bluuebunny/crossref_metadata_2025 huggingface dataset:
On the inverse problem of transport theory with azimuthal dependence
Authors: McCormick N. J. , Veeder J. A. R.
Published: March 2003

The infinite medium inverse problem with an azimuthally dependent plane source leads to integral moments of the intensity over all space and angle. A new relationship has been derived between the moments and the coefficients of the expansion of powers of ν in terms of the gmk(ν) polynomials which arise in transport problems without azimuthal symmetry. This relationship has been used to obtain an improved method for determining the moments.
Transmission problems for the Helmholtz equation
Authors: Kress R. , Roach G. F.
Published: March 2003

A straightforward treatment of these problems is given which appears to avoid many of the previously encountered difficulties. Admittedly some generality is lost by assuming that the various associated parameters ki are not space dependent within their respective domains of definition, Di. Nevertheless, by means of the approach offered here, such problems can be analyzed in just one function space; more general existence and uniqueness theorems can be obtained; there is no need to regularize the operators involved; and, above all, the solutions can be expressed in terms of certain boundary integral equations which, computationally, offer good prospects.
Functional integrals over anticommuting variables and the one-dimensional scattering problem
Authors: Samuel Stuart
Published: March 2003

Functional integrals over anticommuting variables are used to obtain a scattering formula for smooth localized potentials in one dimension. Via a calculational trick, the functional integral is evaluated to obtain the transition matrix coefficients as an expansion in [k′ (x)/k (x)] (k (x) ={ (2m/h/2)[E−V (x)]}1/2). This expansion is shown to have a simple physical interpretation.
An inversionlike integral equation in the multidimensional case
Authors: Cornille Henri
Published: March 2003

In this paper and in the following, we deduce inversionlike integral equations (from which we can construct a class of potentials without introducing the data) in the case of a system of n linear first-order partial differential equations with different coordinate variables. The partial differential part of the linear operator is a diagonal matrix with each element acting only on a particular coordinate.
Correlations in an N-mode laser
Authors: Hioe F. T.
Published: March 2003

Analytic expressions for the correlations of the light emitted by an N-mode laser are given. We study in particular a special case of strongest couplings and show, for example, that at steady state, the second order cross intensity correlation tends toward a negative value, −1/(N−1), for large pump parameters. We also study the time dependent solutions, and express the second order amplitude and intensity correlations of the emitted light in terms of the eigenvalues and eigenfunctions of a Schrödinger-type differential equation which reduces to that studied by Risken for N=1 and to that studied by M-Tehrani and Mandel for N=2. Analytic expressions which approximate the eigenvalues of this differential equation for a general N are given.
Lie theory and the wave equation in space–time. 4. The Klein–Gordon equation and the Poincaré group
Authors: Kalnins E. G. , Miller W.
Published: March 2003

A detailed classification is made of all orthogonal coordinate systems for which the Klein–Gordon equation in space–time, ψtt−Δ3ψ=λψ, admits a separation of variables. We show that the Klein–Gordon equation is separable in 261 orthogonal coordinate systems. In each case the coordinate systems presented are characterized in terms of three symmetric second order commuting operators in the enveloping algebra of the Poincaré group. This paper also consitutes an important step in the study of separation of variables for the wave equation in space–time ψtt−Δ3ψ=0, and its relation to the underlying conformal symmetry group O(4,2) of this equation.
Boundary condition solutions of the generalized Feller equation
Authors: Lehnigk Siegfried H.
Published: March 2003

Solutions of the generalized one-dimensional autonomous parabolic Feller equation for given boundary conditions are established. Since a basic solution is known, the Green–Riemann technique is used. It leads to two Green–Riemann limit functions relative to subsets of the space of two parameters connected with the equation. Properties of these limit functions are discussed. These functions are then used to establish boundary condition solutions in the form of unilateral convolutions involving as boundary conditions those functions which are summable over every nonnegative compact interval. Finally, it is shown that, relative to two subsets of the space of two equation parameters, there exist initial and boundary condition solutions.
The structure of the many-body wavefunction for scattering
Authors: L’Huillier M. , Redish Edward F. , Tandy P. C.
Published: March 2003

We show that the scattered part of the many-body wavefunction initiated by two incoming clusters is given by a fully connected operator acting on the initial channel state. The structure of this operator suggests a division of the full wavefunction into two-cluster components. A set of coupled equations in both the differential and integral form is then derived for these components. These equations have structure and properties similar to the three-body equations of Faddeev. We demonstrate that each component has outgoing waves in a unique two-cluster partition. The transition amplitude for any final arrangement can therefore be extracted directly from the outgoing waves in the relevant components.
Optical analysis of resonances in a velocity-dependent potential
Authors: Sesma J. , Vento V.
Published: March 2003

Resonances in a velocity-dependent square well potential are analyzed in terms of multiple reflections of the incident wave on the internal walls of the potential well. The results differ considerably from those obtained for static potentials with a similar analysis.
A particle model based on stringlike solitons
Authors: Enz U.
Published: March 2003

