bluuebunny/crossref_metadata_2025 huggingface dataset:
On equivalence of parabolic and hyperbolic super-Hamiltonians
Authors: Kuchař Karel
Published: March 2003

Three types of super-Hamiltonians occur in generally covariant field theories: linear in the momenta (hypersurface kinematics), parabolic in the momenta (parametrized field theories on a given Riemannian background), and hyperbolic in the momenta (geometrodynamics). Three simple models are discussed in which the linear or parabolic super-Hamiltonian can be cast, essentially by a canonical transformation, into an equivalent hyperbolic form: (1) The scalar field propagating on a (1+1) -dimensional flat Minkowskian background, (2) hypersurface kinematics on a (1+n) -dimensional flat Minkowskian background, and (3) geometrodynamics of a (1+2) -dimensional vacuum spacetime. The implications for constraint quantization are mentioned.
Random linear systems and temporal homogeneity
Authors: Vasholz David P.
Published: March 2003

The class of random linear systems having stochastic Green’s functions whose moments are invariant under arbitrary uniform translations of all time variables is defined and investigated. It is pointed out that this class is very broad, including, for example, virtually all treatments of wave propagation through a random medium. Proceeding by analogy with quantum field theory the quantities 𝒢 and M, related to the first and second moments of the stochastic Green’s function, are defined. Various properties of 𝒢 and M (which in quantum field theory correspond respectively to a propagator and an elastic scattering amplitude) are discussed, and it is shown that they may be conveniently used to describe the principal physical effects induced by transmission through a randomly fluctuating system. Specific examples are given in which these quantities are explicitly calculated and used to illustrate the general results.
Invariant properties of n-point functions and n-point functionals connected with the translational invariance of the formal measure
Authors: Hańćkowiak Jerzy
Published: March 2003

We discuss invariant properties of the generating functionals resulting from the translationally invariant formal measure used to define these functionals. The functionals considered depend on functions defined on five-dimensional space, and we relate to them n-point functionals and n-point functions. We derive equations for the above quantities, and we consider the connection with four-dimensional n-point quantities.
On the Palatini method of variation
Authors: Tsamparlis Michael
Published: March 2003

The Palatini method of variation is compared with the Hilbert method for symmetric metrics and affine connections. It is found that the two methods are in general inequivalent. The Hilbert method is recommended as being more general.
Tachyonic scalar waves in the Schwarzschild space–time
Authors: Dhurandhar S. V.
Published: March 2003

The scalar wave equation of a tachyon is investigated in the background of Schwarzschild geometry. The scalar field is split up into partial waves of all integral momentum states and the space development of each partial wave is studied as it approaches the singularity. The problem is mainly considered in the light of the assumption that the tachyon mass-parameter is comparable to the mass of a atomic particle while the black hole mass is comparable to that of an average star. The reflection and transmission properties of these partial waves at the effective potential barrier, arising partly from their angular momentum and partly from the curvature of space–time are discussed. It is found that in the radial case (l=0) the criteria for the bounce are different from the purely classical behavior of spacelike geodetic trajectories.
On independent sets of basis functions for irreducible representations of finite groups
Authors: Kopský Vojtĕch
Published: March 2003

Two theorems on bases of irreducible representations of finite groups are compared. It is stressed that their validity depends upon the functional sets for which they are formulated. The first theorem, which states that there are as many linearly independent (modulo the identity representation) sets of basis functions as is the dimension of the representation, is shown to hold only if the considered functional set constitutes a field. Otherwise, more such sets are necessary as shows the second theorem (extended Noether’s theorem), which is limited to polynomial algebra. The second theorem seems to be more apt for explicit construction of functional bases.
Scattering theory for Stark Hamiltonians involving long-range potentials
Authors: Zorbas J.
Published: March 2003

A time-dependent and stationary scattering theory is developed for operators of the form H=H0+V, H0=−Δ+E⋅x with V a long-range potential having the asymptotic form V (x) =O (‖x‖−l) as ‖x‖→∞, 0<l⩽1/2.
The interaction of the gravitational and electromagnetic fields
Authors: Lovelock David
Published: March 2003

Various sets of conditions are presented which a reasonable theory might be expected to satisfy, in attempting to explain the interaction of the gravitational and electromagnetic fields. It is shown that each of these sets leads inevitably to the Einstein—Maxwell field equations. Attention is also drawn to the fact that these equations must be modified if it is furthermore demanded that Maxwell’s equation in flat space—time be an exact solution of them.
Rigorous results on ferromagnetic lattice spin systems. I
Authors: Karaki Yukihiko
Published: March 2003

The Lee–Yang theorem was extended to the case of the correlation functions of the Ising ferromagnets (s=1/2). Each adjacent pair of zeros of the (n+1)th correlation function in the complex fugacity plane is separated by one and only one zero of the nth correlation function (n=0,1,2,...,N−1), and none of zeros of each function degenerate except for the infinite temperature in the completely connected system. The first Griffiths’ inequality for the correlation function was elaborated such as 〈σ1σ2⋅⋅⋅σn〉⩽ tanhn(mh/kT). The inequality for the free energy in the presence of the external field was obtained as −mh⩽ (h,T)−ℱ (0,T) ⩽−kT log[cosh(mh/kT)].
Nonbijective canonical transformations and their representation in quantum mechanics
Authors: Kramer P. , Moshinsky M. , Seligman T. H.
Published: March 2003

