bluuebunny/crossref_metadata_2025 huggingface dataset:
Poisson’s formulas for wave propagation in a superfluid
Authors: Murray J. C.
Published: March 2003

The general solution of the initial-value problem for wave propagation in a superfluid is established. A uniqueness theorem is also proved for the associated initial-boundary value problem.
An alternative approach to the normal frequencies of a randomly disordered linear chain
Authors: Weilenmann Jürg
Published: March 2003

An attempt is made to gain some insight into the statistical character of the normal frequencies of a long chain of harmonic oscillators with randomly disordered masses. Instead of being concerned with the limit L→∞ of a chain whose random characteristics do not depend on its length L, the paper deals with the so-called diffusion limit where the ’’size’’ of the randomness in each of the masses tends to 0 like L−1/2.
On the definition and properties of generalized 3-j symbols
Authors: Raynal Jacques
Published: March 2003

Whipple’s work on the symmetries of 3F2 functions with unit argument is applied to study the properties of 3-j symbols generalized to any arguments. It turns out that there are twelve sets of ten formulas (twelve sets of 120 generalized 3-j symbols) which are equivalent in the usual case. Whipple’s parameters r provide a better description of the symmetries than the Regge symbol.
Unitary analytic representations of SL(3,R) and hadronic Regge sequences
Authors: Güler Y.
Published: March 2003

The unitary, analytic representations of the covering group SL(3,R) are determined in the space of functions H (z) which are derived from homogeneous functions of degree −b1. Four Regge trajectories, {N}, {ρ}, {π}, and {Δ}, are associated with these representations.
Integral representations of particular integrals of a class of inhomogeneous linear ordinary differential equations
Authors: Johnston George L.
Published: March 2003

A method of obtaining integral representations of particular integrals of a class of inhomogeneous second-order linear ordinary differential equations is presented. The integrands of the representations are exp[F (z;t)], where F (z;t) =z2a (t)+zb (t)+c (t), z is the independent variable of the differential equation, and a, b, and c are initially unspecified functions of the variable of integration, t. The lower limit of the contours of integration is zero. The upper limits of integration and the contours along which the integral is taken are initially unspecified. In the general class of inhomogeneous differential equations considered, the coefficients of the dependent variable and its derivatives are polynomials in z with complex constants and the homogeneous term is exp(k2z2+k1z+k0), where the kn are complex constants. One imposes the conditions that the application of the homogeneous operator to the assumed form of integral representation give the integral of −∂F/∂t, that exp[F (z;0)] be equal to the inhomogeneous term of the differential equation, and that the limit of expF as t approaches the upper limit along the contour of integration be zero. By equating coefficients of different powers of z separately to zero, one obtains a set of coupled equations for a, b, and c. The basic class of inhomogeneous differential equations to which the method is applicable is determined by requiring that a, b, and c be algebraic or elementary transcendental functions of t. The class of equations to which the method is applicable is extended to include inhomogeneous terms of the form znexp(k2z2+k1z+k0), where n is a positive integer, by repeated differentiation of integral representations of members of the basic class with respect to k1, treated as a parameter. More general inhomogeneous terms may be treated by superposition and, in appropriate cases, by approximation in terms of sets of orthogonal functions.
Slavnov–’t Hooft identities in Mandelstam’s formalism
Authors: Naito Seichi
Published: March 2003

In Mandelstam’s gauge-independent quantization formalism, Slavnov identities are shown to originate from the fact that auxiliary Green’s functions in various gauges (Feynman gauge, Landau gauge, etc.) satisfy the same fundamental equation. Furthermore, we have the practically important result that the infinite number of Slavnov identities are obtained in concise and concrete form. With the help of this form, we are able to easily derive various ’t Hooft identities, which assure us of the gauge independence and the unitarity of the S matrix.
Asymptotic simplicity is stable
Authors: Geroch Robert , Xanthopoulos Basilis C.
Published: March 2003

Consider an asymptotically simple solution of Einstein’s equation. It is shown that any internally generated, first-order perturbation of the metric, as a consequence of the linearized Einstein equation, preserves asymptotic simplicity to first order.
Branching rules for the subgroups of the unitary group
Authors: Braunschweig D. , Hecht K. T.
Published: March 2003

Expressions are given in terms of simple matrices d for the reduction of the Kronecker (outer) product of two or more irreducible representations which can be characterized by Young patterns. These are then used to obtain practical formulas for branching rules. The needed matrices d can be constructed by a very efficient recursive process.
A theory of the electromagnetic two-body interaction
Authors: Kracklauer Aloysius F.
Published: March 2003

A theory of the electromagnetic two-body interaction is described which leads to equations of motion solvable by local (numerical) integration.
Scalar–vector instantons in n dimensions: Surface terms
Authors: Cahill K. , Comtet A.
Published: March 2003

By an analysis that respects surface terms, it is shown that the equations of motion for a non-Abelian gauge field Aaμ coupled to a scalar field Φi possess no regular, finite-action solutions in n-dimensional Euclidean space except for n=4, with Φ trivial, and for n<4.
The quantum mechanical Poincaré and Galilei groups
Authors: Cattaneo U.
Published: March 2003

