bluuebunny/crossref_metadata_2025 huggingface dataset:
On dynamical groups: Classification of Lie algebras with Galilei subalgebras
Authors: Doebner H. D. , Hennig J.
Published: February 2004

Because of the pure group theoretical approach to the free nonrelativistic particle through an integrable irreducible representation of the quantum mechanical Galilei (Lie) algebra G, it is reasonable to construct so-called dynamical (Lie) algebras D which possess an integrable representation describing interacting (nonrelativistic) systems. Such dynamical algebras D should contain the geometrical subalgebra G0 of G, spanned by the mass operator, the momentum, the angular-momentum and the position operators. Furthermore, the relation between the free and the interacting system is simplified if the one-dimensional Lie algebra T generating free time translations is a subalgebra of D. Hence preferred candidates for D are those Lie algebras L which possess a subalgebra isomorphic to G or to G0, i.e., those L for which an injective homomorphism ε:G→ε(G)⊂L or G0→ε(G0)⊂L exists. ε is called an embedding of G or of G0 in L. Our main result is a complete classification of (i) all nonsemisimple L with Levi decomposition L=S[addition in left half circle]F with G or G0 embedding ε such that S⊂ε(G) or S⊂ε(G0) (ii) all complex semisimple L̄ with an embedding of the complex extension of G, (iii) all real simple L being real forms or realifications of the lowest dimensional L̄ (i.e., A5, B3, C4) with G-embedding.

The result gives a fairly complete list of all candidates for dynamical nonrelativistic algebras. The physical aspects of two of them, the conformal Galilei algebra Gc and a limitable dynamical algebra Dt, are discussed. A method for the construction of physically useful integrable representations for Gc and Dt is given. Some general properties of nonrelativistic and of relativistic dynamical algebras with G-embeddings are considered.
Limit of the most degenerate representations of SO(p,1)
Authors: Ardalan F.
Published: February 2004

The limit of the group SO(p,1), for large Lorentz transformations, are studied. It is found that the basis functions of the most degenerate representations of SO(p,1), constructed according to the subgroups SO(p) and SO(p−1,1), asymptotically tend to the basis functions, constructed according to the corresponding contracted subgroups. This result is applied to the matrix elements of SO(p,1) to derive novel relations. The limit of the overlap functions are considered.
Lattice Green's function for the diced lattice
Authors: Horiguchi T. , Chen C. C.
Published: February 2004

It is shown that the lattice Green's function for the diced lattice is expressed in terms of the one for the triangular lattice. The distribution function of the squared frequency is shown by a graph and compared with the one for the honeycomb lattice.
Concerning conservation laws resulting from geometric invariance groups for field theories
Authors: Plybon Benjamin F.
Published: February 2004

A geometric symmetry group is defined as a point transformation of a Riemannian manifold combined with a transformation law for the field as a geometrical object. A covariant definition of invariance of an action integral is given. It is shown that geometric invariance groups can be determined from knowledge of a tensor S,βα which can be computed from the density function L in the action integral. A general form for conservation laws due to geometric symmetry is given. Results are applied to electromagnetic fields and it is shown that the Bessel-Hagen conservation laws represent all of the possible conservation laws for electromagnetic fields arising from geometric symmetry.
Eight-vertex model on the honeycomb lattice
Authors: Wu F. Y.
Published: February 2004

The most general vertex model defined on a honeycomb lattice is the eight-vertex model. In this paper it is shown that the symmetric eight-vertex model reduces to an Ising model with a nonzero real or pure imaginary magnetic field H. The equivalent Ising model is either ferromagnetic with e2H/kT real or antiferromagnetic with e2H/kT unimodular. The exact transition temperature and the order of phase transition in the former case are determined. As an application of the result we verify the absence of a phase transition in the monomer-dimer system on the honeycomb lattice.
Closed-form expressions of matrix elements and eigenfunctions from ladder-operator considerations
Authors: Hadinger G. , Bessis N. , Bessis G.
Published: February 2004

Within the Schrödinger-Infeld-Hull factorization scheme, it is shown that, by suitable transformations, the ``accelerated'' or ``ν-step'' ladder operator can always be brought to a simple canonical form, i.e., the νth derivative operation. Thus, one obtains a closed form expression of the eigenfunctions involving a Rodrigues' formula. The necessary and sufficient condition that this Rodrigues' formula generates classical orthogonal polynomials is found to be equivalent to the factorizability condition. Consequently, a closed form expression of any matrix element (diagonal or off-diagonal) on the basis of the eigenfunctions of any factorizable equation is easily derived from the calculation of one unique particular integral. In most cases, this last integral is known analytically. The Kepler problem is reinvestigated as an example. As a concluding remark, further applications of the method are considered.
A pair of coupled quantum anharmonic oscillators
Authors: Halpern Francis R.
Published: February 2004

The energy levels of a pair of coupled anharmonic oscillators are studied. The technique employed is to find two approximately canonical coordinate momentum pairs. Particular emphasis is placed on the qualitative dependence of the coordinate and momentum operators on the quantum numbers.
The evaluation of ``Kondo'' and other integrals of arbitrary range
Authors: Louat Norman
Published: February 2004

