by means of a nonlinear (Riccati) matrix differential equation
Authors: Rasmussen C. H. , Rawitscher G. H.
Published: March 2003

A scattering matrix function is defined, which obeys a nonlinear (Riccati) matrix differential equation, containing two coupling potential matrices U and W, which are slowly vanishing, and which are mildly oscillatory and rapidly oscillatory, respectively. The scattering matrix is the limiting value of this scattering function. The equation is first transformed to separate the effects of U and W, thereby yielding separate equations in each. The long range effects of U and W are included in approximations for the scattering matrix, errors are assessed, and a prescription is outlined for the numerical computation of these approximations. In the case where the effect of W is entirely neglected beyond a certain point, the approximation obtained by Alder and Pauli [Nucl. Phys. 128, 193 (1969)] is recovered. An assessment of the error in this approximation is obtained.
An extended Levinson’s theorem
Authors: Osborn T. A. , Bollé D.
Published: March 2003

We investigate the form Levinson’s theorem takes when the two-body scattering amplitude is not decomposed into partial waves. It is found that the theorem changes its structure in this case and is not merely the sum over angular momentum of the well-known partial wave results. The energy dependent quantity that replaces the partial wave phase shift turns out to be the trace of the two-body time delay operator. This extended version of the theorem remains valid for scattering by nonspherically symmetric potentials.
On Bogoliubov transformations for systems of relativistic charged particles
Authors: Ruijsenaars S. N. M.
Published: March 2003

A simple expression for the normal form of the unitary operator implementing a Bogoliubov transformation on a system of relativistic charged particles is obtained. Necessary and sufficient conditions for the transformation to be unitarily implementable are rederived.
Convolution and H-equations for operator-valued functions with applications to neutron transport theory
Authors: Kelley C. T.
Published: March 2003

The Wiener–Hopf factorization of certain-valued functions is related to operator-valued generalizations of Chandrasekhar’s H-functions. These functions satisfy a nonlinear system and may be computed by an iterative scheme. A general transport equation is solved in terms of these functions. The equation for steady-state transport in one space dimension with isotropic scattering and continuous energy dependence is discussed as an application.
Relativistic rotation and the anholonomic object
Authors: Corum James F.
Published: March 2003

The purpose of this communication is to call attention to the conceptual economy provided by the object of anholonomity for the theory of relativity. This geometric object expresses certain consequences of relativity theory and provides a single, simple framework for discussing a variety of phenomena. It particularly clarifies the description of relativistic rotation. The relativistic rotational transformation of the four coordinate differentials of flat space–time generates a set of anholonomic, or inexact differentials, whose duals are an orthogonal set of basis vectors. How should a rotating observer interpret physical events referred to such orthogonal, but anholonomic frames? The answer to this question rests upon the origin and physical significance of the object of anholonomity. It is demonstrated that not only is the rotational Lorentz transformation an anholonomic transformation, but that the intrinsic anholonomic effects are essential to interpreting rotational phenomena. In particular, the Sagnac effect may be interpreted as the physical manifestation of temporal anholonomity under rotation. The Thomas precession of a reference axis may be interpreted as a consequence of the spatial anholonomity of the rotating frame. Further, the full four-dimensional covariance of Maxwellian electrodynamics, under a relativistic Lorentz rotation, is possible only with the inclusion of anholonomic effects. Schiff attempted to explain the vanishing of the electromagnetic field tensor in the frame of an observer rotating about a charged spherical capacitor, in terms of an interaction with the distant stars. However, if one employs a Lorentzian rotation and the ensuing orthogonal anholonomic reference frames, an explanation is possible without gravitationally induced currents. The anholonomic approach clarifies the distinction between the physically different operations of source rotation and observer rotation in a flat space–time. It is finally concluded that a consistant theory of relativistic rotation, satisfying the principle of general covariance, inherently requires the presence of the object of anholonomity.
Partial-wave analysis for supersymmetric scattering amplitudes
Authors: Jarvis P. D.
Published: March 2003

The reduction of the direct product of two unitary irreducible representations of supersymmetry into a direct sum of UIR’s is carried out for the massive case, and the Clebsch–Gordan coefficients are written down. The supersymmetric coupling of the different spin components of a multiplet arises from the use of the ’’superhelicity’’ basis (superhelicity κ=−j0,−j0+1,...,j0−1,j0) in which the spin is not diagonal. Here j0=O,1/2,1,... is the ’’superspin,’’ and the ordinary helicity, λ, is given by λ=κ or κ±1/2. The physical results are retrieved by transforming back to the spin basis after the reduction. The results of the reduction are used to analyze the scattering processes 1→2+3 and 1+2→3+4 for particles belonging to supersymmetric multiplets. The ordinary partial wave helicity amplitudes are given in terms of a small number of reduced partial wave superhelicity amplitudes corresponding to given total superspin. By continuing the latter to complex superspin, it is shown how, in the high-energy limit in the crossed channel, a singularity in one superhelicity amplitude contributes to the high-energy behavior of several different spin channels.
Stationary gravitational fields of a dually charged perfect fluid
Authors: Das A. , Kloster S.
Published: March 2003