In the present paper we analyze the representations in quantum mechanics of classical canonical transformations that are nonbijective, i.e., not one-to-one onto. We take as the central example the canonical transformation that changes the Hamiltonian of a one-dimensional oscillator of frequency κ−1 into one of frequency k−1 where κ, k are relatively prime integers. For the particular case k=1, the mapping of the original phase space (x,p) onto the new one (x̄, p̄) is κ to 1 and the equivalent points in (x,p) are related by a cyclic group 𝒞κ of linear canonical transformations. When formulating this problem in Bargmann Hilbert space, the canonical transformation can be related to the conformal transformation w=zκ, which again is κ to 1 and where a group 𝒞κ also appears. This cyclic group proves fundamental for the determination of representations of the conformal transformation in Bargmann Hilbert space. To begin with, it suggests that while we can take in the original Bargmann Hilbert space a single component function, in the new Bargmann Hilbert space we must take a κ component one. In this way we can map in a one-to-one fashion the states and operators in the old and new Bargmann Hilbert spaces. When translating these results to ordinary Hilbert space, we get in an unambiguous way the quantization of the observables appearing in the equations that determine the representation of the classical canonical transformation relating oscillators of frequencies κ−1 and k−1. Furthermore, we also get the solutions of these equations, and the resulting representation is unitary. While our discussion is restricted to the problem mentioned above, in the concluding section we indicate our surmise for deriving systematically the unitary representation in quantum mechanics of arbitrary canonical transformations.
On the Weyl coefficients of SO(n)
Authors: Wong M. K. F.
Published: March 2003

It is shown that the representation functions of SO(n) can be obtained from those of SO(n−1) by calculating the Weyl coefficient of SO(n), which is equal to the representation function of SO(n) calculated at ϑ=π/2. Thus the problem of calculating the representation functions of SO(n) is reduced to its calculation at a particular value of ϑ (=π/2), instead of a whole range of values of ϑ. The Weyl coefficients of SO(3), SO(4), and SO(5) are explicitly obtained and discussed in detail. It is shown that the Weyl coefficients of SO(n) are all expressible as sums and products of 3-j symbols of SO(3) and normalization factorials. We also conclude that the representation functions of all orthogonal groups (as well as unitary groups) are ultimately reducible to the representation function of SO(2), i.e., eimϑ, multiplied by corresponding Weyl coefficients. Therefore, all representation functions of SO(n) and U(n) are ultimately expressible as Fourier series, whose coefficients can be explicitly calculated if one so wishes.
Scaling invariance of helical curve motion and soliton equations
Authors: Pereira Nino R.
Published: March 2003

The scaling properties of the equations describing the motion of helical curves determine the scaling of the associated nonlinear evolution equations. Only two polynomial scaling-invariant evolution equations can be found. Of these, the nonlinear Schrödinger equation has the physically correct scaling invariance, but the modified Korteweg–de Vries can not be connected to realistic helical curves.
Wavefunctions of identical particles
Authors: Bloore F. J. , Swarbrick S. J.
Published: March 2003

We present a description of the quantum mechanical states of a system of n indistinguishable particles moving on a manifold M by C/S2- valued functions ψ′ defined on the configuration space Mn/Sn. These functions satisfy one of two homotopy conditions, which characterize the particles as bosons or fermions. Any closed curve of Mn/Sn which does not intersect the diagonals can be classified as even or odd according to whether its lifts to Mn have end points in Mn which are even or odd permutations of each other. For bosons, ψ′ must map any such closed curve which also avoids kerψ′ onto an even number of basic loops of (C−{0})/S2. For fermions, ψ′ must map such even loops of Mn/Sn onto an even number, and odd loops onto an odd number, of basic loops of (C−{0})/S2.
Time-dependent scattering theory for infinite delta function potentials in one dimension
Authors: Dollard John D.
Published: March 2003

Existence of the Mo/ller wave operators is proved for a system of n quantum mechanical particles interacting through infinite delta function potentials in one dimension.
Killing vectors in plane HH spaces
Authors: Finley J. D. , Plebański J. F.
Published: March 2003

Employing the spinorial approach to the structure of hyperheavens, we integrate completely the Killing vector equations for plane (case I) hyperheavens, reducing them to one master equation of an extremely plausible form. (In this process, optimally simple gauges are demonstrated for each Petrov type.) The mechanism of generating Ernst potentials by Killing vectors is then investigated, and explicit forms are given. Also, some interesting preliminary study of Killing spinors of type D (0,k) in heavens is presented.
Error bounds for the complex-coordinate method
Authors: McCartor Gary
Published: March 2003

In this paper we derive calculable bounds for the error in two-body s-wave scattering calculations done by the complex-coordinate method. In the process we derive a bound on the error in the Born approximation. The utility of the results is discussed in light of simple examples.
Lower hybrid solitary waves
Authors: Yu M. Y.
Published: March 2003