It is pointed out that integrals over arbitrary ranges and indefinite integrals may often be obtained very simply by the methods of contour integration.
The power spectrum of the Mellin transformation with applications to scaling of physical quantities
Authors: Moses H. E. , Quesada A. F.
Published: February 2004

The Mellin transform is used to diagonalize the dilation operator in a manner analogous to the use of the Fourier transform to diagonalize the translation operator. A power spectrum is also introduced for the Mellin transform which is analogous to that used for the Fourier transform. Unlike the case for the power spectrum of the Fourier transform where sharp peaks correspond to periodicities in translation, the peaks in the power spectrum of the Mellin transform correspond to periodicities in magnification. A theorem of Wiener-Khinchine type is introduced for the Mellin transform power spectrum. It is expected that the new power spectrum will play an important role extracting meaningful information from noisy data and will thus be a useful complement to the use of the ordinary Fourier power spectrum.
Cancellation of the Green's function in the generation of continuum bound states by nonlocal potentials
Authors: Krause Thomas O. , Mulligan Bernard
Published: February 2004

Continuum bound states (CBS) are known to appear in the spectra of some nonlocal scattering equations. We give a simple derivation of the presence of these states consistent with the requirement that such states occur for zeros of the Fredholm determinant. Examination of the form of the nonlocal potential necessary to the generation of a CBS shows that CBS solutions appear only when the potential has the effect of cancelling the Green's function in the kernel of the integral equation. Several examples from the literature are cited to demonstrate this characteristic feature of CBS.
Motion of charged particles in homogeneous electromagnetic fields
Authors: Honig Eli , Schucking Engelbert L. , Vishveshwara C. V.
Published: February 2004

An invariant geometrical description of the world lines of charged particles in arbitrary homogeneous electromagnetic fields is presented. This is accomplished through the combined use of the Frenet-Serret equations and the Lorentz equation. The results apply to flat as well as Riemannian space-time. The intrinsic scalars associated with these curves (i.e., their curvatures and first and second torsions) are found to be constants of the motion when they are well defined. Moreover, they form simple relationships with the field invariants as well as with the energy and momentum densities of the rest frame fields. When they are evaluated in the instantaneous rest frame of the particle, the Frenet vectors lend themselves to simple physical interpretation. It is shown that one cannot distinguish in an intrinsic geometrical manner between the curves of positive and negative charges. The same is true for positive and negative magnetic monopoles if they exist. In such a case, however, one would be able to distinguish intrinsically between ordinary and magnetic charges. The effect of duality rotations of the field tensor on the Frenet scalars is studied. A physical realization of the Frenet frame is obtained by considering the classical description of spin precession. Finally the Frenet formalism is applied to timelike Killing trajectories. These are shown to closely resemble the world lines of charged particles in homogeneous electromagnetic fields.
On stress-energy tensors
Authors: Goedecke G. H.
Published: February 2004

An old but not well-known formal method is detailed and used to obtain the symmetrized stress-energy tensor from Noether's theorem applied to Poincaré-covariant Lagrangian field theories. A variation in a standard method is presented and used to obtain the corresponding canonical stress-energy tensor, valid in arbitrary curvilinear coordinates, in the limit of Lorentz metric. These two tensors are shown to be equal, in each case, for scalar, Maxwell, Dirac spinor, coupled Maxwell-Dirac, and vector (non-Maxwell) Lagrangian field theories.
Regge lattice and Lie-algebra representations
Authors: Flato Moshé , Snellman Håkan
Published: February 2004

A possible description of Regge trajectories in terms of an irreducible representation of the Lie algebra of the 11-parameter Weyl group is proposed.
Properties of the (: φ4 :)1 + 1 interaction Hamiltonian
Authors: Gidas Basilis
Published: February 2004

Using a convergent expansion of the resolvent of the Hamiltonian H=H0+λ V, V=∫d x×(x):φ4:(x),g(x)∈C0∞,g(x)⩾0, we give a simple proof of (a) the self-adjointness of the Hamiltonian and (b) the volume independent lower bound of the vacuum energy per unit volume. Also, we obtain some coupling constant analyticity properties of the Hamiltonian, and the limit (H0+λν−z)−1→(H0−−z)−1, z ∈ρ(H0) in norm as |λ|→0 uniformly in {λ:|argλ|<π}.
On the self-adjointness of the Lorentz generator for (: φ4 :)1 + 1
Authors: Gidas Basilis
Published: February 2004

An alternative proof to that provided by Jaffe and Cannon of the self-adjointness of the local Lorentz generator for the (: φ4 :)1 + 1 quantum field theory is given. The proof avoids the use of second-order estimates and a singular perturbation theory.
Distribution of the lowest eigenvalue for a class of random matrices
Authors: Ullah Nazakat
Published: February 2004

The random matrix theory is applied to the ensemble of partially diagonalized shell-model Hamiltonian matrices. Using the analogy with the distribution of the poles of the unitary collision matrix, an expression for the joint probability density function of the eigenvalues is derived for the present ensemble. An approximation is used to work out a closed form expression for the probability density function of the lowest eigenvalue. Two simple examples are considered to see what this probability density function looks like.
Unification of the external conformal symmetry group and the internal conformal dynamical group
Authors: Barut A. O. , Bornzin G. L.
Published: February 2004