This paper deals with two scalar fields ϑ (x,y,z,t) and φ (x,y,z,t) which are governed by two coupled nonlinear differential equations. Some of the spatial field distributions of ϑ and φ are topologically stable and represent solitons in three-dimensional space. The simplest stable solitons are identified with the electron and the positron. The asymptotic solutions of the fields are studied. ϑ is shown to fall off asymptotically as ±a/r, where a is a constant related to the elementary charge and r the distance from the ’’site’’ of the soliton.
Approximate symmetry groups of inhomogeneous metrics: Examples
Authors: Spero Alan , Baierlein Ralph
Published: March 2003

By definition, an N-dimensional positive-definite inhomogeneous metric is not invariant under any N-parameter, simply-transitive continuous group of motions. Nonetheless, it is possible to construct a group (simply-transitive and of N parameters) that comes closest to leaving the given metric invariant. We call this group the approximate symmetry group of the metric. In an earlier paper, we described a technique for constructing the approximate symmetry group of a given metric. Here, we briefly review that technique and then present some examples of its application. All two-dimensional metrics are analyzed, and simple criteria are given for determining their approximate symmetry groups. Three three-dimensional metrics are investigated: the invariant hypersurfaces of the Kantowski–Sachs space–times and two families of hypersurfaces in the Gowdy T3 space–times. The approximate symmetry group of the former is found to be of Bianchi Type I and those of the latter may be I or VI0. Defining, via our technique, a measure I of the magnitude of a metric’s inhomogeneity, we study the time dependence of I for the hypersurfaces in the Gowdy metric. We find it is possible in some cases for these hypersurfaces to approach homogeneity (I→0) both in the asymptotic future and near the initial singularity. Finally, we constant a homogeneous background metric for these hypersurfaces.
A no-go theorem for polarization structure
Authors: Goldstein Gary R. , Moravcsik Michael J.
Published: March 2003

It would be extremely advantageous, from the point of view of the planning of experiments and of the testing of theoretical models by such experiments, if a representation of the reaction matrix could be found such that the differential cross section is given by the absolute value squared of a single amplitude, and the simplest type of polarization experiments are expressed in terms of functions involving only two amplitudes each. It is shown that, within the framework of a set of plausible and very weak constraints, such a representation does not exist.
On the charged Kerr–Tomimatsu–Sato family of solutions
Authors: Yamazaki Masatoshi
Published: March 2003

The charged Kerr–Tomimatsu–Sato family of solutions with arbitrary integer distortion parameter δ for gravitational fields of spinning masses is presented. The Bonnor–Misra–Pandey–Srivastava–Tripathi–Wang family of solutions is also referred to.
Simple analytic expressions for the Coulomb off-shell Jost functions
Authors: van Haeringen H.
Published: March 2003

The off-shell Jost functions have been introduced by Fuda and Whiting. We give simple closed expressions for fC,l(k,q), the off-shell Jost functions for the Coulomb potential, and we derive their connection with the ordinary Coulomb Jost functions fC,l(k).
Simple proof of no position operator for quanta with zero mass and nonzero helicity
Authors: Jordan Thomas F.
Published: March 2003

That there is no Newton–Wigner position operator in an irreducible unitary representation of the Poincaré group for zero mass and either variable helicity or fixed nonzero helicity is proved formally using familiar operator algebra and transformations and bringing out relevant properties of operators in the representation. In the case of fixed helicity, a pair of irreducible representations with opposite helicities is considered, so the parity operator is defined; then the correct parity transformation is assumed for the position operator.
Solution of a modified Lamé equation with an integral term
Authors: Hagelstein P. L.
Published: March 2003

We consider an equation which occurs in the stability analysis of a passively modelocked laser system in which the pulses overlap. The equation is related to a Lamé equation and can be written su (x) ={d2/dx2−[(2−m)−6dn2(x,m)]}u (x) −εℱK(m)−K(m)u (x′)dn(x′,m) dx′ (1+ν2d2/dx2)dn(x,m), where s is an eigenvalue and ε and ν are arbitrary parameters which need not be small. The eigenfunctions satisfy periodic boundary conditions u (x+2K (m)) =u (x). The eigenvalue s is proportional to the rate of growth of perturbations of the steady state pulse, and so we focus on finding the conditions under which no eigenvalue s is positive. We find that ε=2/{ξ (m)−ν2[2E (m)−(2−m) ξ (m)]} marks the stability boundary, where E (m) is the elliptic integral of the second kind and ξ (m) is a function defined within the paper. This result is exact.
The intelligent states. I. Group-theoretic study and the computation of matrix elements
Authors: Rashid M. A.
Published: March 2003

In this first of a series of papers, a group-theoretic study is presented of the quasi-intelligent states which are a generalization of the intelligent states satisfying equality in the Heisenberg uncertainty relation ΔJ12ΔJ22? (1/4) ‖〈J3〉‖2. A method based on the knowledge of a certain generating function is given for the calculation of matrix elements of polynomials in the infinitesimal generators of the rotation group between quasi-intelligent states. Examples of such computations are also included to exhibit the improvement and efficiency of the present methods.
Three- and four-wave interactions in plasmas
Authors: Boyd T. J. M. , Turner J. G.
Published: March 2003