Stationary field equations in the presence of a charged perfect fluid with both electric and monopole currents in isometric motion are studied. It is shown that the eight-parameter group of transformations which preserve the stationary electrovac equations can also be applied to dually charged sources. In the case of dually charged dust an equilibrium condition ρ= (σ*σ)1/2 implies a functional relationship between ReΓ and the complex potentials Φ and Φ*. Furthermore, it is proved that when ρ≠0 and σ≠0, the additional assumption of an arbitrary linear relationship between Γ and Φ leads uniquely to the Israel–Spanos class of solutions.
Renormalization group structure for translationally invariant ferromagnets
Authors: Baker George A. , Krinsky Samuel
Published: March 2003

We introduce a correlation function description of the renormalization group approach to critical phenomena. Our work is based on treating the renormalization group operator as a linear mapping on the set of Ursell functions, rather than as a nonlinear mapping on the space of Hamiltonians. We mainly consider the ’’mean-spin’’ renormalization group, but the closely related ’’decimation’’ transformation is also considered. Using this approach, we demonstrate for a suitable class of system that the spectrum of the renormalization group operator is bounded and countably infinitely degenerate. We give counterexamples to the notion that there must be convergence to a renormalization group fixed point. Our formulation of the renormalization group is sufficiently general so that convergence to a fixed point does not necessarily imply hyperscaling, i.e., the vanishing of the anomalous dimension of the vacuum, ω*. In the case of convergence to a fixed point we find δ= (d+σ−ω*)/(d−σ−ω*), with ω*?0 necessarily. Above the critical temperature we are able to prove that convergence is obtained to the ’’infinite temperature fixed point,’’ which result generalizes the central limit theorem to ferromagnetically correlated variables.
Asymmetric gas thermodynamics
Authors: Shahinpoor M.
Published: March 2003

We consider a gas in which the density and temperature fields are spatially and timewise nonuniform. We then show that on the basis of the entropy principle the stress tensor is nonsymmetric. This nonsymmetry of the stress thensor is shown to be the deriving force behind the creation the microrotational fields and dynamic spatial polarizations in the gas. It is also shown that the nonsymmetric part of the stress tensor arises out of the interaction of gradient fields of temperature and density.
Group theory of the collective model of the nucleus
Authors: Chacón E. , Moshinsky M.
Published: March 2003

In the present paper we extend the group theoretical analysis of a previous publication to obtain explicitly, as a polynomical in sinγ, cosγ, the function φλμlk(γ) required in the discussion of the quadrupole vibrations of the nucleus. The states appearing in the collective model 〈νλμLV〉=F1λ(β) ΣKφλμLK(γ) DL*MK(φi), l= (ν−λ)/2, are then defined, as Fλl(β), DL*MK(φi) are well known. All matrix elements required in the collective model of the nucleus are related then with the expression (λμL;λ′μ′L′;λ″μ″L″= ∂π0ΣKK′K″ (LL′L″KK′K″) φλμLK(γ) φλ′μ′L′K′ (γ) φλ″μ″L″K″ (γ)sin 3γdγ, which is a reduced 3j-symbol in the O(5) O(3) chain of groups.
Investigations of space-times with four-parameter groups of motions acting on null hypersurfaces
Authors: Lauten W. T. , Ray J. R.
Published: March 2003

An investigation of all metric having a four-parameter group of symmetrics with null three-dimensional orbits is made. An attempt to solve the Einstein field equations using various simple energy-momentum tensors, with on exception, gives incompatible sets of equations. The exception is a solution for a null fluid possessing the G4I1 group of symmetries.
The bundle boundary in some special cases
Authors: Johnson Russell A.
Published: March 2003

We examine a class of two-dimensional Lorentz manifolds which are ’’singular’’ in a certain sense. It is shown that, for such a manifold (M, g), the bundle boundary is a single point whose only neighborhood is all of M̄ [the bundle completion of M; see B. G. Schmidt, Gen. Rel. Gravitation 1, 269–80 (1971)]. The four-dimensional Schwarzschild and Friedmann–Robertson–Walker solutions are then investigated. We show that the bundle completions of these spaces are not Hausdorff.
Variation method and nonlinear stability problems
Authors: Hsieh Din-Yu
Published: March 2003

The direct variational method, developed for studying the asymptotic behavior of a wide class of nonlinear oscillation and wave problems, is extended to the study of the nonlinear stability problems. For systems which are unstable against small distrubances but stable against finite amplitude disturbances, the variational method can yield significant results in regimes even far away from the critical region. T The procedure of the variational method is illustrated by applications is various physical problems: the Duffing oscillation, a model wave equation for an unstable mechanical system, the two-stream instability in plasma, and the nonlinear Kelvin-Helmholtz stability problem.
Renormalized off-energy-shell Coulomb scattering
Authors: Zorbas J.
Published: March 2003

The complex-energy distorted plane waves for scattering via a general class of two-body Coulomb-like potentials are shwn to satisfy off-energy-shell Lippmann-Schwinger equaions in the case of two particle scattering and appropriately iterated Weinberg-Van Winter and Faddeev equations in the case of three particle scattering. A renormalized off-energy-shell formalism is defined for scattering involving more than one charged fragment in either the incoming or outgoing channel. The existence of limit to real energies of the normalized off-energy-shell formalism is verified.
Phase-space approach to relativistic quantum mechanics. I. Coherent-state representation for massive scalar particles
Authors: Kaiser Gerald
Published: March 2003