The two common applications of O(4,2) as a conformal group on external space-time coordinates and as a dynamical group on internal relative coordinates are combined into a unified algebraic structure for composite systems. A method is given for obtaining from this structure infinite-component wave equations and a discrete, linearly increasing mass spectrum.
Lie theory and separation of variables. 3. The equation ftt−fss =γ2f
Authors: Kalnins E. G. , Miller W.
Published: February 2004

Kalnins has related the 11 coordinate systems in which variables separate in the equation ftt−fss =γ2f to 11 symmetric quadratic operators L in the enveloping algebra of the Lie algebra of the pseudo-Euclidean group in the plane E(1,1). There are, up to equivalence, only 12 such operators and one of them, LE, is not associated with a separation of variables. Corresponding to each faithful unitary irreducible representation of E(1,1) we compute the spectral resolution and matrix elements in an L basis for seven cases of interest and also give overlap functions between different bases: Of the remaining five operators three are related to Mathieu functions and two are related to exponential solutions corresponding to Cartesian type coordinates. We then use these results to derive addition and expansion theorems for special solutions of ftt−fss =γ2f obtained via separation of variables, e.g., products of Bessel, Macdonald and Bessel, Airy and parabolic cylinder functions. The exceptional operator LE is also treated in detail.
Exponentially small scattering amplitude in high energy potential scattering. II
Authors: Paliov (Lev) A. , Rosendorff S.
Published: February 2004

The high energy, small angle Glauber-Molière scattering amplitude of spherical symmetric potentials, which are expandable in ascending even powers of r and singular in coordinate space, is calculated. The singularities are poles of order n(= 1,2,⋯) off the real axis. As in the nonsingular case the amplitude decreases like exp (− qb) as a function of the momentum transfer q. However, the dependenc of b on q is quite different. Unlike in the nonsingular case it reaches a finite value at infinite energy. Also, in contradistinction to the nonsingular case, the first Born approximation under certain conditions holds in the whole range of validity of the scattering angles.
Remarks on the Klauder phenomenon
Authors: DeFacio B. , Hammer C. L.
Published: February 2004

An elementary discussion is given of a phenomenon discovered by Klauder. In Klauder's phenomenon H = H0 + λV does not converge to H0 as the positive real parameter λ→0+. We discuss domain questions of the operators, and also operator forms and operator extensions. The implications of this phenomenon for ``gauge theories'' are given, and new examples, which include the massless limit for particles of arbitrary spin and an integral operator, are given.
Polarization of electrons in screened Coulomb scattering
Authors: Ridener F. L. , Good R. H.
Published: February 2004

In this paper the effects of screened-Coulomb scattering on electron polarization are calculated. The results apply to elastic electron scattering by light atoms at moderate energies. The calculation is carried out to second order in αZ; in this order the change in magnitude of the polarization first occurs. For arbitrary initial polarization, the final polarization vector is expressed explicitly as a function of initial polarization, momentum, and scattering angle. The effects of screening on polarization is discussed. In the low energy region, a few hundred eV, there is a significant effect on the output polarization of an input unpolarized beam.
Representation and differential geometry of the semisimple Lie groups
Authors: Yeh Hsin-Yang
Published: February 2004

A systematic method is presented whereby any compact Lie group of n-real parameters is dealt with from an infinitesimal approach with the representative matrix method based on a group of inner automorphisms suggested in a previous paper. The group manifold, defined in terms of a metric of group parameters, is identified as a Riemannian one in which these parameters play a role of n curvilinear coordinates. Riemannian geometry is thus valid in the group manifold, and geometric quantities are explicitly calculated in terms of the symmetric or (0) connection by a straightforward application of the ordinary procedure of tensor analysis. A new and simpler method of computing the invariant volume element is presented within this framework. Furthermore, we discuss in detail the group of inner automorphisms for the calculation of the matrix element of finite rotations for any irreducible representation (abbreviated MEFRIR). It is found that our method works very well and yields right and left vector fields together with a set of 2n equations to be satisfied by the MEFRIR. The global properties of the group may, therefore, be obtained as a solution to these equations. Moreover, it provides not only the generalized Maurer-Cartan equations, the Lie structure formulas, two parameter groups of point transformations and the adjoint group, but also two additional nonsymmetric (+) and (−) connections with zero curvature, which do not possess any preassigned metric but possess two absolute parallelisms. Thus, our results on differential geometry completely agree with Cartan and Schouten's. A link between differential geometry and representations is presented by the right and left vector fields which are explicitly calculable in terms of the n parameters and through which geometric quantities, e.g., the Riemann tensor, the Ricci tensor, and the scalar curvature, of any connection are explicitly displayed. A theorem relating both the vector fields to the metric tensors is also included. Finally, the l (rank of the group) invariant differential equations to be satisfied by the MEFRIR are cast in the covariant (or Lie derivative) forms in any connection. Examples of the invariant equations are given for SU(2), SO(3), and SU(3). The two invariant equations of the latter can be cast in terms of the eigenvalues of isospin and hypercharge upon carrying out charge and hypercharge quantizations; in this connection, a new nonrelativistic wave equation to be satisfied by SU(3) multiplets as a generalization of the Schrödinger equation of the symmetric top is also proposed.
A curiosity concerning angular momentum
Authors: Newman Ezra T. , Winicour Jeffrey
Published: February 2004