The nonlinear interaction of three and four waves in a warm magnetized plasma is studied using the Lagrangian formalism. General expressions for the coupling coefficients are obtained in each case. Coupled-mode equations describing four-wave interactions have been derived and solved. The extension of the theory to the interaction of random phase waves and weak inhomogeneity is also discussed.
Discrete finite nilpotent Lie analogs: New models for unified gauge field theory
Authors: Kornacker Karl
Published: March 2003

To each finite dimensional real Lie algebra with integer structure constants there corresponds a countable family of discrete finite nilpotent Lie analogs. Each finite Lie analog maps exponentially onto a finite unipotent group G, and is isomorphic to the Lie algebra of G. Reformulation of quantum field theory in discrete finite form, utilizing nilpotent Lie analogs, should elminate all divergence problems even though some non-Abelian gauge symmetry may not be spontaneously broken. Preliminary results in the new finite representation theory indicate that a natural hierarchy of spontaneously broken symmetries can arise from a single unbroken non-Abelian gauge symmetry, and suggest the possibility of a new unified group theoretic interpretation for hadron colors and flavors.
A theory of classical limit for quantum theories which are defined by real Lie algebras
Authors: Drühl Kai
Published: March 2003

A theory of classical limit is developed for quantum theories, the basic observables of which correspond to elements in some real Lie algebra L0. For both quantum and classical systems based on L0 the basic observables are contained in a unique universal algebra. This is the universal enveloping algebra 𝒰 for the quantum case, and a universal commutative Poisson algebra ℒ for the classical case. 𝒰 and ℒ are connected by a system of contraction maps. For certain sequences of representations and of vector states defined by them renormalized expectation values of the quantum variables are shown to converge to values of the corresponding classical variables at some point in the classical phase space. The classical phase space is obtained as a limit of certain systems of coherent states. The general theory is illustrated by several examples and counterexamples.
Characterization of certain stationary solutions of Einstein’s equations
Authors: Chitre D. M.
Published: March 2003

A scheme is proposed to characterize Tomimatsu–Sato solutions of Einstein’s equations. It categorizes an infinite series of solutions, the lowest (nonflat) members of which are the Schwarzschild solution for the static case and the Kerr solution for the stationary case.
Fourth degree Casimir operator of the semisimple graded Lie algebra (Sp(2N); 2N)
Authors: Bednař Miroslav , Sachl Vladimir
Published: March 2003

The Casimir operators of the graded Lie algebra (Sp(2N);2N) [denoted also by OSp(1/2N) in the literature] are discussed. A general method, according to which the higher degree Casimir operators of the graded Lie algebras, in our case of the (Sp(2N);2N), can be constructed is developed. It is shown that the third degree Casimir operator of this graded Lie algebra does not exist. The Casimir operator of the fourth degree is derived explicitly.
A note on recoupling coefficients for SU(3)
Authors: Millener D. J.
Published: March 2003

A 6- (λμ) coefficient, denoted by Z and different from the usual U coefficient, associated with a specific recoupling of three irreducible representations of SU(3), is defined. A general 9- (λμ) coefficient, analogous to the unitary 9-J coefficient of the angular momentum Racah algebra, is then expressed in terms of the Z coefficient and two U coefficients. In this way problems associated with the existence of outer multiplicities in the products of irreducible representations of SU(3) are circumvented.
Solution of the almost-Killing equation and conformal almost-Killing equation in the Kerr spacetime
Authors: Taubes Clifford Henry
Published: March 2003

Four linearly independent classes of vector solutions to the generalized almost-Killing equation in the Kerr spacetime are presented in terms of Teukolsky’s radial and angular functions. The vector solutions which are asymptotic to the ten Minkowski-space Killing vectors are given by way of example.
Spatial conformal flatness in homogeneous and inhomogeneous cosmologies
Authors: Spero Alan , Szafron Duane A.
Published: March 2003

In the past few years there has been a growing interest in cosmological models which are not spatially homogeneous. The assumption of spatial homogeneity simplifies the Einstein equations to ordinary differential equations. If the assumption of spatial homogeneity is relaxed, some other symmetries are needed to make the Einstein equations mathematically tractable. The recently discovered solutions of Szekeres have been found to possess an interesting type of symmetry: The three spaces orthogonal to the fluid flow are conformally flat. Herein, we prove a theorem restricting the possible inhomogeneous cosmologies with conformally flat 3-surfaces. We determine which spatially homogeneous models admit conformally flat 3-surfaces. This information, although interesting in its own right, will serve as a guide in determining those spatially homogeneous models that may be generalized by retaining spatial conformal flatness but relaxing the condition of spatial homogeneity.
On the separability of the sine-Gordon equation and similar quasilinear partial differential equations
Authors: Osborne Anthony , Stuart Allan E. G.
Published: March 2003

The separability of the sine-Gordon equation (SGE) is defined and studied in detail. We find a general class of dependent-variable transformations under which the SGE is separable. This class may be reduced to a two-parameter generalization of the usual transformation adopted, by requiring the transformations to reduce to the identity in the linear limit of the SGE (i.e., the Klein–Gordon equation). The method developed for studying the separability of the SGE is then applied to more general quasilinear equations and a discussion of the limitations of the method, and of separable solutions in general, is also given.
Noncompletely reducible representations of the Poincaré group associated with the generalized Lorentz gauge
Authors: Rideau G.
Published: March 2003