We construct a family of equivalent representations Uλ (λ≳0) of the restricted Poincaré group 𝒫↑+ for a massive scalar particle on spaces 𝒦λ of functions defined over ’’phase space’’ Pλ. Each Pλ is a submanifold of the forward tube, and 𝒦λ consists of restrictions on holomorphic solutions of the Klein–Gordon equation to Pλ. Each 𝒦λ has a resolution of the identity in terms of ’’coherent states’’ ez, zεPλ, which are wavepackets characterized by an invariant extremal property.
Curvature invariants and space–time singularities
Authors: Thorpe John A.
Published: March 2003

This paper collects together in a general setting observer dependent curvature invariants for space–time and applies them to an analysis of curvature singularities. Observer dependent quantities, such as energy and momentum densities and tidal stresses, are dependent not only on the space–time point but also on the observer’s 4-velocity. The properties of these invariants are discussed, and it is shown that they completely describe the behavior of curvature along timelike curves. In particular, curvature singularities can be characterized by unboundedness of these invariants.
Symmetries of ultralocal quantum field theories
Authors: DeFacio B. , Hammer C. L.
Published: March 2003

The symmetries of the gradient free ultralocal model quantum field theories are studied. The internal parameter λ introduced by J. R. Klauder is replaced by an r-component vector and used to obtain an r-vector ultralocal field operator φ̃. Then ultralocal many-body models with translational and rotational symmetry are set up by partitioning λ⃗ into N, 3-d ’’relative internal coordinates.’’ Hartree-type 1/N limits are studied in this model and found to be accurate only if contributions from ‖χ⃗‖≳≳0 are negligible. A brief sketch is given of how to produce more general UN and pairing interaction ultralocal models.
Pseudoparticle configurations in two-dimensional ferromagnets
Authors: Woo G.
Published: March 2003

It is proved that all the finite energy solutions to the field equations of the two-dimensional Heisenberg ferromagnet theory are topologically stable.
Bivector field theories, divergence-free vectors and the Einstein–Maxwell field equations
Authors: Lovelock David
Published: March 2003

A new derivation of the complete set of the Einstein–Maxwell field equations is presented which involves neither a variational principle nor the existence of a vector field (the so-called 4-potential). Unlike previous derivations, this derivation can therefore be used to motivate the Einstein–Maxwell field equations independently of the assumption of the existence or nonexistence of magnetic monopoles.
The classical action in nonrelativistic quantum mechanics
Authors: Truman Aubrey
Published: March 2003

We obtain some new results on the role played by the classical action in nonrelativistic quantum mechanics. The results are of the same genre as those derived previously by Nelson from the Trotter product formula. Here we work with the exact expression for the classical action not the approximate one as used by Nelson. Our results give a precise relationship between classical mechanics and quantum mechanics for a fairly wide class of potentials. The results are derived by using the properties of a new definition of the Feynman path integral ℱ introduced in an earlier paper.
Dispersive properties and observables at infinity for classical KMS systems
Authors: De Cannière J. , Pulè J. , Vanheuverzwijn P. , Verbeure A.
Published: March 2003

For infinite classical dynamical systems, satisfying the KMS condition, relations between asymptotic dispersive and cluster properties are proved. The local structure of the algebra of observables is explicitly characterized by the Poisson bracket commutant, and it is proved that the algebra of observables at infinity are constants of the motion.
Noncentral potentials: The generalized Levinson theorem and the structure of the spectrum
Authors: Newton Roger G.
Published: March 2003

Fredholm theory is applied to the Lippmann–Schwinger equation for noncentral potentials. For a specified wide class of potentials it is proved that the modified Fredholm determinant cannot vanish for real k≠0. The point k=0 is examined and the analog of the distinction between zero-energy bound states and zero-energy resonances for central potentials is found. A generalized Levinson theorem is proved.
Covariant inverse problem of the calculus of variations
Authors: Ahner Henry F. , Moose Allan E.
Published: March 2003

The solution of the covariant inverse problem of the calculus of variations (that of finding a Lagrangian for a given set of dynamical equations) is presented as a generalization flat space formalism of Atherton and Homsy. Known Lagrangians such as those for the complkex scalar field, vector gauge fields, and Einstein’s equations are used as examples. Additional insight into the formalism is provided by new examples that include a two-tensor theory, a method for obtaining conservation laws directly from dynamical equations, and a Hamiltonian formulation for higher order, nonlinear, differential equations.
The class of continuous timelike curves determines the topology of spacetime
Authors: Malament David B.
Published: March 2003

The title assertion is proven, and two corollaries are established. First, the topology of every past and future distinguishing spacetime is determined by its causal structure. Second, in every spacetime the path topology of Hawking, King, and McCarthy codes topological, differential, and conformal structure.
Polarization theorem for diffractive excitation at large momentum transfer
Authors: Actor Alfred
Published: March 2003