We show that for classical, relativistic particles (or systems of noninteracting particles) one can interpret the intrinsic (or spin) angular momentum as arising from a center of mass world line displaced from the real Minkowski space into complex Minkowski space. This interpretation is then connected with the Penrose theory of twistors. It is further shown that if the complex center of charge coincides with the complex center of mass, the resulting particle has the Dirac value of the gyromagnetic ratio, i.e., (e/mc). For massless particles, there is no unique complex line about which the angular momentum vanishes-instead, there is a complex 2-surface, which can be considered to be a Penrose twistor.
Singular perturbation method in neutron transport theory
Authors: Mika Janusz
Published: February 2004

We consider equations of evolution with a small parameter in a Banach space. The method of singular perturbations is applied to derive inner and outer asymptotic solutions. It is shown that the neutron transport equation coupled with the equation for the concentration of delayed neutron precursors, if considered in the Hilbert space of square integrable functions, satisfies all the requirements set up in the paper.
On mass zero indecomposable representations of the Poincaré group
Authors: Mathews P. M. , Seetharaman M. , Simon M. T.
Published: February 2004

Considering the space of massless-particle wavefunctions transforming locally according to the irreducible representation D(m,n) of the homogeneous Lorentz group, we determine explicitly, by a direct and elementary method, the matrices constituting the (reducible but indecomposable) representation of Lorentz transformations with respect to a helicity basis.
Rigged Hilbert space formalism as an extended mathematical formalism for quantum systems. II. Transformation theory in nonrelativistic quantum mechanics
Authors: Melsheimer O.
Published: February 2004

Results of a previous paper are used to obtain a rigorous mathematical formulation of the transformation theory of nonrelativistic quantum mechanics within the framework of rigged Hilbert spaces.
On the geometrization of neutrino fields. II
Authors: Ludwig Garry
Published: February 2004

In a previous paper neutrino fields with positive (or negative) energy density were geometrized in the sense of Rainich, Misner, and Wheeler. The present paper deals with the geometrization of neutrino fields which do not satisfy such an energy condition.
Applications of infinite order perturbation theory in linear systems. I
Authors: Wu S. Y. , Tung C. C. , Schwartz M.
Published: February 2004

The applicability of infinite order perturbation theory to linear systems is exhibited. The technique involves a generalization of the method developed by Wu and Taylor and can be used to study systems described by the equations of the following form Vnnun + Vn,n+1un+1 + Vn,n−1 × un−1 = Eun, where the coupling coefficients V′nn's depend on n. The wide range of application of the generalized method is demonstrated by using it to study systems as different as the plane rotator in an external field on the one hand and the dynamics of a disordered chain on the other.
Scattering of plane longitudinal elastic wave by a large convex rigid object with a statistically corrugated surface. II. Far field solution
Authors: Fan W. , Chen Y. M.
Published: February 2004

The far field solution for the scattering of plane longitudinal elastic wave by a large convex rigid object with a statistically corrugated surface is obtained and the effective reflection and diffraction coefficients are deduced.
Thermodynamics of a mixture of fermions and bosons in one dimension with a repulsive δ-function potential
Authors: Lai C. K.
Published: February 2004

The thermodynamics of a mixture of fermions and bosons is derived on the basis of two ansätze about the roots of a set of algebraic equations.
Elastic scattering in the Kerr metric
Authors: Bose S. K. , Wang M. Y.
Published: February 2004

The differential cross section for scattering from a source whose gravitational field is described by the Kerr metric is evaluated.
Theory of self-reproducing kernel and dispersion inequalities
Authors: Okubo Susumu
Published: February 2004

The theory of the self-reproducing kernel by Aronszajn has been investigated for a Hilbert space with norm ‖f‖2=(1/2π) ∫ 02πd(θ|f(ei θ)|2+(1/π) ∫ −11dx λ(x)|f(x)|2,where f(z) is a H2 function and λ(x) is a nonnegative summable function. The self-reproducing kernel of this space satisfies an integral equation. The dispersion inequalities for various problems in the high energy physics can be treated in unified and generalized manner by this theory.
Ising models derived from binary lattice gases
Authors: Runnels L. K.
Published: February 2004

Transformations of two-component lattice gases are studied. The original binary lattice gas has the Widom-Rowlinson type of interaction: infinite repulsion between nearby unlike particles and no interaction between like particles (except that multiple site occupancy is forbidden). The first transformation is to an equivalent one-component lattice gas, with many-body interactions-some attractive, some repulsive. The second transformation is to the isomorphic Ising spin system, having many-spin interactions-some ferromagnetic and some antiferromagnetic. All interaction functions are obtained as explicit geometrical derivates of the mutual exclusion ``sphere'' of the original binary system. The results are discussed in light of recent theories of phase transitions of Ising models with symmetry-breaking many-spin interactions.
A scattering problem for a straight line segment
Authors: Ranger K. B.
Published: February 2004