From complete resolution of a cohomological equation determining the 1-cocycle of an extension of one mass-null scalar representation by a vectorial mass-null representation of the Poincaré group, we build a one-parameter family of inequivalent noncompletely reducible representations of this group. Each of them leads to a quantum field theory by the Fock quantization process to a description of the electromagnetic field which turns out to be identical with field theories built by others in the general framework of the generalized Lorentz gauge.
Entropy and phase transitions in partially ordered sets
Authors: Dhar Deepak
Published: March 2003

We define the entropy function S (ρ) =limn→∞2n−2ln N (n,ρ), where N (n,ρ) is the number of different partial order relations definable over a set of n distinct objects, such that of the possible n (n−1)/2 pairs of objects, a fraction ρ are comparable. Using rigorous upper and lower bounds for S (ρ), we show that there exist real numbers ρ1 and ρ2;.083<ρ1⩽1/4 and 3/8⩽ρ2<48/49; such that S (ρ) has a constant value (ln2)/2 in the interval ρ1⩽ρ⩽ρ2; but is strictly less than (ln2)/2 if ρ⩽.083 or if ρ⩾48/49. We point out that the function S (ρ) may be considered to be the entropy function of an interacting ’’lattice gas’’ with long-range three-body interaction, in which case, the lattice gas undergoes a first order phase transition as a function of the ’’chemical activity’’ of the gas molecules, the value of the chemical activity at the phase transition being 1. A variational calculation suggests that the system undergoes an infinite number of first order phase transitions at larger values of the chemical activity. We conjecture that our best lower bound to S (ρ) gives the exact value of S (ρ) for all ρ.
Systems of differential inequalities and stochastic differential equations. IV
Authors: Ladde G. S.
Published: March 2003

Consider the system of stochastic functional differential equations x′ (t,ω) =f (t,x (t,ω), xt(ω),ω), xt0(ω) =φ0(ω), where f (t,x (t,ω), xt(ω),ω) is a product measurable n-dimensional random vector functional whenever x (t,ω) is a product measurable random function, and it satisfies the desired regularity conditions to assure the existence of solution process. By developing systems of random differential inequalities, very general comparison theorems in the framework of a vector Lyapunov function are obtained, and, furthermore, sufficient conditions are given for the stability of solutions in probability, in the mean and with probability one.
The optical group and its subgroups
Authors: Burdet G. , Patera J. , Perrin M. , Winternitz P.
Published: March 2003

The optical group Opt(3,1) is a ten-dimensional maximal subgroup of the conformal group of space–time, characterized by the fact that it leaves a lightlike vector subspace in Minkowski space invariant. Thus it is the group underlying the symmetry structure of the parton model in particle physics. The present article is devoted to a complete classification of all closed connected subgroups of Opt(3,1). A list of representatives of all Lie subalgebras of the algebra opt(3,1) is given in the form of tables and many of their properties are established (their invariants, normalizers, isomorphism classes, etc.). Most of the subalgebras of opt(3,1) are also contained in the similitude algebra sim(3,1). We discuss a method for extracting the ’’new’’ subalgebras of opt(3,1) from the list; these will go over into a future list of subalgebras of the conformal Lie algrebra itself.
The gradient formula for the O(5) ⊆O(3) chain of groups
Authors: Castaños O. , Frank A. , Moshinsky M.
Published: March 2003

It is well known how to expand in spherical harmonics the gradient of a radial function in turn multiplied by a spherical harmonic. This expansion involves the use of the Wigner–Eckart theorem for the familiar O(3) ⊆O(2) chain of groups, and leads to Wigner coefficients in the formula together with reduced matrix elements which are simple first order differential operators in the radial variable. In the present paper we extend the above analysis to the application of the momentum operator πm to functions of the collective coordinates αm, m=2,1,0,−1,−2 associated with quadrupole vibrations. The spherical harmonics are now replaced by the complete but nonorthonormal set of functions χλsLM, characterized by the irreducible representations λ,L,M of the O(5) ⊆O(3) ⊆O(2) chain of groups as well as by an extra labelling index s, that were derived in a previous publication. The application of the gradient to a product of a function F (β), β2=Σmαmαm, by χλsLM requires an extension of the Wigner–Eckart theorem for the nonorthonormal basis. Results similar to the ones mentioned in the previous paragraph are obtained, though, of course, now we will have Wigner coefficients in the O(5) ⊆ (3) ⊆O(2) chain which have already been derived and programmed. With the help of the gradient formula we discuss the effect of the operators [π×π]Lm, L=0,2,4, [α×π]Lm, L=1,3 on basis of the O(5) ⊆O(3) chain of groups and indicate some of their applications.
Mesonic test fields and spacetime cohomology
Authors: Doria Francisco Antonio , Abrahão Sergio Murilo
Published: March 2003

We prove the following theorem: Classical spin-0 and -1 mesonic test fields that can be constructed on a given spacetime manifold determine at least some of its de Rham cohomological structure. We explore this result and give some examples. The extension of the present technique to higher spin is also discussed.
Constraints of the Lorentz–Dirac equation
Authors: Cheng Kuo-shung
Published: March 2003