It is found that, in a magnetized plasma, finite amplitude lower hybrid waves can propagate as solitons consisting of localized density cavities together with doublets of electric field spikes. An analytical expression, as well as the corresponding evolution equation, are derived for the small amplitude limit. Such solitons can also exist for many other waves having similar dispersive and nonlinear characteristics.
High-precision determination of the critical screening length for the static screened Coulomb potential
Authors: Kesarwani R. N. , Varshni Y. P.
Published: March 2003

By a combination of analytical and numerical methods, it is determined that the critical screening length for two particles interacting through an attractive static screened Coulomb potential lies between 0.8399032a0 and 0.8399039a0, where a0 is the Bohr radius.
Pseudoscalar transition between a spin-J and a spin-5/2 baryon
Authors: Lee Chien-er , Hong Jung-Kai
Published: March 2003

The decay width for a spin-J baryon decays into a spin-5/2 baryon, and a pseudoscalar meson is expressed in terms of different types of decay amplitudes. The overall ratio among decay amplitudes and the approximate decay width formula are derived by ignoring the higher partial waves.
Semiclassical quantization of a field theoretic model in any number of spatial dimensions
Authors: Ventura I. , Marques G. C.
Published: March 2003

The semiclassical canonical quantization of the nonrelativistic logarithmic theory is done in any number of spatial dimension d. Instead of the usual expansion of the Hamiltonian about the classical fields, we propose an alternative route to semiclassical quantization by making an expansion around the charge operator. When we take the value d=0 in the energy expression, the exact zero-dimensional spectrum is obtained. The mechanism of confinement characteristic of these logarithmic theories is also discussed.
Relativistic spherical stars reformulated
Authors: Glass E. N. , Goldman S. P.
Published: March 2003

The problem of finding static, spherically symmetric, solutions of Einstein’s equations for a perfect fluid is reformulated. A field equation connecting the pressure and density and free of metric components is obtained. Upon finding a solution of this field equation, the metric components are then obtained by quadrature. A solution-generating technique is developed which yields physically valid pressure-density configurations for adiabatically stable stars. Analytic solutions are obtained for the pressure, density, and metric components.
Solitons and the delta function fermion gas in Hartree–Fock theory
Authors: Lieb Elliott H. , de Llano Manuel
Published: March 2003

The quantum-mechanical, fermion, attractive delta function gas in one dimension has many interesting, known physical properties, including some aspects of soliton behavior. Motivated by a desire to test the validity of the HF approximation to many-body systems, we have made a rigorous study of the HF theory of this gas. When the particle number is even we can show that although HF theory does not give energies accurately, it does correctly predict the known qualitative properties; in particular, only two-particle bound states exist.
Variational interpolation
Authors: Pomraning G. C.
Published: March 2003

In a recent article in this journal [E. T. Cheng and R. W. Conn, J. Math. Phys. 17, 683 (1976)], a variational procedure was outlined to interpolate among known values of a functional of the solutions to inhomogeneous linear equations. In this paper, an alternate variational interpolation procedure for inhomogeneous equations is given. This alternate procedure utilizes the same data as the original method, but yields more accurate results. The same formalism can be applied to homogeneous equations, giving an interpolation procedure for homogeneous functionals such as eigenvalues. This refutes the conjecture of the earlier paper that a variational interpolation scheme for eigenvalues may not be possible.
Radiation (damping) in a universe with topologically closed space sections
Authors: Beig R.
Published: March 2003

A soluble model for an interacting oscillator-field system discussed previously is reconsidered with Minkowski space replaced by a Lorentzian static manifold with topologically closed space sections. It is shown that the general solution to the dynamical equations is—in the technical sense—almost periodic in time. In the case of the Einstein universe a more detailed discussion is presented, containing especially a study of the ’’thermodynamic limit’’ in which the radius of the universe tends to infinity.
Borel summability and indeterminacy of the Stieltjes moment problem: Application to the anharmonic oscillators
Authors: Graffi S. , Grecchi V.
Published: March 2003

An indeterminacy criterion is proven for the moment problem associated with the coefficients of a Borel summable power series of Stieltjes type which diverge faster than (2n) !. As an application we show that the Stieltjes type continued fraction corresponding to the Rayleigh–Schrödinger perturbation expansions for the energy eigenvalues of the anharmonic oscillators (x2(m+1) and in any finite number of dimensions) does not converge to the eigenvalues if m≳2. In particular, this implies the nonconvergence of the Padé approximants to the eigenvalues of p2+x2+λx2(m+1) if m≳2.
Entropy of an n-system from its correlation with a k-reservoir
Authors: Lubkin Elihu
Published: March 2003

Let a random pure state vector be chosen in nk-dimensional Hilbert space, and consider an n-dimensional subsystem’s density matrix P. P will usually be close to the totally unpolarized mixed state if k is large. Specifically, the rms deviation of a probability from the mean value 1/n is [(1−1/n2)/(kn +1)]1/2. ’’Random’’ refers to unitarily invariant Haar measure.
A Green’s function for a cubic lattice
Authors: Hioe F. T.
Published: March 2003