An explicit analytical solution is found for the scattering potential produced by a straight line segment. Integral transformations are introduced which map the mixed boundary value problem into one which can be solved by standard Green's function methods.
Expansion-free electromagnetic solutions of the Kerr-Schild class
Authors: Debney George
Published: February 2004

Starting with the general Kerr-Schild form of the metric tensor, d s2=η+l⊗l (where l is null and η is flat space-time), a study is made for those solutions of the Einstein-Maxwell equations in which l is geodesic, shear-free, and expansion-free. It is shown that all resulting solutions must be of Petrov type [4] or type [−] and the Maxwell field must be null. Because of the expansion-free assumption there exist flat and conformally flat gauge conditions on all metrics in this class; i.e., there exist metrics of this Kerr-Schild form which are flat (or conformally flat) but are not Lorentz-related. A method is given for obtaining meaningful solutions to the field equations with the latter gauge equivalence class removed. A simple example of a radiative field of type [4] along a line singularity exhibits how solutions in this class may be generated.
Coherent states and Lie algebras
Authors: Hioe F. T.
Published: February 2004

The Bloch coherent states for a spin or a system of spins and the Glauber coherent states for bosons are examined from the viewpoint of Lie algebras. It is pointed out that the Bloch coherent states are vectors in the space spanned by the basis functions for an irreducible representation of the unitary unimodular group SU(2), and that the Glauber coherent states are vectors in the space spanned by the basis functions for the infinite-dimensional irreducible representation of a contracted group of SU(2). A deeper understanding of many of the useful properties of these coherent states is gained.
Proof of Zwanzig's rule of ``planar'' graphs
Authors: Wulf A.
Published: February 2004

A rigorous proof is given of Zwanzig's conjecture that only planar graphs contribute to the virial coefficients of discreet-orientation models for a fluid of long thin rods. The proof makes use of relations between connected graphs and ``trees''—the simplest type of connected graphs.
Note on space-times that admit constant electromagnetic fields
Authors: Eardley Douglas M.
Published: February 2004

All space-times that admit a covariantly constant, test, electromagnetic field are constructed. All solutions to the Einstein-Maxwell equations with constant electromagnetic field are given.
Gel'fand-pattern technique applied to the physically important SU(3)⊗SU(2)⊂SU(6) decomposition of S U(6)
Authors: Strand Alf E.
Published: February 2004

Explicit and easily computable formulas for the physical quantum numbers I3, Y, and S3, and also two additional quantum numbers for all states spanning an arbitrary irreducible representation of S U(6) are obtained by using Gel'fand-pattern technique. This result is accomplished by establishing a correspondence between the 3 diagonal SU(3)⊗SU(2) generators + 2 ``quark-spin'' generators, and the 5 ``canonical'' generators H1 − H5, the eigenvalues of which are given by the Gel'fand patterns of S U(6) in the ordinary way. The SU(3)⊗SU(2)⊂SU(6) content of the S U(6) representations taken as examples is displayed explicitly. The possibility of doing this suggests that Gel'fand patterns may be useful even in a nonmaximal decomposition, although the patterns are intrinsically linked to the ``canonical'' chain of decomposition: SU(n)⊃U1(1)⊗SU(n−1)⊃U1(1)⊗U2(1)⊗SU(n−2)⊃⋯etc. The procedure developed in the case of S U(6) is generalized to the twofold nonmaximal decomposition of SU(mn)⊃SU(m)⊗SU(n).
Some observations on the operator H=−(1/2)d2/dx2 +m2x2/2+g/x2
Authors: Zirilli F.
Published: February 2004

In the present work we study the differential operator H=−(1/2)d2/dx2 +m2x2/2+g/x2. This operator known as the Hamiltonian of the quantal oscillator has been a matter of study since the beginning of quantum mechanics. Recently, it has become again actual after the paper of Calogero where the correspondent N body problem (developed in many works) is studied. Parisi and the author have used H as Hamiltonian, studying the anomalous dimensions in one-dimensional quantum field theory. Finally, Klauder, using H as a simple degree of freedom example, has studied some qualitative features of quantum theories with singular interaction potentials. In the following work we are going to study H, showing that H is equivalent to ``half an harmonic oscillator'' for the odd and even eigenspaces separately.
On analytic nonlocal potentials. II. Analyticity of the S matrix, for fixed l, its representations, and a dispersion relation for fixed t
Authors: Yao Te Hai
Published: February 2004

For a class of analytic short-ranged nonlocal potentials, we study the analyticity of the S matrix in the k plane, for fixed l, using Fredholm method for the Lippman-Schwinger equation for the partial scattering solution, and contour deformation in the analytic continuation of the S matrix, thereby extending a representation of the S matrix in terms of Fredholm determinants. We also obtain a representation of the S matrix in terms of Jost functions, for l = 0. For a subclass of this class of potentials, we obtain a dispersion relation for the full scattering amplitude, for fixed t in the range 0 ≥ t > − 4γ2, where γ is some parameter of the potential, using summation of the partial amplitude expansion of the full amplitude. Analyticity properties of the partial scattering solution, for all l, and of the regular and Jost solutions, for l = 0, are also discussed.
An approximate interior solution in Brans-Dicke theory
Authors: Mahanta M. N. , Reddy D. R. K.
Published: February 2004