Baylis and Huschilt pointed out that the Lorentz–Dirac equation with the usual constraint [?μ(τ) →0 as τ→∞] for physical solution, may permit two or more solutions to some problems. We impose another constraint to make the physical solution unique.
The asymptotic behavior of bound eigenfunctions of Hamiltonians for single-variable systems
Authors: Morgan John D.
Published: March 2003

An extremely simple technique for examining the asymptotic behavior of bound eigenfunctions of Hamiltonians for single-variable systems is presented. A few simple examples are studied.
Projected basis set for the irreducible representation {2N/2−S,12S}ofU(n)
Authors: Sarma C. R. , Dinesha K. V.
Published: March 2003

The transformation properties of a projected basis for the irreducible representation (IR), {2N/2−S,12S}, of U(n) under the elementary generators of the group have been studied. It has been found that these transformations are identical (to within a phase factor) with those of the standard bases spanning the given IR. The correspondence between this basis set and the standard basis set has also been indicated.
Recoupling coefficients of the symmetric group involving outer plethysms
Authors: Sullivan John J.
Published: March 2003

In a series of papers we have examined the properties of certain double coset matrix elements (DCME) in the representations of the symmetric group SN that act as recoupling coefficients for outer products carried out via alternate subgroup sequences. In this paper we examine these same properties using symmetrized outer products in SN, which are also known as outer plethysms. The notions of double coset representative, symbol, and matrix element are extended to this case using the theory of semidirect products and little groups. The recoupling coefficients between bases symmetry adapted with respect to the usual outer product and the outer plethysm are examined in detail. Because of the Weyl–Schur construction of irreducible tensors, the recoupling theory of SN is central to a unified recoupling theory of the general linear group and its subgroups.
Recoupling coefficients of the general linear group in bases adapted to shell theories
Authors: Sullivan John J.
Published: March 2003

Recoupling coefficients for tensor representations of the general linear group Gl(n) are identified with analogous quantities in representations of the symmetric group SN. Two basis labeling schemes in Gl(n) are considered: (a) uses weights and outer product labels from SN, and (b) uses outer plethysms in SN and labels with respect to some elementary subgroup, usually SU(2). Scheme (a) corresponds to a generalized Gel’fand–Tsetlin basis and is the one usually adopted in elementary particle theories. Scheme (b) corresponds to the basis usually adopted in nuclear and atomic shell theory. The transformation between the two equivalent bases is identified with certain weighted double coset matrix elements (WDCME) of SN. Racah factors are generalized isoscalar factors in scheme (a) and have previously been identified with certain WDCME in that basis. In scheme (b) Racah factors determine the coefficients of fractional parentage (CFP) and are here identified with certain double coset matrix elements (DCME) of SN. Identification of these recoupling coefficients with the analogous quantities in SN exposes new symmetries and orthogonality properties of the coefficients which follow from the representation theory of SN. Some particular examples are verified by coefficients evaluated using well established techniques for SU(2).
Ideal vortex motion in two dimensions: Symmetries and conservation laws
Authors: Chapman David M. F.
Published: March 2003

Each of the conservation laws of the motion of a system of vortices in a two-dimensional ideal fluid are shown to be uniquely associated with one of the symmetry transformations of the system, one of which can be a scale transformation. In the case of an infinite fluid with no boundaries the five symmetry transformations are: (a) two independent translations in space, (b) spatial rotations, (c) translation in time, and (d) the scale transformation t′ =e2ηt, z′k=eηzk, where η is real and zk are the positions of the vortices in the z plane. Two cases of reduced symmetry are examined: the upper half-plane and the interior of the unit circle.
Comments on quantum systems subject to random pulses
Authors: Blume M.
Published: March 2003

An error in a recent paper on this subject by Gzyl is corrected. His results are then identical to those obtained earlier by Clauser and Blume.
Vector bundles, rth order Noether invariants and canonical symmetries in Lagrangian field theory
Authors: Aldaya V. , de Azcárraga J. A.
Published: March 2003

We present a formulation of the ’’canonical’’ transformations of the Dirac theory by using the bundle of r-jets associated with the Dirac vector bundle. This allows us, by means of a variational principle previously introduced, to study in a natural way (through an appropriate Noether theorem) the role which these ’’canonical’’ theories play in the definition of ’’new’’ symmetries. The limit r→∞ corresponds to the equivalence between the canonical and the ordinary symmetries.
Unified theory of direct interaction between particles, strings, and membranes
Authors: Letelier Patricio S.
Published: March 2003

A model of generalized relativistic membranes that contains as special cases, particles, geometric strings and geometric membranes and other new one- and two-dimensional objects is studied. The equations of motion for such objects in direct interaction are studied. The constraints on the interaction due to the freedom of gauge of the free model are solved. A scalar, a vectorial, and a tensorial type of interaction are discussed. Conservation theorems associated with Poincaré invariance of the action are studied, as well as the generalization for action-at-a-distance theories of the action and reaction law.
Random phase wave: A soluble non-Markovian system
Authors: Dewar R. L.
Published: March 2003