Second countable locally compact representation groups for the Poincaré group (resp. for the Galilei group) and for some of its subgroups are constructed in the ’’quantum mechanical case,’’ i.e., when time and space–time inversions are assumed to be represented by antiunitary operators. The question of their uniqueness up to topological group isomorphisms is investigated.
Some classes of exact solutions of the nonlinear Boltzmann equation
Authors: Tenti G. , Hui W. H.
Published: March 2003

We derive and discuss some exact solutions of the full (nonlinear) Boltzmann equation. One of these is the similarity solution recently found by Krook and Wu for the velocity relaxation problem. Other similarity solutions do exist, and we point out their usefulness in the search for exact solutions of the spatially inhomogeneous Boltzmann equation.
An exact solution for a derivative nonlinear Schrödinger equation
Authors: Kaup David J. , Newell Alan C.
Published: March 2003

A method of solution for the ’’derivative nonlinear Schrödinger equation’’ iqt=−qxx±i (q*q2)x is presented. The appropriate inverse scattering problem is solved, and the one-soliton solution is obtained, as well as the infinity of conservation laws. Also, we note that this equation can also possess ’’algebraic solitons.’’
Absence of ordering in a class of real liquids—Application to nematic liquid crystals
Authors: Romerio M.
Published: March 2003

A classical liquid, the constituants of which are characterized by an internal structure described by a compact connected Lie group, is studied. The order parameter of such systems is shown to vanish for dimension smaller than three. The example of nematic liquid crystals is considered.
Summation of partial wave expansions in the scattering by long range potentials. I
Authors: Garibotti C. R. , Grinstein F. F.
Published: March 2003

Punctual Padé approximants are considered as a summation method of the slowly convergent partial wave expansions associated with the scattering by long range potentials. The asymptotic behavior of the family of sequences [n,n+m], with fixed n, of the Padé table, is studied. A set of theorems are proven, which show that their rate of convergence increases rapidly with n. It is noted that these approximants may be computed by means of the recurrent ε and η algorithms.
On time evolution for large quantum systems in superspace
Authors: Mishima Nobuhiko , Petrosky Tomio Yamakoshi
Published: March 2003

A reformulation in a superspace is given for Van Hove and Janner’s perturbation theory based on the two-resolvent method for nonequilibrium quantum statistical mechanics. This is attained by introducing an ordered superoperator in the superspace. As an application of our formalism, the derivation of an asymptotic generalized master equation in a Markovian form is given. Further, it is investigated how a quantum subdynamics theory similar to the Brussels school’s one can be formally constructed. Our subdynamics theory is formulated on every eigenspace of a superoperator (the ss-Hamiltonian) of which the eigenvalue is related to the intrinsic parameter E of Van Hove and Janner’s generalized master equation.
Coherent states and stochastic formulation of quantum mechanics
Authors: Lonke A.
Published: March 2003

For physical systems with Hamiltonians analytic in the position and momentum operators the diagonal matrix elements of the density operator in the coherent state representation may be considered as a phase-space probability measure in the stochastic formulation of quantum mechanics. The correspondence rule relating quantum-mechanical observables to ordinary functions in phase space is obtained. It is shown that the dynamics of the time-dependent phase-space probability densities is again representable in the form of a stochastic process.
On the representation of linear operators in L2 spaces by means of ’’generalized matrices’’
Authors: Ascoli R. , Gabbi P. , Palleschi G.
Published: March 2003

This paper concerns the representation of linear operators of L2 spaces by means of ’’generalized matrices’’ as it is usual, following Dirac, in quantum mechanics and in electronics. The known possibility of representing (on a nuclear test-function space) the bounded operators by means of distribution kernels is shown to extend to all the closable operators whose domain contains the test-function space (hence to all the Hermitian operators whose domain contains the Schwartz space 𝒟 of the infinitely differentiable functions with compact support). The representation of the adjoint operator is considered, and the possibility of representing the product of operators by means of a suitably defined ’’Volterra convolution’’ is studied. In particular it is shown that -algebras of unbounded operators (which are, for instance, generated by the canonical coordinates and momenta and the total energy of most quantum mechanical systems of n particles) may be represented isomorphically by means of distribution kernels, so that the Dirac’s rules on ’’generalized matrices’’ apply in the sense of distributions without further assumptions.
On Lie algebraic properties of the step operators acting on P or confluent P functions
Authors: Mori Masao
Published: March 2003

P functions and confluent P (CP) functions are classified into two and five groups respectively according to the types of the step operators (SO’s) intrinsic to the respective classes of functions. The correspondence between the types of the SO’s and the realizations of the Lie algebras 𝒢 (a,b) and 𝒯6 is established as follows. The modified SO’s acting on P functions (SOP’s) belong to either of the type A and E realizations of 𝒢 (1,0) and 𝒯6 respectively. The modified SOC’s, namely the SO’s acting on CP functions, belong to one of the type B, C′, C″, F, D′ realizations of 𝒢 (1,0), 𝒢 (0,1), 𝒢 (0,0), or 𝒯6.
Three-dimensional solitons
Authors: Newton Roger G.
Published: March 2003