An approximate interior solution of the field equations of Brans-Dicke theory is obtained for a static spherically symmetric metric which can be considered to be an analog of Schwarzschild's interior solution in Einstein's theory.
On the transport properties of van der Waals fluids. II. Explicit calculations
Authors: Resibois P. , Pomeau Y. , Piasecki J.
Published: February 2004

Starting from the formal expansion of an arbitrary transport coefficient X in series of the inverse range γ of a van der Waals potential, we establish the explicit form of the first γ correction to X; we show that it can be expressed solely in terms of the Fourier transform VyL of the long-range interaction and in terms of the equilibrium and transport properties of the short-range reference system. A comparison with previous work on related problems is also given.
Composition of coherent spin states
Authors: Bellissard J. , Holtz R.
Published: February 2004

Clebsch-Gordan coefficients for the S U (2) group are computed in the coherent spin state basis introduced by Radcliffe.
On a boundary value problem for integro-differential equations
Authors: Huss R. , Kalaba R. , Vasudevan R.
Published: February 2004

A boundary value problem of a linear differential-integral equation is converted to a Cauchy system by means of parameter imbedding. Numerical results are shown for an equation from nuclear physics.
Causal boundaries for general relativistic space-times
Authors: Budic R. , Sachs R. K.
Published: February 2004

Let M be a causally continuous space-time. Using indecomposable past and future sets in a symmetric way we construct a causal completion N for M. N is a causal space; the chronology of M in N is the chronology of M. The extended Alexandrov topology for N makes N Hausdorff and M a densely imbedded subspace. M is globally hyperbolic iff either the chronological future or the chronological past of each point in N-M is empty, causally simple iff the causality of M in N is the causality of M. The standard examples of causal completions are special cases.
Clebsch-Gordan problem and coefficients for the three-dimensional Lorentz group in a continuous basis. I
Authors: Mukunda N. , Radhakrishnan B.
Published: February 2004

We have described a new approach to the Clebsch-Gordan problem for the unitary representations of the three-dimensional Lorentz group. We relate the various types of Clebsch-Gordan series to problems in the representation theory of four-dimensional orthogonal and pseudo-orthogonal groups, and thereby achieve a new and better understanding of the structures of the series. At the same time, the Clebsch-Gordan coefficients in a continuous basis are calculated. In this, the first of four papers, the case D+⊗D+ is worked out in detail.
C*-algebraic formalism for coarse graining. I. General theory
Authors: Wolfe John C. , Emch Gérard G.
Published: February 2004

Bernouilli's principle of insufficient reason is formulated in a noncommutative C*-algebraic generalization of probability theory. This idea is developed here for general quantum systems, and a simple illustration of it is given. Subsequent papers in this series will deal with more sophisticated models.
C*-algebraic formalism for coarse graining. II. Momentum coarse graining for Fermi systems in finite volume
Authors: Wolfe John C. , Emch Gérard G.
Published: February 2004

The general C*-algebraic formalism developed by the authors for the coarse-graining operations in quantum statistical mechanics is shown to be applicable to the case of a Fermi system confined in a finite volume.
Time-independent multichannel scattering theory for charged particles
Authors: Gibson A. G. , Chandler Colston
Published: February 2004

Rigorous derivations are given of two time-independent formulas for the multichannel scattering operator for nonrelativistic charged particle systems. The derivations are based on Dollard's time-dependent theory and use techniques of spectral integration. The formulas involve a complex power of the resolvent operator, in contrast to short-range formulas. Bilateral Laplace transforms are used to derive a generalized multichannel resolvent equation and to prove existence and uniqueness of the solution. The formulas are applied to recover the well-known two-body Coulomb scattering amplitude.
The maximal solvable subgroups of the SU(p,q) groups and all subgroups of SU(2,1)
Authors: Patera J. , Winternitz P. , Zassenhaus H.
Published: February 2004

A general method is proposed for obtaining all conjugacy classes of maximal solvable subalgebras of an arbitrary semisimple Lie algebra over a zero characteristic field F. The method is applied to explicitly construct all q+1 maximal solvable subalgebras Sκ of the algebra of SU(p,q) for p≥q>0 (over the field of real numbers). The dimension of Sκ for 0≤κ≤q is (2κ+1)× (p+q−κ)−1 and it contains p+q−κ−1 compact elements. The low-dimensional pseudounitary groups with 0≤p+q≤4, 0≤q≤p are considered in detail and different realizations of the maximal solvable subalgebras are presented. Finally, all subalgebras of the physically interesting algebra SU(2,1) are found (not only the maximal solvable ones). The invariants of the subalgebras are found in all cases when they exist.
Generating functionals determining representations of a nonrelativistic local current algebra in the N/V limit
Authors: Menikoff Ralph
Published: February 2004