The kinematics of two-body collisions with large s and ‖t‖ favors small helicity states (0 for bosons, ±1/2 for fermions) over all larger helicities (supposing one or more particles with spin ⩾1 are involved in the collision). We state and prove this result in the form of a theorem: If there exist no constraints among invariant amplitudes in the kinematic region s≫‖t‖≫ (mass)2 for a two-body process with arbitrary spins, then only the smallest helicity states are important. This is a purely kinematic result, and dynamics can cause physical scattering amplitudes to have different properties, by providing constraints among the invariant amplitudes so as to evade the theorem. Nevertheless, the result is useful in that it clarifies the nature of two-body spin structure when ‖t‖ is large, and enables one to isolate the purely dynamical conditions among the invariant amplitudes which must be satisfied if there is no ’’kinematic polarization’’ of the nature described. In diffractive excitation of higher spin states, sufficiently large values of s and ‖t‖ can be reached to make the theorem of practical interest.
Varieties of symmetry breaking in a class of gauge theories
Authors: Schorr Amir
Published: March 2003

In unified gauge theories, the Higgs particles can interact in various ways. The problem of finding the symmetry-breaking directions can become very complicated in nontrivial cases, where the scalar fields have many interactions. A method is presented which predicts, in a simple way, the possible types of spontaneous symmetry breaking in a theory symmetric under the group U(N1) ⊗⋅⋅⋅⊗U(Nj) ⊗SU(M1) ⊗⋅⋅⋅⊗SU(Mk). Within its framework it is possible to obtain results by drawing a new kind of graph. It is found that in such models, various phases (and hence phase transitions) are possible. There are distinct hierarchies in the symmetry breaking strengths and they are related.
Solitons on moving space curves
Authors: Lamb G. L.
Published: March 2003

It is shown that the motion of certain types of helical space curves may be related to the sine–Gordon equation and to the Hirota equation (and consequently to the nonlinear Schrödinger equation and to the modified Korteweg–de Vries equation). The intrinsic equations that govern the motion of space curves are shown to provide the various linear equations that have been introduced to solve these evolution equations by inverse scattering methods.
Spinorial structures and electromagnetic hyperheavens
Authors: Finley J. D. , Plebański J. F.
Published: March 2003

Following the results of Garcia, Plebański, and Robinson, and the spinorial technique of Finley and Plebański, complex space–times with a null string (therefore, one-sidedly degenerate) are investigated in the presence of the cosological constant and the electromagnetic field. The structure derived by Garcia, Plebański, and Robinson thus acquires a more lucid and concise presentation. The computational procedure is improved considerably, permitting the inclusion of an explicit outline of all calculations involved.
A class of inhomogeneous perfect fluid cosmologies
Authors: Szafron D. A. , Wainwright J.
Published: March 2003

We present a new class of inhomogeneous and anisotropic cosmologies with perfect fluid matter content. The subclass of solutions with vanishing pressure are members of the class of inhomogeneous pressurefree cosmologies recently found by Szekeres. In addition, the Robertson–Walker solution with flat space sections and equation of state p= (γ−1) μ, is contained as a special case. The relation between our solutions and this Robertson–Walker solution in the limit of large cosmological time is studied in detail.
On the field of the quantum mechanical Hilbert space
Authors: Miklavc Adolf
Published: March 2003

The well-known limitations on the field of the quantum mechanical vector space, which, within the framework of the propositional logic of Birkhoff and von Neumann, can be obtained only for systems of dimension greater than or equal to four, are obtained here for all dimensions. The propositional logic fails to provide any information about the quantum systems of dimension less than four and, moreover, one does not know the empirical meaning of one of its basic assumptions. The Jordan algebra approach, on the other hand, which provides the same limitations on the field, also suffers from anomalies in low dimensions and is altogether formal rather than physical. In the present work, which is based on a recent study of the topological properties of quantum states, there are no low-dimensional anomalies and the assumptions have clear empirical meaning.
Stability of solutions of the compressible Navier–Stokes equations
Authors: Gordon Paul
Published: March 2003

The purpose of the paper is to consider the effect of the viscous terms of the compressible Navier–Stokes equations in situations where significant variations of the flow variables occur only over many mean-free paths. Under these conditions it is shown that the magnitude of the viscous terms is comparable to the addition in the inviscid equations of a forcing term which is small relative to appropriately normalized initial data. The appropriate normalization is discussed. Stability, in terms of a stability parameter, is defined relative to such perturbations. A large value of the stability parameter implies that the solution is ill-conditioned. Application of the results proceeds in the following manner. Let Ṽ (t,x,y) be a given solution to the Navier–Stokes equations. Let V (t,x,y) be the corresponding solution to the inviscid equations. Let M be the maximum deviation that occurs between Ṽ and V. From Ṽ, one obtains an ε which represents an upper bound on the magnitude of the viscous terms. If M is not significant, then it is clear, without any further analysis, that the viscous terms are not significant. If M is significant, one proceeds to obtain a lower bound on the stability parameter λ, namely λ⩾M/ε. If ε is small, it is now possible to conclude that the solution Ṽ is ill-conditioned. (If ε is large, the analysis remains valid, but no useful information is obtained.) Two particular applications are made. The first considers the known solutions to shock wave structure equations (particularly the case of the weak shock). The second considers solutions to the incompressible equations. It is shown that in many situations the use of the time-dependent incompressible Navier–Stokes equations is unjustified.
The Fermi method of quantizing the electromagnetic field as a model for quantum field theory
Authors: Carey A. L. , Hurst C. A.
Published: March 2003