The following Green’s function for a cubic lattice is evaluated exactly and expressed in terms of the complete elliptic integrals of the first kind: G (E) = (1/π3) ℱℱℱπ0 dxdydz/[E −a1cosx−a2cosy−a3cosz−a2cosycosz−a1 coszcosx].
Uniform approximations to integral and integrodifferential equations
Authors: Ling Rina
Published: March 2003

Integral and intergrodifferential equations containing a small parameter are studied. An approximate solution is obtained and proved to be uniformly valid in t as the parameter tends to zero.
Variational method and Mathieu equation
Authors: Hsieh D. Y.
Published: March 2003

A variational method is developed to study the linear and nonlinear Mathieu equations. For the linear Mathieu equation, various modes of the Mathieu functions, the characteristic curves, and the stability regions are found, which agree with the established results. The variational method is then applied to the nonlinear Mathieu equation. Approximate periodic solutions of various modes are found in a similar manner, and their stability also investigated.
On the covariant equations of the relativistic electrodynamics of continua. I. General equations
Authors: Maugin G. A.
Published: March 2003

The aim of this series of papers is to develop both the field and constitutive equations for general relativistic electromagnetic continua. In this paper, the formulation starts from first principles of conservation and basic thermodynamical assumptions. This axiomatic character, however, is tempered by the use of results deduced from microscopical arguments by de Groot and Suttorp insofar as relativistically invariant expressions of the ponderomotive force and couple and of the electromagnetic power are concerned. This formulation is given entirely in terms of spatial space–time geometrical objects to facilitate the comparison with the Galilean theory of electromagnetic continua. It provides the thermodynamical cornerstone, i.e., the Clausius–Duhem inequality, in various equivalent forms which will be exploited in Papers II and III for material behaviors of interest in general relativistic, cosmological, and astrophysical problems which involve both the effects of gravitational fields and electric and/or magnetic fields.
On the covariant equations of the relativistic electrodynamics of continua. II. Fluids
Authors: Maugin G. A.
Published: March 2003

Based on the thermodynamical equations and conservation laws of a previous work which synthesized the axiomatic approach to relativistic continuum physics with the acceptance of the relativistically invariant ponderomotive force and couple and electromagnetic power derived by de Groot and Suttorp from a microscopical treatment, this paper develops a constitutive theory for general relativistic electromagnetic fluids. These include nonlinear and linear fluids with electrostriction and magnetostriction effects, dissipative fluids, and the ’’perfect magnetohydrodynamical’’ scheme as the extreme simplified case.
On the covariant equations of the relativistic electrodynamics of continua. IV. Media with spin
Authors: Maugin G. A.
Published: March 2003

The general scheme given in a previous work (Paper I) for the conservation laws and the thermodynamics of general relativistic electromagnetic continua is reexamined in the presence of intrinsic spin and couple stresses (i.e., when the total energy–momentum tensor is not symmetrical). Following two different sets of hypotheses concerning the nature of this spin and of the interactions responsible for the couple stresses, two descriptions of continuous matter emerge from the kinematical and thermodynamical study: first, that of paramagnetic and/or dielectric continua endowed with a rigid microstructure (hence a granular structure of the media) and, second, that of continua endowed with a continuous distribution of electronic spins. The latter scheme provides a phenomenological description of quantum-mechanical effects, which has been previously studied in detail by the author.
The graded Lie groups SU(2,2/1) and OSp(1/4)
Authors: Gürsey Feza , Marchildon Louis
Published: March 2003

We study the graded Lie groups corresponding to the graded Lie algebras SU(2,2/1) and OSp(1/4). General finite group transformations are parametrized, and nonlinear representations are obtained on coset spaces. Jordan and traceless algebras are constructed which admit these groups as automorphism groups.
A Galileian formulation of spin. I. Clifford algebras and spin groups
Authors: Brooke J. A.
Published: March 2003

By generalizing the concept of spin group to the case where the underlying orthogonal space is degenerate, the spin group associated with the homogeneous Galilei group is calculated. In so doing, the Galilei group and its spin group are clearly displayed as stability subgroups of the de Sitter group and its spin group. A notion of Clifford algebra contraction is introduced in the physical (Galilei) case and its relation to Lie algebra contraction is explored. Both the stated generalization of spin group to cases with degenerate bilinear form and the idea of Clifford algebra contraction appear to be new.
Stability of Weiss Ising model
Authors: Ohya Masanori
Published: March 2003

The problems of stability and approach to equilibrium of the Weiss Ising model are studied. Our investigations are performed in the exact and linear response senses in order to compare both theories. The change of a metastable state of the Weiss Ising model is discussed under local perturbations.
Nontranslationally covariant currents and symmetries of the S matrix
Authors: Garber W. D. , Reeh H.
Published: March 2003

Generators of symmetries constructed from nontranslationally covariant currents are defined on scattering states and commute with the S matrix.
Electromagnetic solutions of Brans–Dicke theory of gravitation from Einstein theory
Authors: Johri V. B. , Goswami G. K.
Published: March 2003