Representations will be given for the nonrelativistic local current algebra consisting of ρ(x), the particle number density, and J(x), the flux density of particles. These representations correspond to the N/V limit of (i) a free Bose gas, (ii) Bose gas in an external potential, (iii) free Fermi gas, and (iv) Bose gas (in one dimension) with a two-body interaction potential V(x)=2/x2. In each case the generating functional L(f), the ground state expectation value of exp[iρ(f)], determining the representation will be given. It will also be shown the generating functional satisfies a functional equation of the form [∇ − i∇f(x)](1/i) [δ/δf(x)]L (f) = A(x, (1/i)(δ/δf))L(f) and that the Hamiltonian written in terms of ρ and J has the form H = (1/8)∫dxK̃(x)† [1/ρ(x)] K̃(x) with K̃(x)=∇ρ(x) +2iJ(x)−A(x,ρ).
Complex potential formulation of the axially symmetric gravitational field problem
Authors: Ernst Frederick J.
Published: February 2004

Spin-coefficients and null tetrad components of the Ricci tensor and the Weyl conform tensor are evaluated in terms of a single complex gravitational potential ε, while null tetrad components of the electromagnetic stress energy tensor are evaluated in terms of a second complex potential φ. All the results are expressed elegantly in terms of a differential operator ð, similar to the ``thop'' of Newman and Penrose. The problem of finding physically pertinent stationary axially symmetric Einstein-Maxwell fields is reduced to the search for a complex solution ξ0(x, y) of one nonlinear differential equation subject to simple subsidiary conditions.
On the three-body linear problem with three-body interaction
Authors: Wolfes J.
Published: February 2004

A three-body potential is introduced for which Schrödinger's equation of the three-body linear problem with additional harmonic and inverse cube forces is solved exactly.
Wave propagation in a random medium: A complete set of the moment equations with different wavenumbers
Authors: Lee L. C.
Published: February 2004

Propagation of waves in a random medium is studied under the ``quasioptics'' and the ``Markov random process'' approximations. Under these assumptions, a Fokker-Planck equation satisfied by the characteristic functional of the random wave field is derived. A complete set of the moment equations with different transverse coordinates and different wavenumbers is then obtained from the Fokker-Planck equation of the characteristic functional. The applications of our results to the pulse smearing of the pulsar signal and the frequency correlation function of the wave intensity in interstellar scintillation are briefly discussed.
On the automorphisms of real Lie algebras
Authors: Burdet G. , Perrin M. , Sorba P.
Published: February 2004

We establish some properties of automorphisms of real Lie algebras, which in particular allow us to construct the derivation algebra of a Lie algebra from the derivations of its radical. We apply this construction to some familiar kinematical algebras.
Spectral representation of the pentagon diagram amplitude
Authors: Frederiksen J. S.
Published: February 2004

A method developed in two previous papers is used to derive a double spectral representation with Mandelstam boundary for the pentagon diagram amplitude for the production process A B → C D N. Restrictions on the masses and kinematic invariants for which this representation is valid are found and it is discussed how a representation can be obtained for wider ranges of these variables. Finally, a comparison is made with the results of other authors.
Application of cumulant techniques to multiplicative stochastic processes
Authors: Fox Ronald Forrest
Published: February 2004

The use of cumulant techniques for analyzing time dependent, stochastic matrix expressions of the form 〈T lim ←exp[∫0tB̃(S)d S]〉 is explained. Because cumulants are complicated expressions when B̃(t) does not commute with itself at unequal times, we explicitly work out cumulant expressions up to fourth order. The fourth order terms can be used to demonstrate that noncommutivity prevents the generalization, to time-dependent, stochastic matrices which do not commute with themselves at unequal times, of the result which applies to commuting stochastic processes that states: If the stochastic process is Gaussian, then its cumulant expansion truncates after the second cumulant. Furthermore, it is argued that if the stochastic matrix process is both Gaussian and purely random then the cumulant expansion does truncate after the second cumulant, after all. The significance of this result with respect to the application of approximation involving cumulants is mentioned.
A classification of second-order raising operators for Hamiltonians in two variables
Authors: Boyer Charles P. , Miller Willard
Published: February 2004

We develop a group theoretic method based on results of Winternitz et al. to compute and classify all first- and second-order raising and lowering operators admitted by Hamiltonians of the form H¯=−(1/2)Δ2+V(x,y). The key to our results, which generalize to higher dimensions, is a proof that H¯ admits a second-order raising operator only if the Schrödinger equation separates in Cartesian, polar, or elliptic coordinates.
Variational formulation of the relativistic theory of microelectromagnetism
Authors: Maugin Gérard A. , Eringen A. Cemal
Published: February 2004

By adjoining a set of adequate potentials to the classical electromagnetic potential, it is possible to formulate a variational principle that yields the equations of the micromorphic EM theory proposed by Eringen and Kafadar [J. Math. Phys. 11, 1984 (1970)]. The energy-momentum law for micromorphic EM fields is obtained and constitutive equations are derived for relativistic EM-elastic fields.
Multigroup replication property for external, spherically symmetric problems of transport theory
Authors: Żelazny R. , Duracz T.
Published: February 2004

The replication property for multigroup spherically symmetric external problems in the transport theory is derived and applied to reduce the system of multigroup integral transport equations to a system of planelike singular integral equations, which can be solved by means of well-known methods.
Existence and uniqueness of solutions to Low's problem
Authors: Nedelkov I. P.
Published: February 2004