In a previous paper we demonstrated that the Fermi method for quantizing the electromagnetic field had a rigorous C*-algebra version. Here we investigate some properties of our formalism and show (a) that the Fermi method provides an example of spontaneous symmetry breaking in a quantum field theory, (b) that it raises some interesting questions about automorphisms of Weyl systems, and (c) that it provides a prototype for higher-spin zero-mass field theories.
Asymptotic behavior of integral and integrodifferential equations
Authors: Ling Rina
Published: March 2003

Long time behavior of integral and integrodifferential equations is studied. Some of them are generalizations of the models for the transport of charged particles in a random magnetic field; the solution of the homogeneous integrodifferential equation has an algebraic-logarithmic decay for long times, whereas the solution of the inhomogeneous equation has a slower logarithmic decay.
The decomposition of the tensor product of representations of the symmetric group
Authors: Schindler Susan , Mirman R.
Published: March 2003

The decomposition of the tensor product of two irreducible representations of the symmetric group is studied, providing a foundation for the calculation of the Clebsch–Gordon coefficients. Realizations on spaces of polynomials are emphasized. This leads to tensor coupling coefficients. An iterative formula for the calculation of the tensor coupling coefficients is derived, and symmetry constructions are discussed and shown to lead to a reduction in the calculation needed. A well-defined procedure for the construction of the Clebsch–Gordan coefficients from the tensor coupling coefficients, which works for any multiplicity, is obtained. It may be used for any finite group and, with some modifications, for any compact group.
Affine fields and the operator formulation of augmented scalar fields
Authors: Klauder John R.
Published: March 2003

Affine fields, which can be used to replace the usual canonical fields, and which induce strictly homogeneous transformations of the underlying configuration space, are shown to be relevant in the operator formulation of augmented scalar field models. A characterization of the Hamiltonian and other basic generators by means of the expectation functional of the square of the field replaces the standard one based on the expectation functional of the field. Connection with previous work on augmented models is established through the form of the equation of motion for the field.
On dual series equations involving Konhauser biorthogonal polynomials
Authors: Patil K. R. , Thakare N. K.
Published: March 2003

By using Abel’s integral equations, we solve dual series equations involving Konhauser’s biorthogonal polynomial set of the first kind.
Equatorial circular geodesics in the Kerr–Newman geometry
Authors: Dadhich Naresh , Kale P. P.
Published: March 2003

The conditions for existence, boundedness, and stability are obtained for equatorial circular geodesics in the Kerr–Newman geometry. These conditions are extensions of the Bardeen et al. conditions in the Kerr geometry.
The Kirkwood–Salsburg equations for a bounded stable Kac potential. I. General theory and asymptotic solutions
Authors: Grewe N. , Klein W.
Published: March 2003

We derive for Kac potentials of the form γsψ (λx) an expansion, for all the distribution functions, in powers of γs (s=dimension) and prove for z<?cr that the expansion is at least asymptotic. The coefficients in the expansion are shown to be solutions of linear operator equations similar to the Kirkwood–Salsburg equation. We also explicitly obtain a rather simple expression for the coefficients of γs and show that they are given by solving the Ornstein–Zernicke integral equation with the choice of −βψ (y) for the direct correlation function.
The Kirkwood–Salsburg equations for a bounded stable Kac potential. II. Instability and phase transitions
Authors: Grewe N. , Klein W.
Published: March 2003

We prove that systems interacting via potentials of the form φ (x1,x2) =γsψ (γx12) where ψ is bounded stable and defined on bounded support are unstable to fluctuations of wavenumber k′min≠0 at a particular value v0 of v≡nβ, where n is the density and β=1/kBT in the limit γ→0 (VdW1). We also prove (in the VdW1) that the solution to the equation for the single particle distribution function bifurcates at this same value v0, that the nonconstant solution is periodic and has a reciprocal lattice vector with a magnitude k′min, and that there exists a type of long range order at v0. These results are interpreted to indicate the existence of a spinodal point on the liquid isotherm, and similarities between this system and the known properties of the hard sphere fluid are discussed. A theorem is also proven about the range of activity where one has a unique fluid phase, and it is shown that this system has no coexistence region in the usual sense.
Topology of Euclidean Yang–Mills fields: Instantons and monopoles
Authors: Yoneya Tamiaki
Published: March 2003

We discuss the topological properties of the Yang–Mills fields from a unified point of view of the Wu–Yang global formulation. In four-dimensional Euclidean space, the gauge type is characterized by the second Chern class. The multi-instanton solution recently found by ’t Hooft and generalized by Jackiw, Nohl, and Rebbi is discussed from this point of view. We also discuss the generalization of the topology of instantons and monopoles in higher dimensional spaces and the relation among them.
Notes on the symmetries of systems of differential equations
Authors: Gonzalez-Gascon F.
Published: March 2003