A class of static and nonstatic solutions of the Brans–Dicke theory of gravitation is obtained in the presence of an electromagnetic field. The metric coefficients and fields (both scalar and electromagnetic) are supposed to be functions of any three independent variables. The major result of the paper may be stated as follows: ’’Corresponding to any diagonalizable solution of Einstein’s vacuum field equations in which fields and metric coefficients are functions of not more than three variables, we can generate a solution of the coupled Brans–Dicke Maxwell field equations with nonzero electromagnetic field.’’
A Chebyshev polynomial method for computing analytic solutions to eigenvalue problems with application to the anharmonic oscillator
Authors: Boyd John P.
Published: March 2003

In this work, I present a two-part algorithm which employs Chebyshev polynomials to compute the eigenvalues and eigenfunctions of an ordinary differential equation and to represent their dependence on a problem parameter λ. To illustrate these methods, I apply them to the anharmonic oscillator where the parameter λ is the coupling constant. I show that these techniques are simple, efficient, and easy to program for a computer. Unlike perturbation methods or numerical tables, the Chebyshev algorithms calculate explicit, highly uniform polynomial approximations to each function on any interval on which the function is analytic. Perhaps the most important result of this work is that although the two Chebyshev algorithms are numerical, all the results are analytic—a dramatic counterexample to the conventional wisdom which holds that to obtain nonnumerical solutions, one must use analytic, paper-and-pencil techniques. Thus, the two-part Chebyshev approach, despite its numerical basis, should be regarded principally as a new and powerful method for computing analytic solutions which will succeed where ordinary (and even extraordinary) perturbation methods fail.
The homotopy groups of condensed matter physics
Authors: Mermin N. D.
Published: March 2003

The classes of distinct point and line defects in ordered media and the laws governing their combination, are determined by the fundamental group of the order parameter space π1, the second homotopy group π2, and the group of automorphisms induced in π2 by the action of π1. A simple algorithm is given for computing all of these algebraic structures for a quite general family of ordered forms of condensed matter.
Lorentz subgroup analysis of the Lie algebra of Sp(8,R) and a null-plane, boson realization
Authors: Staunton L. P.
Published: March 2003

An algorithm is given for the construction of the Lie algebra of Sp(2N, R), integral N?3, in the form in which the tensor character of the generators under the action of a Lorentz subgroup is apparent. A specific realization of the algebra of Sp(8,R) in terms of four boson operators is presented, along with the tensor form of the complete algebra classified under the (unique) full null-plane Lorentz subalgebra. The identities obtaining for the specific boson operator realization employed for Sp(8,R) are listed, use of which permits subsidiary conditions for four boson constrained systems to be expressed in terms of Lorentz invariants.
On the coupling of logics
Authors: Zecca Antonio
Published: March 2003

A scheme for the coupling of physical systems is proposed within an axiomatic approach to quantum mechanics.
A method for computing scattering phase shifts and eigenvalues of the Schrödinger equation with singular potentials
Authors: Naundorf Friedrich F.
Published: March 2003

An algorithm is given for computing the scattering phase shifts and eigenvalues of the Schrödinger radial equation with singular potentials. As an application we treat the hydrogen atom with fine structure in the nonrelativistic theory.
Lie theory and the wave equation in space–time. 5. R-separable solutions of the wave equation ψt
t−Δ3ψ=0
Authors: Kalnins E. G. , Miller W.
Published: March 2003

A detailed classification is made of all orthogonal coordinate systems for which the wave equation ψtt−Δ3ψ=0 admits an R-separable solution. Only those coordinate systems are given which are not conformally equivalent to coordinate systems that have already been found in previous articles. We find 106 coordinates to given a total of 368 conformally inequivalent orthogonal coordinates for which the wave equation admits an R separation of variables.
A variational principle for transport theory
Authors: Kanal Madhoo , Moses Harry E.
Published: March 2003

A maximal variational principle is used to construct an infinite medium Green’s function for treating the boundary value problems of the linear transport theory (neutron and radiative). For the neutrons we consider the one-speed case and correspondingly for the radiative transfer the monochromatic case. The scattering properties of the medium are presumed to be dependent on the relaxation length. Thus, for the neutrons the secondary production function depends on the neutron’s relaxation length and for the radiative transfer the albedo for single scattering is dependent on the optical depth. These two functions are kept arbitrary so that a large class of problems can be covered. The basic principle involves a functional which is an absolute maximum when the trial function is an exact solution of an integral equation of the Fredholm type. The kernel of the integral equation is required to satisfy certain symmetry and boundedness properties. We also exhibit an interesting relation between the absolute maximal and Schwinger’s stationary variational principles, which in general is neither a maximum nor a minimum.
A class of multidimensional nonlinear Langmuir waves
Authors: Wang P. K. C.
Published: March 2003

Nonlinear Langmuir waves in a plasma governed by the dimensionless equations i∂E/∂t=−∇2E+nE, ∂2n/∂t2 =∇2[n+g (‖E‖2)] are studied, where E is the complex amplitude of the high-frequency electric field, n is the low frequency perturbation in the ion density from its constant equilibrium value, and g is a given function of ‖E‖2. General conditions for the existence or nonexistence of a class of multidimensional solitary-wave and nonlinear periodic travelling-wave solutions in the form E(t,x) =h(k⋅x−vt) and n (t,x) =s (k⋅x −vt) are established. The results are applied to the special cases: (i) g (‖E‖2) =‖E‖2 corresponding to the usual pondermotive force, and (ii) g (‖E‖2) =K[1−exp(−‖E‖2)], K is a positive constant, representing ion density saturation.
Null infinity is not a good initial-data surface
Authors: Geroch Robert
Published: March 2003