The averaged propagator and the corresponding mass operator (non-Markovian particle-wave collision operator) of a particle being accelerated by a random potential are constructed explicitly in a model system. The model consists of an ensemble of monochromatic waves of random phase, such as arises in narrow-bandwidth plasma turbulence, and is particularly interesting as a system exhibiting strong trapping. An essential simplifying feature is that the propagator is evaluated in oscillation-center picture, which greatly simplifies the momentum-space operators occurring in the problem, and leads to a remarkable factorization of the mass operator. General analyticity and symmetry properties are derived using a projection-operator method, and verified for the solution of the model system. The nature of the memory exhibited by the mass operator is briefly examined.
Quantum generalization of Kolmogorov entropy
Authors: Srinivas M. D.
Published: March 2003

The framework of quantum probability theory is employed in the investigation of ergodic properties of quantum dynamical systems. In the process certain basic notions of quantum information theory are developed. These are used to demonstrate the existence of a quantum Kolmogorov entropy which has the same operational significance as in classical theory. The notion of a quantum K-system is also introduced.
Generation of stationary axisymmetric Einstein–Maxwell fields
Authors: Tanabe Yukio
Published: March 2003

A method is presented which allows one to generate new solutions from old ones. Kinnersley’s functions u, v, w associated with the old solutions must be stationary, axially-symmetric, and satisfy a linear equation a*u+b*v−c*w=0. The method generalizes work of Bonner and Misra et al. who obtained a electric/magnetic dipole solution from the Kerr solution.
Theorem on the representations of SO(n) groups
Authors: Fisher Kurt , Ahner Henry F.
Published: March 2003

It is shown that SO(n) groups (n≳5) that possess a c-number Lorentz Casimir operator F do not have infinite-dimensional representations. Accordingly these groups cannot support new positive-energy wave equations of Staunton type. In an appendix Staunton’s spin-1/2 positive-energy wave equation is extended, in an analogous manner to that used by Rarita and Schwinger (RS) on Dirac’s equation, to yield positive-energy wave equations for arbitrary spin. It is noted that analogous auxiliary conditions to those of RS do not hold. Stationary solutions for low spin are listed.
On the application of the generalized quantal Bohr–Sommerfeld quantization condition to single-well potentials with very steep walls
Authors: Fröman Nanny , Fröman Per Olof
Published: March 2003

This investigation concerns some model potentials with very steep walls, for which the quantal Bohr–Sommerfeld half-integer quantization condition, if necessary generalized to correspond to modified phase-integral approximations of arbitrary order, and used without or with higher-order corrections included, can be used for obtaining, very accurately, the energy eigenvalues of the bound states, apart possibly from the lowest ones. One of the cases treated is the potential proportional to cot2x, for which a modified Bohr–Sommerfeld half-integer quantization condition yields the energy eigenvalues exactly. That the Bohr–Sommerfeld half-integer quantization condition is applicable to potentials with very steep walls may at first sight seem surprising in view of the well-known fact that the energy eigenvalues of a square-well potential with infinitely high walls are obtained exactly from the Bohr–Sommerfeld integer quantization condition, i.e., the quantization condition obtained by replacing (s+1/2) π by (s+1) π in the right-hand member of the Bohr–Sommerfeld half-integer quantization condition. From the study of a potential with horizontal bottom and linearly rising walls, which goes over into a square well when the inclination of the walls tends to zero, it can easily be understood, why the half-integer quantization condition is appropriate when the steep walls have a finite slope.
Quantum theory and Hilbert space
Authors: Marlow A. R.
Published: March 2003

Two theorems are proven which show that any orthomodular partially ordered set (hence, in particular, the orthologic of questions on a physical system) can be embedded in the lattice of closed subspaces of a Hilbert space in such a way that the standard trace formula of quantum theory can be used to calculate all probabilities. Possible conclusions from these results and from the existence of counterexamples to stronger conjectures are then discussed.
Light-cone finite normal products
Authors: Lowenstein John H. , Speer Eugene R.
Published: March 2003

A graphical subtraction procedure for constructing the perturbative Green functions of light-cone finite, multiply localized products of fields is proposed. The existence of the Green functions as tempered distributions is proved, together with the properties of light-cone finiteness and localization on a line segment. The derivation of light cone expansions is sketched, but not treated in detail.
The ionization T matrix
Authors: Zorbas John
Published: March 2003

The existence of the energy-shell limit of the ’’post’’ and ’’prior’’ forms of the half-off-shell T matrix is considered for N-particle scattering involving at most one charged fragment in the incoming channel. An approximate expression for the T matrix corresponding to the ionization of an uncharged fragment, consisting of two charged particles, by a charged particle is proposed.
Higher order modified potentials for the effective phase integral approximation
Authors: Floyd Edward R.
Published: March 2003

Higher order modified potentials for the effective phase integral approximation are derived from first principles. Application is made to computing eigenvalues for a nearly free wavefunction in a lattice potential.
On nonlinear transformations for time-dependent polynomial Hamiltonians
Authors: Leach P. G. L.
Published: March 2003

A formal method is demonstrated for the transformation of polynomial Hamiltonians with time-dependent coefficients to time-independent polynomial Hamiltonians. The transformation functions are themselves polynomials in the canonical variables with time-dependent coefficients. These coefficients are determined by sets of first order linear differential equations. The results apply equally well to multidimensional problems. The work is a generalization of the author’s earlier work on time-dependent linear transformations for quadratic Hamiltonians.
Towards an invariant for the time-dependent anharmonic oscillator
Authors: Leach P. G. L.
Published: March 2003