The concept of symmetry of the solutions of a system of differential equations is clarified. The functional character of the symmetry transformations is stressed in contrast with the pointlike character of the ordinary transformations considered by Lie. It is shown that any differential equation of arbitrary order possesses infinitely many symmetries, in strong contrast with a general theorem denying the existence of pointlike transformations of symmetry for an arbitrary differential equation of order greater than one. The relevance of local differential symmetries in theoretical mechanics is discussed, and some unsolved questions are raised.
Fibre-bundle structure of thermodynamic states
Authors: Maduemezia Awele
Published: March 2003

It is shown how the requirement that the Gibbs’ ensemble average 〈A〉=Tr(e2HbA)/TrA, b=−(1/2) kT, of any physical quantity A be formally expressible as an expectation value (Pb‖A‖bP)/(Pb‖bP) over a thermodynamic state ‖Pb), naturally leads to the realization of (Pb‖, as a cross section of a fibre bundle ϑ (G) with fibre G, over a manifold M of pressure states P as base space, where G is the infinite-dimensional Lie group {exp(Hb +unPn); −∞<b, un<∞} generated by H (Hamiltonian) and {Pn; n=1,2,⋅⋅⋅}, the sequence of projectors on the eigenvector subspaces of H. The group G is thus partly parametrized by the temperature variable b.
Pairing in the limit of a large number of particles
Authors: Richardson R. W.
Published: March 2003

Expressions for the ground and excited state energies of a system of nucleons interacting through pairing forces are given as a power series in inverse powers of the number of particles. The expressions are valid for systems with superfluid ground states and either J=0 or L=0 pairing. The first three terms in the expansion are given explicitly, and they exhibit excitations with both vibrational and rotational (in isospin space) character. Analytical and numerical results are given for a model system with a two-level single-particle spectrum.
Self-avoiding random walks: Some exactly soluble cases
Authors: Dhar Deepak
Published: March 2003

We use the exact renormalization group equations to determine the asymptotic behavior of long self-avoiding random walks on some pseudolattices. The lattices considered are the truncated 3-simplex, the truncated 4-simplex, and the modified rectangular lattices. The total number of random walks Cn, the number of polygons Pn of perimeter n, and the mean square end to end distance 〈R2n〉 are assumed to be asymptotically proportional to μnnγ−1, μnnα−3, and n2ν respectively for large n, where n is the total length of the walk. The exact values of the connectivity constant μ, and the critical exponents λ, α, ν are determined for the three lattices. We give an example of two lattice systems that have the same effective nonintegral dimensionality 3/2 but different values of the critical exponents γ, α, and ν.
A generalized prolongation structure and the Bäcklund transformation of the anticommuting massive Thirring model
Authors: Morris H. C.
Published: March 2003

The prolongation structure method of Wahlquist and Estabrook is generalized to Grassmann algebra valued differential forms and used to determine a Bäcklund transformation for the equations of the anticommuting massive Thirring model.
Remarks on the asymptotic behavior of the ’t Hooft’s magnetic monopole
Authors: Chernavskii D. S. , Kerner R.
Published: March 2003

We investigate the asymptotic behavior of the ’t Hooft’s solution at r→0 and r→∞. Using the methods of the qualitative theory of ordinary differential systems, we are able to derive the asymptotic form of the solution up to a higher approximation than in ’t Hooft’s original paper [G. ’t Hooft, Nucl. Phys. B 79, 276 (1974], as well as show that the Prasad–Sommerfield’s exact solution can be considered as an analytical limit of the ’t Hooft’s solution for μ2→0, λ→0. Some remarks on the stability of the monopole close the paper.
On projective symmetries of dynamical systems
Authors: Iwai Toshihiro
Published: March 2003

The present paper is concerned with symmetry transformations of a dynamical system defined on the tangent bundle of a Riemannian manifold. Of present interest are infinitesimal symmetry transformations of the vector field which defines the dynamical system on the tangent bundle. It is known that a class of such transformations entails infinitesimal projective transformations leaving the vector field invariant. Symmetry algebras formed by such projective transformations are studied. It is shown which dynamical systems admit large symmetry algebras. As a result, two kinds of dynamical systems are determined, which have the base Riemannian manifolds of constant curvature with dimensions n?4. The systems are generalizations of the classical harmonic oscillator and Kepler problem usually considered in Euclidean spaces. First integrals quadratic in the velocities are obtained, which are also generalizations of the well-known quadratic integrals for the above classical systems.
Integral equations for even parity perturbations of hot perfect fluid nonrotating neutron stars
Authors: Cazzola P. , Lucaroni L. , Semenzato R.
Published: March 2003

In the present paper, in the framework of the linearized Einstein equations, systems of two integral equations are set up, which describe coupled sound and gravitational waves associated with small perturbations of hot nonrotating neutron stars made of a perfect fluid. Suitable majorizations are given for the successive iterations in view of obtaining the asymptotic distribution of large eigenfrequencies.
On the inverse scattering problem for a class of spin–orbit and central potentials
Authors: Hooshyar M. A.
Published: March 2003

The nonrelativistic scattering of spin-1/2 particles by a certain class of central and spin–orbit potentials is considered. The potential coefficients associated with the phase shifts of all physical angular momenta at a fixed energy are deduced. It is shown that the construction does not lead to a unique solution and the found set of potential coefficients depend on two arbitrary constants. Finally the potential coefficients associated with transparent spin–orbit and central potentials are explicitly constructed.
Sequences of Z2⊗Z2 graded Lie algebras and superalgebras
Authors: Rittenberg V. , Wyler D.
Published: March 2003