Using an inverse Radon transform we generate an integro–differential evolution equation in three space dimensions that has soliton solutions which vanish at large distances in all directions. The equation is of second order in time and invariant under translations and rotations. The shapes of the solitons are generally changed by their nonlocal interactions, but their number and velocities are conserved. The method lends itself to other equations.
On the calculation of the probability density at the origin for an s-state
Authors: Fröman Nanny
Published: March 2003

Phase-integral formulas for the probability density at the origin of an s-state are derived, on various assumptions as to the behavior of the potential in the neighborhood of the origin. In particular, the analog of the Fermi–Segrè formula is given for the case that the potential is regular at the origin.
Raising and lowering operators for the orthogonal groups
Authors: Bincer Adam M.
Published: March 2003

A formalism for obtaining shift operators for all classical groups in the form of tensor operators is described in application to the orthogonal groups. This formalism is also applicable to the irreps in the discrete series of the noncompact versions of the classical groups.
Normalization coefficients for the O(n) shift operators
Authors: Bincer Adam M.
Published: March 2003

Normalization coefficients are derived for the shift operators of O(n) introduced previously. The resultant normalized lowering operator for O(n) is presented in a form analogous to the U(n) case.
I. Exact relations among correlation functions of inherently nondynamic interacting systems
Authors: Haley Stephen B.
Published: March 2003

The standard basis operator (SBO) equation of motion is solved exactly for the class of interacting many-body Hamiltonians which can be constructed from a complete set of mutually orthogonal projection operators. This class includes the Ising model Hamiltonians. Two integration procedures are presented: (1) term by term integration over the poles of the SBO double-time temperature-dependent Green’s functions in the spectral representation; (2) direct integration of the time-dependent equation of motion of an SBO. An ensemble average expression relating correlation functions among systems in different energy states is derived. For the Ising model this expression relates correlation functions of spin clusters of different orders, and it is analogous to a relation derived from the master equation under equilibrium conditions.
The projective Lie algebra of the Lorentz group and homographic transformations
Authors: Bacry H.
Published: March 2003

The Lorentz group is used as the group of homographic transformations on the Riemann sphere. Its Lie algebra is shown to have a very simple interpretation with the aid of cross products and constellation formalism. This property is used to give a constellation description of the Clebsch–Gordan series for the product of two states of spin 1.
A second order calculation of the adiabatic invariant of a charged particle spiraling in a longitudinal magnetic field
Authors: Chehab R.
Published: March 2003

The change of the action integral of a charged particle spiraling in a slowly varying longitudinal magnetic field is investigated. The method used to solve this two-dimensional problem is a generalization of Vandervoort’s analysis of a one-dimensional system. It is based on a canonical transformation of the usual conjugate coordinates and momenta into a set of four variables of the action-angle type. The new canonical equations are solved by a method of iteration, and the solution is used to calculate the change of the adiabatic invariant. Our results are analogous to those obtained with the approximations derived by Hertweck and Schlüter and by Chandrasekhar. We have compared our analytic results to those obtained by numerical integration of the equation of motion in the case of a magnetic solenoid with a slowly decreasing field.
Solitonlike solutions of the elliptic sine–cosine equation by means of harmonic functions
Authors: Leibbrandt G.
Published: March 2003

Exact solutions of the elliptic sine–cosine equation ∂2ψ/∂x2+∂2ψ/∂y2=sin(ψ+g) are derived in two space dimensions with the aid of a new Bäcklund transformation and by exploiting the properties of the harmonic function g (x,y). Two generating formulas are developed which allow us to generate without additional quadratures an infinite number of real solutions α and infinitely many imaginary solutions iβ. Some α solutions behave like solitons and can be labeled by a topological quantum number. Which solutions are solitonlike and which are not depends decisively on the analytic structure of g and its domain of harmonicity in the ℛ2 plane.
Asymptotic behavior of group integrals in the limit of infinite rank
Authors: Weingarten Don
Published: March 2003

We show that in the limit N→∞ integrals with respect to Haar measure of products of the elements of a matrix in SO(N) approach corresponding moments of a set of independent Gaussian random variables. Similar asymptotic forms are obtained for SU(N) and Sp(N). An application of these results to Wilson’s formulation of lattice gauge theory is briefly considered.
Asymptotic steady-state solution in the functional random-walk model
Authors: Hosokawa I.
Published: March 2003

The maximum-entropy (equilibrium) state of the functional random-walk model of a closed many-particle system is known, but there has been no direct proof that this state represents the steady solution of the basic functional equation in the model. Here, a direct proof of it is given for the asymptotic case where the average particle-number density is extremely large.
The algebra of color
Authors: Domokos G. , Kövesi-Domokos S.
Published: March 2003

We construct an algebra of (local) dynamical variables which satisfies the triality rule for quarks and an exact superselection rule between leptons and quarks. This algebra is isomorphic to a noncommutative Jordan algebra; hence, it is power associative. Inner derivations are constructed explicitly: Their algebra is isomorphic to Lie SU(3); the latter can be identified with the group of color symmetry.
A new formula for the spinor norm
Authors: Perroud M.
Published: March 2003