In the framework of S-matrix theory, the partial scattering amplitudes are sought as a solution of a certain problem involving analyticity, unitarity, and crossing symmetry. This problem, with a condition of analyticity which is weaker than the usual one, is called Low's problem in this paper. By means of the fixed-point theorems of Schauder and Banach-Cacciopoli, conditions for the existence and uniqueness of solutions to Low's problem are given.
Properties of two-phase ``cell materials''
Authors: Brown William Fuller
Published: February 2004

``Symmetric cell materials'' and ``asymmetric cell materials'' were defined by Miller in connection with the physical properties (such as the effective dielectric constant) of two-phase solid mixtures. It is shown here that while the ``symmetric cell material'' is self-consistent, the ``asymmetric cell material'' is not: The postulated three-point probabilities do not add up to the correct one-point probabilities. A self-consistent generalization of the ``symmetric cell material'', based on the requirement that a certain integral must reduce to an integral over a finite region, is developed, and one construction procedure for producing such a material is described.
Some unitarity bounds for finite matrices
Authors: Mennessier G. , Nuyts J.
Published: February 2004

We study the problem of obtaining the bounds on the modulus of one element of a finite unitary matrix once the values of the moduli of a set of other elements are given. The problem is solved in simple cases, and indications of more general cases are given. This question is interesting from a physical point of view since it leads to direct inequalities between sets of partial waves. It would also be useful to extend this kind of results to the continuous matrices where inequalities on cross sections could be obtained.
On the spontaneous breakdown of compound symmetries
Authors: Cicogna G. , de Mottoni P.
Published: February 2004

We consider the spontaneous breakdown of a symmetry group G which is the direct product of two groups: G=A×B. We study the conditions under which the breakdown of G entails that of both A and B. Our results are corroborated by an explicit example, where G is S U2 × L, L being the Lorentz group, and such that any spontaneous breakdown of G entails that of both S U2 and L.
Symmetries of extended 3j coefficients
Authors: D'Adda A. , D'Auria R. , Ponzano G.
Published: February 2004

This paper studies the symmetries of a function which generalizes the 3j coefficients of SU(2) and of SU(1,1) involving discrete unitary representations. As a by-product of the analysis, the symmetries of the SU(1,1) coefficient are obtained.
Can outside fields destroy black holes?
Authors: Hájíček Petr
Published: February 2004

Stationary, axisymmetric, asymptotically flat space-times with a black hole surrounded by matter rings, disks, or shells are considered. A certain set of invariant functions, called local invariants, is defined which contains full information about the metric and electromagnetic field in a small electrovacuum neighborhood of the horizon. The local invariants are shown to satisfy an inequality, which is a generalization of the well-known Kerr-Newman inequality m2>a2+e2, and which places an upper bound on the gravimagnetic, electric, and magnetic field strengths as measured at the surface of the black hole, independently of whether the fields are produced by the black hole itself or originate in outside sources.
Complex structures and representations of the Einstein equations
Authors: Brans Carl H.
Published: February 2004

The space-time model of general relativity is that of a four-dimensional manifold M, with a metric of Minkowski signature. The space of two-forms on M is endowed with a natural complex structure, J, generated by the star duality operator. The existence of such a structure is an accidental characteristic of the dimension four and of the metric signature. The full differential geometric structure equations are expressed in this two-form language and it is pointed out that the weakened Einstein empty space equations, i.e., Rab −(1/4)gabR =0, reduce to the condition that the curvature form commute with J. This fact, together with the isomorphism of the two-form space with the Lorentz Lie algebra, l0, are then shown to provide the basis for the importance of the various complex representations of l0, such as S O (3,C) and the spinor S L (2,C), in understanding the real geometry of Einstein spaces. In fact, the complexified Einstein structure equations naturally divide into two sets, each the complex conjugate of the other, each involving only one-half of the basis.
Absence of trivial subrepresentations from tensor products of unitary representations of pseudo-orthogonal groups
Authors: Fulling S. A.
Published: February 2004

A unitary tensor product representation of the group S O0(1,n), n =2,3,4, does not contain the trivial representation as a discrete direct summand unless each of the factors does.
Statistical mechanical approaches to fluid turbulence
Authors: Lee Jon
Published: February 2004

In the moment formulation, the direct-interaction approximation equations have been derived by developing perturbation about three different states: the laminar flow (Wyld), a turbulent flow (Kraichnan), and the Gaussian random process (Phythian). Along the parallel line, the pertubation theories in the distribution function formulation have also been developed about the same three states: the laminar flow (Balescu-Senatorski), a turbulent flow (Herring), and the Gaussian random process (Edwards). Herring's modal energy and averaged Green's equations are the basic turbulence equations of the distribution function formalism. The modal energy equation, however, represents the simultaneous-time limit of Kraichnan's covariance equation. This paper provides a unified statistical mechanical framework for the three turbulence theories of the distribution function formalism. We have first revised the derivation of Balescu and Senatorski and then presented an alternate method for Herring's self-consistent-field approximation in terms of the action-angle variables. Finally, we have shown that Edwards' theory cannot give the totally correct stationary dynamics because it is not possible to uniquely determine the dynamic friction and diffusion coefficient in the distribution function formulation.