Applying methods similar to those used for classical Lie superalgebras (Z2 graded algebras), we construct sequences of Z2⊕Z2 graded Lie superalgebras. In this way one obtains the spl(m,n,r,s), osp(m,n,r,s), P1(m,r), P3(m,n), ospP3(m,n), P1,2(m), and Q (m) series. We also give series of Z2⊕Z2 graded Lie algebras. Closed forms for superdeterminants and determinants of Z2⊕Z2 graded matrices are presented.
Mechanical response and the initial value problem
Authors: Uzes C. A.
Published: March 2003

Solutions to canonical mechanical equations are considered as functionals of a source function σ, which parametrizes the source. The coefficients of the functional Taylor series expansions in σ for the solutions are constructed from an infinite sequence of time ordered Poisson brackets, which in turn can be expressed in terms of the derivatives of the solution to the homogeneous equation with respect to its initial canonical momenta. Thus the functional Taylor series expansion is formally defined once the initial value problem for the possibly nonlinear homogeneous equation has been solved. A time ordered exponential operator acting on the homogeneous solution, which may be viewed as a ’’response’’ extension of the Lie series operation, simply represents the series expansion.
Scattering in the depth direction for an anisotropic random medium
Authors: Leitman M. , Schwartz N. , Beran M. J.
Published: March 2003

We consider in this paper the asymptotic nature of scattering in the depth direction in an anisotropic random medium like the ocean. We use the coherence equation developed previously. It is shown that as the propagation distance goes to infinity, the integral of the square of the coherence function, {Γ̄}, approaches zero. [The integral of {Γ̄} itself remains constant as a result of conservation of energy.] It is pointed out, however, that the approach to zero is expected to be very slow once we are well into the multiple-scatter region. For most practical cases, a quasi-asymptotic state is reached for which the integral of the square of {Γ̄} is approximately a finite constant and the shape of {Γ̄} no longer changes.
Tensor fields invariant under subgroups of the conformal group of space-time
Authors: Beckers J. , Harnad J. , Perroud M. , Winternitz P.
Published: March 2003

This work is concerned with the characterization of tensor fields in (compactified) Minkowski space which are invariant under the action of subgroups of the conformal group. The general method for determining all invariant fields under the smooth action of a Lie group G on a manifold M is given, both in global and in local form. The maximal subgroups of the conformal group are divided into conjugacy classes under the Poincaré group and the most general fields of 1-forms, 2-forms, symmetric (0,2) tensors and scalar densities which are invariant under representatives of each class (as well as certain other subgroups) are then determined. The results are then discussed from the viewpoint of physical interpretation (as, e.g., electromagnetic fields, metric tensors, etc.) and applicability; in particular, for studies of spontaneously or otherwise broken conformal invariance.
On the interaction of the type λx2/(1+g
x2)
Authors: Mitra A. K.
Published: March 2003

The ground state and the first two excited state energy levels for the interaction of the type λx2/(1+gx2) have been calculated nonperturbatively as the eigenvalues of the one-dimensional Schrödinger operator defined by Au=−u′′+x2u+λx2u/(1+gx2). The Ritz variational method in combination with the Givens–Householder algorithm has been used for numerical computations.
Complex p
p waves and the nonlinear graviton construction
Authors: Curtis W. D. , Lerner D. E. , Miller F. R.
Published: March 2003

We show how to construct all of the complex pp waves using the nonlinear graviton construction of Penrose.
Symmetries of the stationary Einstein–Maxwell equations. IV. Transformations which preserve asymptotic flatness
Authors: Kinnersley William , Chitre D. M.
Published: March 2003

We give a series of transformations βk, k=0,1,... which may be used to generate new stationary axially-symmetric vacuum solutions from ones already known. These transformations have the important property of preserving asymptotic flatness. As one example of their use, we show how to generate the Kerr metric from Schwarzschild. As a second example, we generate a new five-parameter vacuum solution which contains the δ=2 Tomimatsu–Sato solution as a special case.
A unified radon inversion formula
Authors: Deans Stanley R.
Published: March 2003

A Radon inversion formula which holds in spaces of even or odd dimension n is obtained for functions which admit to a certain general decomposition. The inversion formula which is one member of a Gegenbauer transform pair is used to generate some interesting definite integrals involving special functions. Legendre and Tchebycheff transform pairs are discussed as special cases of the general result.
Generalized Hamilton–Jacobi theories
Authors: Baumeister Richard
Published: March 2003

The generalized momenta of a dynamical system with n degrees of freedom may be given a Clebsch representation in terms of independent scalar functions and gradients thereof. The canonical equations imply certain differential relations which must be satisfied by these scalars. If the dynamical system is nonrelativistic, the differential relations are shown to be a generalization of the classical Hamilton–Jacobi theory. Similar results are obtained if the dynamical system is relativistic. A multiple integral variational principle, whose Euler–Lagrange equations imply the equations of motion and an equation of continuity, is formulated. As an example, it is shown that the Einstein field equations for an incoherent matter field and the geodesic equations of motion may be derived from a single fourfold variational principle. The usual energy-momentum tensor for such a matter field emerges as a by-product of the variational principle.
A general commutator equation in the algebra of spin operators
Authors: Jha Dhirendra Kumar
Published: March 2003