A formula is established, valid for all real pseudo-orthogonal groups, permitting an easy computation of the spinor norm of any pseudo-orthogonal matrix. It is a generalization of the well-known criterion used for O(3,1) according to which the spinor norm is determined by the sign of the last element of a Lorentz matrix.
Topological cohesion
Authors: Cahill K. , Stoltzfus N.
Published: March 2003

It is shown that suitably regular, finite-energy solutions of the Yang–Mills–Higgs equations are nondissipative whenever their initial data are topologically significant.
Existence of instantaneous Cauchy surfaces
Authors: Budic Robert , Gotay Mark J. , Gowdy Robert H.
Published: March 2003

Several properties of instantaneous Cauchy surfaces are obtained. It is shown that a strongly causal spacetime admits an instantaneous Cauchy surface through each of its points, that there is a close and reversible relationship between these surfaces and maximal open globally hyperbolic subsets, that every instantaneous Cauchy surface is contained in a maximal instantaneous Cauchy surface, and that the latter surface is a maximal achronal surface which separates spacetime into past, present, and future. Some other properties of instantaneous Cauchy surfaces are discussed along with a refinement of an earlier topology change property.
Solution of a second-order integro–differential equation which occurs in laser modelocking
Authors: Hagelstein P. L.
Published: March 2003

We solve the following integro–differential equation for the eigenfunction u (x): su (x) ={d2/dx2−[1−6sech2(x)]}u (x) −εℱ∞−∞u (x′)sech(x′) dx′ (1+ν2d2/dx2)sech(x), where s is the eigenvalue and ε and ν are arbitrary parameters which need not be small. This equation occurs in laser modelocking theory in the analysis of pulse stability, and s is proportional to the rate of growth of perturbations. We expand the eigenfunction u (x) in terms of a convenient basis set Λ (x,k) satisfying −k2Λ (x,k) =[d2/dx2+6sech2(x)]Λ (x,k). We find two discrete eigenfunctions u0(x) and u1(x) and a continuum u (x,s). We find that the lowest eigenvalue s0(ε) is −3 at ε=0 for finite or zero ν, and that the point where s0 =0 the parameters ε and ν obey ε=2/(1−ν2). This is the zero growth point at which no eigenfunction u (x) has a positive eigenvalue s.
N-body quantum scattering theory in two Hilbert spaces. II. Some asymptotic limits
Authors: Chandler Colston , Gibson A. G.
Published: March 2003

Within the framework of two-Hilbert space scattering theory the existence of the strong Abel limit of a certain operator is proved, leading to the following results. A generalized Lippmann identity is derived that is valid for all channels, rather than only two-body channels. On shell equivalence of the prior, post and AGS transition operators is rigorously proved, thus closing a gap in previous proofs. Results concerning the existence of the scattering operator as a strong, rather than weak, Abel limit are presented, and their implications with respect to the problem of unitarity are discussed. Finally, the possibility of exploiting operator limits of the Obermann–Wollenberg type is studied, with negative results.
An investigation of some of the kinematical aspects of plane symmetric space–times
Authors: Carlson George T. , Safko John L.
Published: March 2003

A short review of the literature on plane symmetric space–times (PSSTS) is given in the Introduction. The rest of the paper concerns itself with an investigation of some of the kinematical aspects of PSSTS, i.e., properties of PSSTS which do not depend on the field equations. In particular, the existence of four special coordinate systems is considered. It is shown that the existence of these coordinate systems is not guaranteed for a general Ck (k⩽1) plane symmetric metric (PSM). For k=2, two of the coordinate systems exist in a weak sense whereas the existence of the other two is not guaranteed in any sense. A local intrinsic type classification is introduced in Sec. 3, and it is shown that the existence of an extra Killing vector is correlated to the classification. Finally, the local equivalence of two given PSSTS is considered in Sec. 4. It is shown that some algebraic equations arise from the analysis. These algebraic equations may lead directly to the solution of the problem of the local equivalence of two given PSSTS.
A note on representation of para-Fermi algebra
Authors: Jagannathan R. , Vasudevan R.
Published: March 2003

Representation of para-Fermi algebras is obtained utilizing the operators of a single Fermi field. In analogy with Kalnay’s para-Grassman algebras, para-Clifford algebras are defined in terms of Fermi operators.
Nonuniqueness in the inverse scattering problem
Authors: Devaney A. J.
Published: March 2003

The inverse scattering problem consists of determining the functional form of a scattering potential given the scattering matrix A (k0s, k0s0) for all scattering directions s and one or more values of the wave vector k0s0. In this paper it is shown that within the framework of the first Born approximation the inverse scattering problem as defined above does not possess a unique solution. It is also shown that within the framework of exact (potential) scattering theory the problem does not admit a unique solution given only the scattering matrix for a single fixed value of the wave vector k0s0 as data. The final section in the paper considers scattering experiments using incident fields other than plane waves and where knowledge of the scattered field at all points exterior to the scattering volume is available as data. It is found that, within the framework of exact scattering theory, the data generated by any single such experiment is not sufficient to uniquely specify the scattering potential while, within the framework of the first Born approximation, the data generated by any finite number of such experiments is not sufficient to uniquely specify the potential.
Classical and relativistic vorticity in a semi-Riemannian manifold
Authors: Dupré Maurice J. , Rosencrans Steven I.
Published: March 2003