An example is given of a space–time which is asymptotically flat and globally well-behaved, and yet which admits a nonzero Maxwell field, with zero source, having no incoming radiation from past null infinity.
On the generation of new solutions of the Einstein–Maxwell field equations from electrovac spacetimes with isometries
Authors: Hauser Isidore , Ernst Frederick J.
Published: March 2003

We present transformation formulas which facilitate the determination of the metrics, electromagnetic fields, connections and Weyl tensors of those electrovac spacetimes which result when a given solution of the Einstein–Maxwell equations with an isometry is subjected to the transformations of the Kinnersley group. Several applications of our calculational procedures are given as illustrations, and a number of general theorems are presented. In particular, we infer that when we apply such techniques to the only known solution of Petrov type N with twisting principal null rays, the new solutions which result will be algebraically general.
Nonlinear realizations of the direct product of two Lorentz groups on a skew-symmetric tensor space
Authors: Dalton B. J.
Published: March 2003

In this paper, we present a study of exact, infinitesimal, nonlinear realizations of the direct product (L1×L2) of two Lorentz groups on an antisymmetric tensor space η. Included in this study is a detailed discussion of the second order (L1×L2)/L+ coset realizations where L+ is the symmetric Lorentz subgroup. Invariant metric forms defined on η are exhibited and compared with invariant metric forms obtained in some previous studies of coset realizations.
The distribution function for stretched dipoles in an applied electric field
Authors: Mason D. P. , McIlroy D. K.
Published: March 2003

An expression is derived for the distribution function of an assemblage of ion pairs in the presence of a uniform applied electric field, for the most interesting and important case, namely when the interaction force between the components of such stretched dipoles is unshielded Coulombic. Our derivation makes use of results obtained previously when determining, by means of a perturbation technique, the relative increase in the dissociation constant of a weak electrolyte due to an applied electric field. The expression we obtain for the ion-pair distribution function agrees with that given previously by Onsager [J. Chem. Phys. 2, 599 (1934)], whose derivation has never been published in full.
Linear response theory revisited. I. The many-body van Hove limit
Authors: van Vliet K. M.
Published: March 2003

A critical discussion of linear response theory is given. It is argued that in the formalism as it stands no dissipation is manifest. A physical reinterpretation for the case of a system in weak interaction with a reservoir is given. Mathematically this means that the van Hove limit, as well as the large system limit, is applied to the time-dependent Heisenberg operators of the Kubo formalism. The reduced operators can be put in a very compact form, viz.,BRα(t) =[exp(−Λdt)]Bα, where Bα is a Schrödinger operator and Λd is the Liouville space superoperator corresponding to the transition operator of the master equation. In this form the relaxation character of the transport expressions, and the approach to equilibrium is at once evident. New expressions for the generalized susceptibility and conductivity in this limit are presented. Also, the Onsager relations and other symmetry properties are confirmed.
The intelligent states. II. The computation of the Clebsch–Gordan coefficients
Authors: Rashid M. A.
Published: March 2003

In this second of a series of papers on quasi-intelligent states, we give a general method for the computation of the Clebsch–Gordan coefficients for these states. In a special case, these coefficients are found to be closely related to the Clebsch–Gordan coefficients of the rotation group. We also discuss the nonuniqueness resulting naturally from the overcompleteness of these states.
Path integrals for solving some electromagnetic edge diffraction problems
Authors: Lee S. W.
Published: March 2003

Electromagnetic edge diffraction problems involving parallel half-planes are traditionally attacked by the Wiener–Hopf technique, or asymptotically for a large wavenumber (k→∞) by ray-optic techniques. This paper reports a novel method in which the electromagnetic wave equation is first converted to a heat equation via the Laplace transform. The heat equation together with the original boundary condition is next solved approximately in terms of a path integral over the Wiener measure. For several examples involving two parallel half-planes, the path integral is evaluated explicitly to yield an asymptotic solution of order k0 for the field on the incident shadow boundary. Those solutions agree with the ones derived by traditional techniques, but are obtained here in a much simpler manner. In other examples involving multiple half-planes, the use of a path integral leads to new solutions. We have not succeeded, however, in generating higher-order terms beyond k0 in the asymptotic solution by path integrals.
Cylindrically symmetric dust distributions in rigid rotation in Brans–Dicke theory
Authors: Bandyopadhyay Nikhilendu
Published: March 2003

A solution for the field equations of Brans–Dicke theory for the case of a cylindrically symmetric dust distribution in rigid rotation has been obtained. The exact solution shows the existence of closed timelike lines as also infinities of mass density, B−D scalar, etc., at finite proper distance from the axis of symmetry just as in the corresponding general relativistic case.
On a possible experiment to evaluate the validity of the one-speed or constant cross section model of the neutron-transport equation
Authors: Siewert C. E.
Published: March 2003