An algebraic method of spin operators was developed by Jha and Valatin to solve (a) the Hamiltonian of the isotropic and anisotropic xy model in a one-dimensional lattice of N spin 1/2 particles and (b) the partition function of the Ising model in the absence of magnetic field in two dimensions. The pair of fermion operators used to explain BCS theory in superconductivity were shown to be related to a set of spin operators of Jha and Valatin in a very simple way. Onsager’s Lie algebra for diagonalizing the partition function of the Ising model was found to be included within the said commutator algebra of the spin operators. The structure constants of the algebra are so simple as to allow the entire algebra to be casted in one general commutator equation. In the present paper, the author presents the proof of a general equation from which all sets of commutator relationships existing among the elements of the algebra directly follow.
Bogoliubov transformations, propagators, and the Hawking effect
Authors: Lapedes A. S.
Published: March 2003

The thermal spectrum of radiation, seen by suitable observers using ’’Unruh particle detectors,’’ in de Sitter spacetime is recovered using Bogoliubov transformation techniques. Previous attempts by other authors at calculating particle production in de Sitter spacetime, prior to the discovery of thermal radiation using propagator techniques failed. The discrepancy between these previous mode mixing calculations, and the calculations presented here, are traced to ’’de Sitter invariant’’ versus ’’observer dependent’’ formalisms. One consequence is that the initial vacuum state chosen for the quantum field is not unique.
Causality in homogeneous spaces
Authors: Chinea F. J.
Published: March 2003

A simple proof is given of the microcausality of quantum fields defined on certain homogeneous pseudo-Riemannian spaces. The proof is group theoretic in nature and does not depend on the detailed form of the generalized Pauli–Jordan propagator. As an illustration, applications are given to de Sitter and anti-de Sitter spaces; in the latter case, it is shown that the commutator of any boson field vanishes for any pair of points in the space.
The Bäcklund problem for the equation ∂2z/∂x1∂x2= f (z)
Authors: Shadwick W. F.
Published: March 2003

The Bäcklund problem for the equation ∂2z/∂x1∂x2=f (z) is discussed for analytic functions f, using the procedure of Estabrook and Wahlquist, starting from a Lagrangian formulation. The condition d2f/dz2 =kf, k constant, necessary for the existence of nontrivial Bäcklund maps when the space of new dependent variables is R, is shown to be closely related to the structure of the Lie algebra SL(2,R).
On the exact scattering solution of the Schrödinger and Dirac equations with a short range potential
Authors: Banerjee S. N. , Chakravorty S. N.
Published: March 2003

The total and partial wave scattering amplitudes in the Schrödinger equation with a short range potential have been derived. The Dirac equation for a short range potential has been exactly solved analytically for all partial waves for positive energies, and an expression for the S1/2 wave phase shift has been explicitly deduced.
Exact solitary ion acoustic waves in a magnetoplasma
Authors: Shukla P. K. , Yu M. Y.
Published: March 2003

It is shown that finite amplitude ion acoustic solitary waves propagating obliquely to an external magnetic field can occur in a plasma.
A generalized eigenvalue distribution
Authors: Handelman Michael
Published: March 2003

The statistical properties of the eigenvalues of random unitary matrices may be determined from the joint probability density function of the matrix eigenvalues. Earlier theorems have derived the density function for the unitary and symplectic circular ensembles from that for the circular orthogonal ensemble. A method is presented here for successively eliminating variables from the probability density function for the orthogonal circular ensemble; the method generalizes an earlier result, and the resulting function appears to represent the behavior of eigenvalues from a new series of matrix ensembles.
Beam propagation in focusing media with random-axis misalignments: Second- and higher-order moments
Authors: Besieris Ioannis M.
Published: March 2003

A novel statistical technique which allows the asymptotic evaluation of second- and higher-order averaged observables related to the stochastic complex parabolic equation is applied to the problem of beam propagation in a focusing medium characterized by random-axis misalignments. Analytical and numerical results concerning on- and off-axis statistics (e.g., the variance of intensity fluctuations, modal power transfer, the probability distribution density of the log-irradiance, etc.) are presented, and comparisons are made with previously reported findings.
The general coupled anharmonic oscillators and the coherent state representation
Authors: Bose S. K. , Tripathy D. N.
Published: March 2003

We obtain a first order perturbation solution for a system of 2m, unequal mass, coupled oscillators perturbed by anharmonic terms of homogeneous power 4p of the position variables in the coherent state representation.
A generalization of the spherical harmonic gradient formula
Authors: Bayman B. F.
Published: March 2003

The familiar gradient formula is generalized by replacing the gradient operator by an arbitrary solid harmonic of the gradient operator. The result is applied to various multipole expansions of angular momentum eigenstates.
Constraint on the compound depolarization factor of aligned ellipsoids
Authors: Twersky Victor
Published: March 2003

The bulk parameters for random distributions of aligned ellipsoidal particles with nonsimilar ellipsoidal exclusion surface (the locus of the minimum separation of particle centers) can be specified by a compound depolarization factor D. It is shown that D is positive for all physically realizable values of the fraction of space occupied by particles.