It is shown that a form of the Cauchy–Lagrange formula for the evolution of vorticity in a barotropic flow generalizes to the case of ideal fluid motion on higher-dimensional Riemannian or semi-Riemannian manifolds.
The groups of Poincaré and Galilei in arbitrary dimensional spaces
Authors: Elizalde E. , Gomis J.
Published: March 2003

In arbitrary dimensional spaces the Lie algebra of the Poincaré group is seen to be a subalgebra of the complex Galilei algebra, while the Galilei algebra is a subalgebra of Poincaré algebra. The usual contraction of the Poincaré to the Galilei group is seen to be equivalent to a certain coordinate transformation.
Corrigendum to ’’Covariant inverse problem of the calculus of variations’’
Authors: Ahner Henry F. , Moose Allan E.
Published: March 2003

Our recent work showing how to obtain covariant Lagrangians for certain classes of field equations is extended to cases where the field appears to order λm (m⩽−2) and also to cases where metric variations are taken.
Continuum S state wavefunctions for the Debye potential by Ecker–Weizel approximations
Authors: Talukdar B. , Chaudhuri R. N. , Das U. , Banerjee P.
Published: March 2003

Analytical expressions for the continuum eigenfunctions for the Debye (Yukawa) or shielded Coulomb potential are derived by using Ecker–Weizel approximations. The results are used to obtain the S matrix in closed form.
The Lorentz group in the oscillator realization. I. The group SO(2,1) and the transformation matrices connecting the SO(2) and SO(1,1) bases
Authors: Basu Debabrata
Published: March 2003

The unitary transformation connecting the SO(2) and SO(1,1) bases for the principal and discrete series of representations of the three-dimensional Lorentz group is determined by using the oscillator representation technique. The Hilbert space and the SO(1,1) basis, in this realization, have a simple appearance while the compact basis appears as the solution of an ordinary differential equation reducible to the confluent hypergeometric equation by a simple substitution. The Taylor expansion of this solution obtained by the use of certain functional identities yields the continuous spectrum of the SO(1,1) representations and the unitary transformation from the compact to the noncompact basis after the Sommerfeld–Watson transformation.
A simple derivation of the Onsager–Machlup formula for one-dimensional nonlinear diffusion process
Authors: Yasue Kunio
Published: March 2003

Transforming the Fokker–Planck equation into a self-adjoint form the Onsager–Machlup formula for a one-dimensional nonlinear diffusion process is derived rigorously. By approximating the Wiener measure by an n-gate cylinder measure, an equation of motion for the most probable path is also derived.
Ground state representation of the infinite one-dimensional Heisenberg ferromagnet. III. Scattering theory
Authors: Babbitt Donald , Thomas Lawrence
Published: March 2003

This article gives a complete description of the scattering for the spin 1/2 Heisenberg ferromagnetic chain in its ground state representation.
Lower energy bounds for translation-invariant atomlike systems
Authors: Hall Richard L.
Published: March 2003

A system of N identical particles with masses m1 interact with each other via a pair potential V and with an additional particle of mass m0 by the pair potential U, and the system obeys nonrelativistic quantum mechanics. A general lower bound formula is derived for the ground-state energy, which reduces to Coleman’s result in the special case m0=∞. The lower bound is compared with the exact energy for the harmonic oscillator problem V (x) =k21x2 and U (x) =k02x2, which has recently been solved exactly (Hall).
Slow motion approximation in predictive relativistic mechanics. I. Approximated dynamics up to order c−4
Authors: Martin J. , Sanz J. L.
Published: March 2003

We obtain the most general two-body system relativistic invariant having a Newtonian limit up to c−4 order. In particular, it includes the scalar, gravitational, and other well-known dynamics up to c−2 order. It also includes to c−4 order the dynamics obtained recently by Lapiedra and Mas in predictive relativistic time symmetric electrodynamics.
General algebraic theory of identical particle scattering
Authors: Bencze Gy. , Redish Edward F.
Published: March 2003

We consider the nonrelativistic N-body scattering problem for a system of particles in which some subsets of the particles are identical. We demonstrate how the particle identity can be included in a general class of linear integral equations for scattering operators or components of scattering operators. The Yakubovskii, Yakubovskii–Narodestkii, Rosenberg, and Bencze–Redish–Sloan equations are included in this class. Algebraic methods are used which rely on the properties of the symmetry group of the system. Operators depending only on physically distinguishable labels are introduced and linear integral equations for them are derived. This procedure maximally reduces the number of coupled equations while retaining the connectivity properties of the original equations.
Field equations and integrability conditions for special type N twisting gravitational fields
Authors: Ernst F. J. , Hauser I.
Published: March 2003

We let SNT designate a special kind of twisting type N gravitational field solution of the Einstein field equations, viz., one for which there exists a real scalar field χ which satisfies (∇[αkβ−k[α∇βχ) (∇γ]kδ) tδ=0, where kα is a principal null vector, tαtα =tαkα=0, and tαtα*=1. We obtain some theorems which provide necessary and sufficient criteria for an SNT to be the twisting type N metric discovered by I. Hauser, in Phys. Rev. Lett. 33, 1112 (1974). Field equations, a hierarchy of integrability conditions, and analytic techniques which are applicable to the quest for a new SNT are given. Two tractable SNT subcases are considered in detail.
On the Kerr–Tomimatsu–Sato family of solutions with nonintegral distortion parameter
Authors: Yamazaki Masatoshi
Published: March 2003