The Hamiltonians H= (1/2)(p2+q2)+λ (t) q3 and H̄= (1/2)(P2+Q2)+Q3, where λ̄ (t) =1, are related by time-dependent polynomial canonical transformations. Formulas are constructed for the generating function F2(q,P,t) as well as for the direct relations between (Q,P) and (q,p). These formulas are expressed fairly concisely in terms of time integrals. The form is seen to be applicable to all polynomial transformations of time-dependent anharmonic oscillator systems.
Addendum: On the inverse problem of transport theory with azimuthal dependence [J. Math. Phys. 1
9, 994(1978)]
Authors: McCormick N. J. , Veeder J. A. R.
Published: March 2003

A simplified expression is given for the moments over all space and angle of the intensity arising from an azimuthally-dependent plane source in an infinite medium. This provides a convenient equation for evaluating the mean of even powers of distance of travel of particles.
Foundation of geometrical optics in general relativistic dispersive media
Authors: Anile A. M. , Pantano P.
Published: March 2003

Geometrical optics in dispersive media is rigorously derived from Maxwell’s equations by employing the two-timing method. An effect analogous to Faraday rotation is found for the polarization plane of the wave, with the vorticity of the medium taking the place of the magnetic field.
Exact occupation statistics of two- and three-dimensional lattices of mixed single particles
Authors: Miyazaki Eizo
Published: March 2003

General expressions are derived which exactly describe the ensemble average number of two or three-dimensional structures per arrangement, created when mixed single particles are arranged on a pure or a mixed lattice. The expressions obtained are applied to the calculation of the number of various mixed nearest-neighbor pairs which are important for various phenomena in multicomponent systems.
Multipole wavefunctions for photoelectrons in crystals. IV. The irregular functions and the matching to an impurity
Authors: Strinati G.
Published: March 2003

Extension of the method of partial waves to scattering by an impurity center in a crystal requires the construction of energy eigenfunctions of the unperturbed crystal that are irregular at the center. These irregular solutions of a nonseparable problem are constructed by utilizing the expansion of the Green’s function into the regular solutions symmetry-adapted about the impurity center, which have been obtained earlier. The wavefunction within an impurity can thus be continued throughout the surrounding crystal by matching it at the impurity boundary to a superposition of regular and irregular solutions. This procedure is compared to the current EXAFS treatment of photoabsorption.
Percolation theory on multirooted directed graphs
Authors: Arrowsmith D. K.
Published: March 2003

The multiroot connectedness Puv of a directed graph G between the vertex u and the collection of vertices v ={v1,...,vn} is the probability that there are (directed) paths from u to each of the vertices vi, i=1, ...,n, when each edge and vertex has a given probability of being independently deleted. The properties of the coefficients in the expansion Puv(G) =ΣA′⊆Ad⃗uv(G′) Πa∈A′pa Πw∈V′pw, where A and V are the arc and vertex sets of G respectively, pa(pw) is the probability that an arc a (vertex w) is not deleted, and G′ is the arc set A′ together with its incident vertices V′, are considered. The values of d⃗uv(G) are characterized as follows: d⃗uv(G) is shown to be nonzero if and only if G is coverable by paths and has no directed circuit. For this case d⃗uv(G′) = (−1)tuv+n=(−1)ν(G), where tuv is the maximal number of independent directed paths between u and the set v, and tuv is shown to be equal to ν (G)+n, where ν (G) =‖E‖−‖V‖+1 is the cyclomatic number of G.
Predictive relativistic mechanics
Authors: Hirondel D.
Published: March 2003

We integrate the partial differential equations on the accelerations in predictive relativistic mechanics by means of integro-functional equations. We investigate some problems concerning the Hamiltonian formulation of this mechanics: Poisson brackets of position variables of each particle, Hamilton–Jacobi equations, and Hamiltonian formulation of the separation of the external and internal motions.
Slow motion approximation in predictive relativistic mechanics. II. A noninteraction theorem for interactions derived from the classical field theory
Authors: Martin J. , Sanz J. L.
Published: March 2003

By adopting an Aristotle invariant Lagrangian formalism (equivalent to canonically representing only this subgroup of the Poincaré group) and imposing a certain separability condition and a Newtonian limit on the Lagrangian, we obtain the most general Lagrangian up to c−3 order that verifies these properties and leads to a relativistic invariant dynamic (i.e., it satisfies the Currie–Hill equations). It contains up to c−2 order, all the Lagrangians known up to the present time. It is shown that the interactions derived from the classical field theory (CFT) do not admit approximated Lagrangians up to c−4 order, and thus this constitutes a noninteraction theorem for said interactions and somehow justifies some authors’ attitudes of abandoning the Lagrangian formalism (dropping the canonical character of position coordinates) when they construct a Hamiltonian formalism for these systems.
Completely integrable systems and symplectic actions
Authors: Adler M.
Published: March 2003