The inverse problem for a half-space is solved (for isotropic scattering) to yield results that suggest an idealized experiment that could be used to evaluate in a new way the validity of the one-speed or constant cross section model of the neutron-transport equation.
Lorentz transformations of observable and ghost particle states in quantum electrodynamics and in a massive gauge theory
Authors: Haller K. , Sohn R. B.
Published: March 2003

Derivations are given of the effect of Lorentz boosts on physical particle and ghost states in quantum electrodynamics. It is shown that the photon helicity is an invariant even though, in general, Lorentz boosts transform the transverse, longitudinal, and timelike components of the vector potential into each other. A similar calculation is made for an Abelian gauge theory in which the particles have dynamical mass.
Exact vacuum solutions of Einstein’s equation from linearized solutions
Authors: Xanthopoulos Basilis C.
Published: March 2003

It is proved that if (M,gab) is an exact vacuum solution of Einstein’s equation, la a null vector field and if lalb satisfies the linearized equation on background (M,gab), then gab+lalb is an exact vacuum solution. Applications to the search for asymptotically flat spacetimes are discussed.
Regge pole behavior in φ3 field theory
Authors: Bergère M. C. , Gilain C.
Published: March 2003

We consider the Feynman amplitudes for all the essentially and crossed planar graphs of the four-point vertex function in φ3 field theory, and we evaluate their behavior at high energy (large s, fixed t). We compute the coefficients of all logarithms for the dominant amplitudes which behave in s−1 (up to logarithms of s). This computation is performed by using the Bogoliubov–Parasiuk–Hepp R operation and the Mellin transform of the Feynman amplitudes. The geometrical structure of the coefficients is such that all logarithms of s of all dominant amplitudes can be summed to give the well-known Regge behavior with signature +. The Regge trajectory verifies an equation which may be solved explicitly in the lowest order approximation; the residue is found to be the ratio of two functions of t, the upper one being factorized into two vertex functions expressed as infinite series and the lower one providing a ghost killing factor.
A technique for analyzing the structure of isometries
Authors: Ashtekar Abhay , Magnon-Ashtekar Anne
Published: March 2003

A new technique is introduced to investigate the structure of isometry Lie algebras. Some general results are first proved by applying this technique to n-dimensional manifolds equipped with metrics of arbitrary signature. A restriction is then made to 3-manifolds representing the space of orbits of the timelike Killing field in stationary space–times. Under the assumption of asymptotic flatness at spatial infinity, a complete description of isometry Lie algebras of these 3-manifolds is obtained. As corollaries, several results about symmetries of stationary isolated systems in general relativity are proved.
Multiplicity-free 6-j symbols and Weyl coefficients of U(n): Explicit evaluation
Authors: Wong M. K. F.
Published: March 2003

An explicit expression has been obtained for all known multiplicity-free 6-j symbols of U(n), i.e., 6-j symbols of the following three types, where anyone of its columns consists of (1) two totally symmetric representations, (2) one totally symmetric and one conjugate to the totally symmetric, and (3) two conjugate to the totally symmetric. The symmetry properties of the multiplicity-free 6-j symbols of U(n) under permutation of columns, inversion of any two columns, and conjugation are given. Some general theorems concerning the multiplicity-free 6-j symbols of U(n) or more precisely, the multiplicity-free 6-j symbols of the ’’SU(n) type’’ have been obtained. Since the Weyl coefficients of U(n) are basically 6-j symbols of U(n−1), we also conclude that the Weyl coefficients of U(n) have been explicitly obtained. This result implies that the d function of U(n) can be completely and explicitly written down in terms of the Weyl coefficients.
Conditional probabilities and statistical independence in quantum theory
Authors: Srinivas M. D.
Published: March 2003

The problem of defining conditional probabilities and the notion of statistical independence in quantum theory is analyzed. It is shown that (unlike in classical probability theory) the conditional probabilities of a given set of events can be determined only if the sequence of all the experiments performed on the system is also specified. Such a specification is necessary also for the concept of statistical independence to become physically meaningful.
On the higher approximations of the K-harmonics method
Authors: Castilho Alcarás J. A.
Published: March 2003

Exact formulas for the calculation of two-body central interactions in the K-harmonics method are derived. These formulas hold for any approximations and account for diagonal and off-diagonal matrix elements as well.
Bifurcation from rotationally invariant states
Authors: Sattinger D. H.
Published: March 2003

Bifurcation in the presence of the rotation group is investigated. The covariant bifurcation equations are derived using the familiar angular momentum operators of quantum mechanics. Variational methods are also discussed. It is shown that the quadratic terms either vanish for odd l or possess a gradient structure for even l. This result is generalized to the case of an arbitrary simply reducible group. Applications to problems in geophysics and elasticity theory are discussed.
The Feynman maps and the Wiener integral
Authors: Truman Aubrey
Published: March 2003