The generalization of the Kerr–Tomimatsu–Sato family of solutions for gravitational fields of spinning masses to the case of the arbitrary positive nonintegral distortion parameter δ is conjectured.
Symmetries of the 6j coefficient
Authors: Venkatesh K.
Published: March 2003

The equivalence between the two sets of 4F3(1) S for the 6j coefficient is explained through two sets of equalities. It is shown that the 144 symmetries can be partitioned into 12 sets of 12 each, depending on the number of terms in the series representation for the 6j coefficient. The 12-element group, recently discussed by Lockwood, is shown to account for only 12 symmetries of the 6j coefficient.
Neutrino fields in axially and reflection symmetric space–times
Authors: Herrera L. , Jiménez J.
Published: March 2003

It is shown that there exist no physically significant (i.e., nonsingular) solutions to the Einstein-neutrino field equations in an axially and reflection symmetric space–time.
Canonical Fourier transforms
Authors: Hudson R. L. , Peck S. N.
Published: March 2003

An analog of the Fourier–Plancherel transformation is developed which maps to themselves the ’’square-traceable’’ operators in the von Neumann algebra generated by a quantum-mechanical canonical pair (p,q). The role of translation-invariant integral is played by the trace. The Fourier transform is given formally by X̄ (p′,q′) =sinαtrp,q e−iα(pp′+qq′)X (p,q), where α is a fixed parameter in the interval of (0,π). Comparisons are made with other Fourier-type transformations associated with a canonical pair.
Colliding plane gravitational waves
Authors: Halil Mustafa
Published: March 2003

New exact solutions of the vacuum Einstein field equations are constructed which describe the collision of plane gravitational waves. These solutions generalize those of Szekeres by relaxing the requirement of collinear polarization.
Convergence of the Debye expansion for the S matrix
Authors: Cruz A. , Sesma J.
Published: March 2003

The convergence of the Debye expansion for the scattering of a scalar wave by a homogeneous sphere of complex refraction index, or, equivalently, of two particles interacting via a complex rectangular well (or barrier) potential, is considered. The interest of the results lies mainly in their applicability to hadron–nucleus and nucleus–nucleus collisions.
Summation of partial wave expansions in the scattering by long range potentials. II. Numerical applications
Authors: Garibotti C. R. , Grinstein F. F.
Published: March 2003

The numerical application of a sequence transformation method proposed in a previous work is considered for the calculation of differential cross-sections corresponding to processes where long range interactions are important. The advantages of the approach, as a summation algorithm for the partial wave expansion of the scattering amplitude, are shown for the cases of scattering by the Lennard–Jones, repulsive inverse square, and Coulombic potentials, and for the scattering of electrons by helium in the intermediate energy range. Furthermore, the method proves to be a regularizing procedure for divergent and oscillating partial wave expansions.
On the matrix representation of closed linear operators: An extension of the Von Neumann’s theory
Authors: Epifanio G. , Trapani C.
Published: March 2003

The general theory of the matrix representation of operators in scalar product space is examined. It is proved that an extension of the Von Neumann’s theory on the matrix representation of closed symmetric operators in Hilbert space is possible for a larger class of closed operators. A necessary and sufficient condition for the existence of a matrix representation of operators in ’’Von Neumann’s sense’’ is given.
Exact solutions of some multiplicative stochastic processes
Authors: Wódkiewicz K.
Published: March 2003

The theory of multiplicative stochastic processes with completely and quasicompletely random Gaussian statistics is discussed. Operator valued equations with stochastic coefficients are solved exactly for various types of statistics using the path integral technique. Generalizations of previous results for such stochastic processes are obtained.
Matrix elements for infinitesimal operators of the groups U(p+q) and U(p,q) in a U(p) ×U(q) basis. II
Authors: Klimyk A. U. , Gruber Bruno
Published: March 2003

The general expressions derived in Ref. 1 for the matrix elements of the infinitesimal operators of the groups U(p+q) and U(p,q) in a U(p) ×U(q) basis are utilized in this article to obtain explicit expressions for the matrix elements of the infinitesimal operators of (a) the degenerate series representations of U(p,q) in a U(p) ×U (q) basis, and (b) the representations of U(p+q) with highest weight (m1,0, ..., 0, m2) in a U(p) ×U(q) basis. The operator which unitarizes the U(p+q) representations considered is given in explicit form.
Gaussian quantum stochastic processes on the CCR algebra
Authors: Lindblad Göran
Published: March 2003