We study results on a class of completely integrable systems, for instance, with Hamiltonian H (x,y) = (1/2) 𝒥ni=1y2i +𝒥i<j(xi−yj)−2 +α𝒥ni=1x2i, using quotient manifolds induced by symplectic group actions, which enables us to integrate the systems and understand their complete integrability. In addition, we give a natural interpretation for the scattering maps associated with these systems.
Matrix elements for infinitesimal operators of the groups U(p+q) and U(p,q) in a U(p) ×U(q) basis. I
Authors: Klimyk Anatoli U. , Gruber Bruno
Published: March 2003

In this article explicit expressions are obtained for the action of the infinitesimal operators of the principal nonunitary series representations of the groups U(p,q) in a U(p) ×U(q) basis. It is moreover shown how the finite dimensional irreducible representations of the group U(p,q) and the group U(p+q) with respect to a U(p) ×U(q) basis are obtained from the principal nonunitary series representations of the group U(p,q).
Sum rules for the matrices of the generators of SU(3) in an SO(3) basis
Authors: Partensky A. , Quesne C.
Published: March 2003

We consider various sum rules for the semireduced [i.e., reduced with respect to SO(3)] matrix elements of the generators of SU(3) in a basis of an irreducible representation [pq] corresponding to the group reduction SU(3) ⊆SO(3) ⊆SO(2). We use basis states which diagonalize an additional labeling operator K, but avoid their explicit construction. We build all the needed operators from the two independent SU(3) vector operators X and V, where X= (L,Q) is made of the SU(3) generators and V= (VL, VQ) is defined in terms of them. First we obtain an analytical formula for the linear sum rule satisfied by the diagonal semireduced matrix elements of Q. Then, from the set of quadratic equations fulfilled by the semireduced matrix elements of Q and VQ, we obtain explicit expressions for the quadratic sum rules satisfied by these quantities. All the above-mentioned sum rules are independent of the selection made for K. When K is defined as the third order operator L.VL, we show that a relation between some nondiagonal matrix elements of Q and VQ exists enabling the determination of a k-weighted quadratic sum rule for the semireduced matrix elements of Q. As by-products of the preceding results we obtain general formulas for the eigenvalues k of K for all the values of L whose multiplicity does not exceed 3, and we show that we are able to compute analytically the individual matrix elements of Q for not too high dimensionalities by working out the case of the irreducible representation [10,5].
Stokes multipliers for a class of ordinary differential equations
Authors: Hinton F. L.
Published: March 2003

A new method is presented for calculating the Stokes multipliers for a class of linear second-order ordinary differential equations. The Stokes multipliers allow the asymptotic solutions of these equations to be continued across the Stokes lines on which they are dominant. The differential equations, of the class considered here, have an irregular singular point at infinity and a singular point at the origin, which may be either regular or irregular. The Stokes multipliers, as functions of the coefficients in the differential equation, are obtained in the form of convergent infinite series, whose terms must be obtained from the solution of recursion relations, which are derived. In the case of Whittaker’s equation (when the origin is a regular singular point), the known results are obtained analytically. When the origin is an irregular singular point, numerical evaluation of the series is necessary, but the method seems to be quite efficient for use with digital computers. In the special case of an equation, with two irregular singular points, which can be transformed to Mathieu’s equation, the numerical results for the Stokes multiplier show good agreement with available known results for the characteristic exponents of Mathieu’s equation.
Noether’s theorem, time-dependent invariants and nonlinear equations of motion
Authors: Ray John R. , Reid James L.
Published: March 2003

Noether’s theorem is applied to a Lagrangian for a system with nonlinear equations of motion. Noether’s theorem leads to a time-dependent constant of the motion along with an auxiliary equation of motion. Special cases of this invariant have been used to quantize the time-dependent harmonic oscillator. We also discuss the solution of the original equations of motion in terms of the solutions to the auxiliary equation.
Gravitational duality and Bäcklund transformations
Authors: Papanicolaou N.
Published: March 2003

We analyze various forms of duality symmetry transformations occurring in the theory of axially symmetric gravitational fields and their relation to standard Bäcklund transformations. Appropriately interpreted, duality rotations provide genuine Bäcklund transformations for the fundamental SL(2,R) invariants associated with the metric, consisting of elementary algebraic substitutions; thereby the construction of the metric reduces to the solution of linear equations.
Self-graviting fluids with cylindrical symmetry. II
Authors: Letelier P. S.
Published: March 2003

The Einstein field equations for an irrotational perfect fluid with pressure p, equal to energy density ρ are studied when the space–time has cylindrical symmetry with no reflection symmetry. The coordinate transformation to comoving coordinates is discussed. The energy and the Hawking–Penrose inequalities are studied. Particular classes of solutions are exhibited.
Quantum soliton and classical soliton
Authors: Matsumoto H. , Oberlechner G. , Umezawa M. , Umezawa H.
Published: March 2003

The interaction between quanta and a static soliton is discussed in the boson theory. As a natural consequence, there appears the quantum coordinate associated with the position of the soliton, which leads to a quantum or classical behavior of the soliton depending on its size and the experimental conditions. It will be shown that the presence of the quantum coordinate (or collective coordinate) is required by the equal-time canonical commutation relation.
Gauge field singularities and noninteger topological charge
Authors: Schaposnik F. A. , Solomin J. E.
Published: March 2003

We study the behavior of singular gauge field configurations under gauge transformations and we determine the relation between noninteger topological charge and the possibility of displacing singularities.