By introducing the family of Feynman maps ℱs, we show that our earlier definition of the Feynman path integral ℱ=ℱ1 can be obtained as the analytic continuation of the Wiener integral E =ℱ−i. This leads to some new results for the Wiener and Feynman integrals. We establish a translation and Cameron–Martin formula for the Feynman maps ℱs, having applications to nonrelativistic quantum mechanics. We also estalish a (weak) dominated convergence theorem for ℱ1=ℱ.
The theory of superselection rules. I. A class of inequivalent, irreducible *-representations of the canonical commutation relations of the free electromagnetic field
Authors: Ekhaguere G. O. S.
Published: March 2003

We begin here the rigorous construction of new superselection sectors for the free quantum electromagnetic field by exhibiting a wide class of inequivalent irreducible *-representations of the canonical commutation relations of the electromagnetic field. The *-representations constructed here satisfy all the axioms of Haag and Kastler, except possibly Poincaré covariance. In a forthcoming paper, the construction of the new superselection sectors is completed with the study of the spectrum condition for the *-representations.
Direct-inverse problems in transport theory. 1. The inverse problem
Authors: Kanal Madhoo , Moses Harry E.
Published: March 2003

For the inverse problem treated here we use the results of an experiment which measures the total angular-dependent column density as compared to the measurement which provides information on the angle integrated spatial-dependent angular density (or the specific intensity). We use two methods of approach. One, the Legendre expansion method and two a maximal variational principle. In particular we demonstrate how the variational principle yields a very convenient representation of the scattering kernel (or the phase function) in terms of a basis consisting of Case eigenfunctions for the isotropically scattering medium.
Inönü–Wigner contractions of the real four-dimensional Lie algebras
Authors: Huddleston P. L.
Published: March 2003

All Inönü–Wigner contractions of the real four-dimensional Lie algebras are found. The results are summarized in tables.
Unitarily equivalent multiparticle Hamiltonian systems yielding equal scattering for corresponding states
Authors: Sáenz A. W. , Zachary W. W.
Published: March 2003

Consider a pair of nonrelativistic N-particle (N?2) systems with unitarily equivalent Hamiltonians H and W*HW. Typically, W*HW involves nonlocal multiparticle interactions even when only local pair interactions are present in H. For the respective cases when H involves short-range interactions alone and also when it involves long-range ones, sufficient conditions are established in order for a scattering amplitude of the first system pertaining to any states in given entry and exit channels to equal the amplitude of the second system pertaining to corresponding states. This is accomplished by a time-dependent approach. The correspondence in question assigns to each channel state of the first system a channel state of the second system in a bijective and intuitively natural manner. Nontrivial examples are given of unitary operators W for which the above equality holds for all channels of these systems. This applies to a large class of interactions in H, including interactions with suitable long-range parts. The present work is the theoretical foundation of a new method of the authors, discussed elsewhere, for investigating many-body nuclear forces phenomenologically.
On the equivalence of quantum mechanics and a certain class of Markov processes
Authors: Davidson Mark
Published: March 2003

Some new results in the stochastic model of quantum mechanics are derived. The origin of the noncommutative algebra of quantum mechanics is given a simple interpretation within the stochastic model. Quantum expectations of mixed functions of coordinates and momenta are related to stochastic averages.
On critical probabilities in percolation theory
Authors: Wierman John C.
Published: March 2003

Several versions of the concept of critical percolation probability are discussed in the bond percolation problem on the square lattice. Critical probabilities are also employed as technical devices in the proofs of two new results. First, there is a critical probability pT below which all moments of the cluster size are finite. Secondly, an infinite connected cluster of open bonds exists with positive probability if and only if any angular sector contains an infinite connected cluster of open bonds with positive probability. An expression is derived for the expected number of open clusters per bond in the percolation model, relating to the problem of rigorously justifying a critical probability result of Sykes and Essam.
Pointwise ergodic theory on operator algebras
Authors: Radin Charles
Published: March 2003

We extend Birkhoff’s pointwise ergodic theorem from classical mechanics to the overlap with quantum mechanics.
Generalized C-metric
Authors: Ernst Frederick J.
Published: March 2003

We describe a procedure for generalizing static axially symmetric solutions of the vacuum Einstein field equations, and employ this procedure to append an external gravitational field to the C-metric black hole solution. We conjecture that if the strength of the appended gravitational field is chosen appropriately, our generalized C-metric will serve as a better model for an accelerating black hole than the original C-metric.
Hydrodynamic fluctuation theories
Authors: Fox Ronald Forrest
Published: March 2003

Incompatible theories for hydrodynamic fluctuations far from full equilibrium are described and compared. The two types of approach are compared with the well established near equilibrium theory of hydrodynamic fluctuations. They are also checked for internal consistency and it is shown that one of the approaches checks out as inconsistent. The other approach is recommended as a valid approaach.
A time-symmetric tachyon universe
Authors: Srivastava Sushil K. , Pathak Mahendra P.
Published: March 2003

The momentum flux (ρ) and contrast momentum flux (K=δρ/ρ) are investigated in an open time-symmetric model of the tachyon universe containing different types of tachyon fluid, when η≪η0. It has also been shown that pressure turns negative when η≪η0. In the light of this approximation, how the physical situation changes in the model has been discussed. The tetrad technique has been used as a mathematical tool.