We define a stationary Gaussian quantum stochastic process (GQSP) on the C*-algebra of the canonical commutation relations over a real symplectic Hilbert space. Physically GQSPs can describe diffusion with non-Markovian memory effects in quantum harmonic oscillators of arbitrary dimension. We find that in analogy with the commutative case a GQSP is completely specified by a operator-valued autocovariance function satisfying certain positive definiteness and reality conditions. The autocovariance function also determines the response of the system to a class of time-dependent generalized forces, and it has a spectral representation in terms of a positive operator-valued measure.
Casimir invariants and characteristic identities for generators of the general linear, special linear and orthosymplectic graded Lie algebras
Authors: Jarvis P. D. , Green H. S.
Published: March 2003

We present the commutation and anticommutation relations, satisfied by the generators of the graded general linear, special linear and orthosymplectic Lie algebras, in canonical two-index matrix form. Tensor operators are constructed in the enveloping algebra, including powers of the matrix of generators. Traces of the latter are shown to yield a sequence of Casimir invariants. The transformation properties of vector operators under these algebras are also exhibited. The eigenvalues of the quadratic Casimir invariants are given for the irreducible representations of ggl(m ‖ n), gsl(m ‖ n), and osp(m ‖ n) in terms of the highest-weight vector. In such representations, characteristic polynomial identities of order (m+n), satisfied by the matrix of generators, are obtained in factorized form. These are used in each case to determine the number of independent Casimir invariants of the trace form.
An approximation method for electrostatic Vlasov turbulence
Authors: Klimas Alexander J.
Published: March 2003

Electrostatic Vlasov turbulence in a bounded spatial region is considered. An iterative approximation method with a proof of convergence is constructed. The method is nonlinear and applicable to strong turbulence.
A new method of matrix transformations. II. General theory of matrix diagonalizations via reduced characteristic equations and its application to angular momentum coupling
Authors: Kim Shoon K.
Published: March 2003

A general formalism is given to construct a transformation matrix which connects two matrices A and B of order n×n satisfying any given polynomial equation of degree r, p(r)(x) =0; r?n. The transformation matrix TAB is explicitly given by a polynomial of degree (r−1) in A and B based on p(r)(x). A special case where B is a diagonal matrix Λ equivalent to A leads to the general theory of matrix diagonalizations with the transformation matrix TAΛ, which can be made nonsingular with a proper choice of Λ. In another special case where B is a constant matrix with the constant being a simple root λν of p(r)(x), the transformation matrix TAB reduces to the idempotent matrix Pν belonging to the eigenvalue λν of A. Based on the relation which exists between TAΛ and Pν, one can construct a transformation matrix U which is more effective than TAΛ and becomes unitary when A is Hermitian. Illustrative examples of the formalism are given for the problem of angular momentum coupling.
Micu-type invariants of simple Lie algebras
Authors: Agrawala Vishnu K.
Published: March 2003

An algorithm is presented for computing the eigenvalues of Micu-type invariants for Lie algebras Ar, Br, Cr, and Dr. Inasmuch as the definitions of these invariants is recursive and not in terms of a closed formula, only a recursion relation is obtained for computation of their eigenvalues, which is easily programmable on a computer. Some of the formulas developed here are valid in arbitrary complex semisimple Lie algebras and may be useful in other contexts.
On the asymptotic behavior of the derivatives of Airy functions
Authors: Maurone Philip A. , Phares Alain J.
Published: March 2003

We present a noniterative functional solution to the three-term recursion relation satisfied by the higher order derivatives of the Airy function. This solution allows one to obtain the asymptotic behaviors of these derivatives for large argument and also for large order.
Schwinger equations
Authors: Hańćkowiak Jerzy
Published: March 2003

A compact description of the Schwinger equation is given and its different transformations and projections are considered.
One particle reduced density matrix of impenetrable bosons in one dimension at zero temperature
Authors: Vaidya H. G. , Tracy C. A.
Published: March 2003

We compute exactly the one particle reduced density matrix ρ (r) of a system of impenetrable bosons in one dimension at zero temperature. We do this by relating ρ (r) to a certain double scaling limit of the transverse correlation function of the one-dimensional spin 1/2 X–Y model. We study the asymptotic behavior of ρ (r) for large r. This expansion contains oscillatory terms which arise due to the intrinsic quantum mechanical nature of the problem. We use these results to discuss the analytic structure of the momentum density function n (k).
Electromagnetism without monopoles is possible in nontrivial U(1) -fibre bundles
Authors: Asorey M. , Boya L. J.
Published: March 2003

If the first homotopy group of a spacetime manifold M is p cyclic with p≳1, we prove that there exists (p−1) nontrivial and nonequivalent fibre bundles on M with gauge group U(1) in which all the connections describe electromagnetic gauge fields without monopoles. Some spacetimes verifying this condition are introduced. This stresses the physical relevance of the difference between the first Chern classes with integer coefficients and those with real coefficients.
Matrix representation of the kinetic theory differential operator
Authors: Weinert Ulrich
Published: March 2003

A general scheme is given to determine the matrix representation of the differential operator of the kinetic theory of gas mixtures, i.e., the streaming operator in the one-particle phase space. The matrix elements are evaluated explicitly for the Burnett basis functions and a Lorentz type external field. The density, temperature, and mean velocity are treated as field quantities in order to assure the applicability of the results to inhomogeneous problems.
Topological solution for systems of simultaneous linear equations
Authors: Antippa Adel F. , Toan Nguyen Ky
Published: March 2003

Using the discrete path approach, we derive an explicit topological expression for the solution of a system of simultaneous linear equations. This is done by establishing a homomorphism between the solution xn, and the set of paths, defined on the corresponding signal flow graph, from all sources to vertex n.
Disequilibrium theory applied to two-spin Glauber model
Authors: Zhang Hwe Ik , Lee Jae Il
Published: March 2003

The macroscopic disequilibrium theory for Markovian relaxation processes is applied to the two-spin Glauber model. The theory is tested rigorously by evaluation of all quantities explicitly. The probability distribution function is shown to be reproduced exactly by the minimal information procedure using the knowledge of certain macroscopic variables. The probability distribution functions obtained using a reduced number of macroscopic observables are examined and the deviations from the exact distribution function are discussed. It is concluded that the disequilibrium situation might be described satisfactorily if we choose a suitable set of macroscopic variables, but the result might crucially depend on the choice of these variables. The entropy deficiency, entropy production, and the first and the second time derivatives of the entropy production are evaluated explicitly for this model. The signs of such quantities are found to be in accordance with the predictions of more qualitative theories.
Even parity junction conditions for perturbations on most general spherically symmetric space–times
Authors: Gerlach U. H. , Sengupta U. K.
Published: March 2003

A new highly efficient and versatile general relativistic perturbational formalism for general matter occupied spherically symmetric space–times is developed. The perturbations are geometrical objects on the two dimensional totally geodesic submanifold spanned by the radial and time coordinates. The geometrical objects are ’’gauge invariant’’ scalars, vectors, and tensors which are independent of infinitesimal coordinate transformations on the background space–time. This article gives the even parity gauge invariant perturbation objects for arbitrary background scalars, vectors, and symmetric tensors on a spherically symmetric space–time. In particular, metric, matter, first and second fundamental forms, as well as vacuum-matter interface gauge invariant perturbations for a collapsing star are given. In addition four even parity continuity conditions across discontinuous timelike hypersurfaces are given. Two are conditions on the metric gauge invariants, one is a condition on the perturbation away from the spherical contour of the interface, and the fourth couples that contour perturbation to the metric gauge invariants.
An extension of the Bonnor transformation
Authors: Fischer Elliot
Published: March 2003

The Bonnor transformation, which maps stationary, axially symmetric vacuum fields into static, axially symmetric Einstein–Maxwell fields is extended to spacetimes possessing only one spacelike Killing vector. The transformation generates two distinct Einstein–Maxwell solutions from any vacuum solution.
Scalar quantum field in an external gravitational field
Authors: Dimock J.
Published: March 2003

We consider a class of Lorentz metrics on R4 which are Minkowskian off a compact set. For each such metric we construct a quantum field operator which satisfies the generalization of the Klein–Gordon equation. The field has a causal commutator and transforms as a scalar under general coordinate transformations. The field determines a unitary scattering operator which is invariant under coordinate transformations.
On the expansion of the propagator in power series of the coupling constant
Authors: Perez R. B.
Published: March 2003

We show by simple rearrangements of the Lippmann–Schwinger equation, that the propagator (Green’s function) of a linear physical field can be expanded in power series valid for values of the coupling constant either close to unity or very large. The new series satisfy the generalized resolvent operator equation first derived by Mockel.
Linearized analysis of inhomogeneous plasma equilibria: General theory
Authors: Lewis H. Ralph , Symon Keith R.
Published: March 2003

A generalized framework is presented for analyzing the linearized equations for perturbations of inhomogeneous plasma equilibria in which there is a collisionless species, some properties of the solutions of the linearized equations are described, and a basis is provided for numerical computations of the linearized properties of such equilibria. It is useful to expland the perturbation potentials in eigenfunctions of the field operator which appears in the linearized equations, and to define a dispersion matrix whose analytical properties determine the nature of the solutions of the initial-value problem. It is also useful to introduce auxiliary functions to replace the usual perturbation distribution functions, and to expand the auxiliary functions in eigenfunctions of the equilibrium Liouville operators. By introducing the auxiliary functions, great freedom is achieved in the choice of the field operator which appears in the linearized equations. This freedom can be useful in some problems to define expansion functions for the potentials that are particularly suitable for studying specific normal modes.
Invariants in enveloping algebras under the action of Lie algebras of derivations
Authors: Abellanas L. , Martínez Alonso L.
Published: March 2003

An upper bound on the number of algebraically independent invariants in an enveloping algebra 𝒰 under the action of a Lie algebra G0 of derivations is obtained. We are able to determine the exact number of invariants for the case [G0,G0]=G0. This generalizes previous results about Casimir invariants.
Microscopic theory of superfluid Fermi systems. I. Binary expansion
Authors: Reichl L. E.
Published: March 2003

This is the first of two papers in which the binary expansion is used to study the properties of hard core fermi systems with broken gauge symmetry. In this paper, which is primarily formal, symmetry-breaking source terms are introduced into the generating function for thermodynamic quantities, and an exact expression is obtained for the generating function in terms of single-particle and two-particle sources and the reaction matrices for the two-body problem. In a subsequent paper, the theory is applied to a dilute hard sphere fluid.