bluuebunny/crossref_metadata_2025 huggingface dataset:
Generalized isoperimetric inequalities. III
Authors: Luttinger J. M.
Published: February 2004

The generalized isoperimetric inequalities for rearranged Green's functions, which have previously been discussed for a rearrangement process analogous to Steiner symmetrization, are obtained for a type of rearrangement analogous to circular symmetrization. It is also shown how rearrangements analogous to spherical and Schwarz symmetrization may be defined and considered as limiting cases of previously discussed rearrangements.
A condition for the applicability of Biedenharn's lemma
Authors: Beck Robert E.
Published: February 2004

Biedenharn's lemma is used to compute the outer multiplicities of the irreducible components of the tensor product of two irreducible representations of a complex simple Lie algebra L with highest weights λ and λ′. The lemma is applicable if for all weights μ of λ, we have that λ′ + μ is a dominant integral form. This paper deduces a condition written in terms of the root system of L and the coordinates of λ and λ′ which is equivalent to λ′ + μ being a dominant integral form for all weights μ of λ.
Facial aspect of superposition principle in algebraic quantum theory
Authors: Chen Etang
Published: February 2004

A facial version of superposition principle is introduced in algebraic quantum theory; similar to the quantum logic approach it exhibits characteristic features of quantum theory. It is shown that any pair of primary states satisfy the superposition principle if and only if they are quasiequivalent. A coherent sector is then defined as a quasi-equivalent class of primary states, which holds for both pure states in quantum theory and pure thermodynamic phases in quantum statistical mechanics.
The mathematical reflection problem
Authors: Chakraborty B.
Published: February 2004

The one-dimensional mathematical problem of finding the scattering amplitude for weak reflection by slowly and continuously varying plane layered media was defined and solved by an extension of the WKB method by Chakraborty. A further study of the solution of this problem near the zeros of the parameters is considered in this note. We find quantities proportional to the energy density and energy flux density. In the last section some speculative remarks about possible lines of future work are made.
The field of real numbers in axiomatic quantum mechanics
Authors: Maczyński M. J.
Published: February 2004

Consider a system of states and observables based on the logic L(V, D) of all φ-closed subspaces of a vector space V over a division ring D with a definite Hermitian form φ. Gudder and Piron have shown that if the system admits a special kind of observable called the smooth maximal observable, then the division ring D must be an extension of the real field. In this paper it is shown that the same conclusion can be obtained from weaker and more physical assumptions which are in principle experiment verifiable.
Operational statistics. II. Manuals of operations and their logics
Authors: Randall C. H. , Foulis D. J.
Published: February 2004

In the first paper of this series, the notion of a manual of operations and its (generalized) sample space was introduced. For each such manual of operations, a so-called logic was constructed. In the present paper, some of the algebraic properties of such logics are identified with the corresponding operational properties of the manual.
Electron in the field of two monochromatic electromagnetic waves
Authors: Berson I. , Valdmanis J.
Published: February 2004

The motion of the electron in the classical as well as in the quantized field of two circularly polarized waves which move in opposite directions is investigated. The spin characteristics of the electron are neglected and it is assumed that the electron and one of the waves move in the same direction. In the classical case the problem is reduced to the solution of the general Mathieu equation, but in the quantum case to the solution of an ordinary second-order differential equation with two irregular points. For particular values of the parameters the analytic expressions of the solution are found. The character of the solution essentially depends on the mutual polarization of waves. The conserved quantity for opposite polarization of waves is the energy of the electron, but for the same polarization it is the momentum of the electron. In the latter case the effective potential depends on the time, and the electron-positron pair creation is allowed.
Invariant imbedding and the resolvent of Fredholm integral equation with composite symmetric kernel
Authors: Bellman Richard , Ueno Sueo
Published: February 2004

Consider a Fredholm, integral equation for f(t, b) with a composite displacement kernel f(t,b)=g(t)+λ∫ab[E(t,y)+F(t+y)] f(y,b)dy, where g(t) is a given forcing function, the parameter λ is defined over 0<λ≤1,0≤a≤t≤b, and the E and F functions are together the displacement kernels. Extending the invariant imbedding method given in our preceding paper [cf. Bellman, Kagiwada, Kalaba, and Ueno, J. Math Phys. 9, 906 (1968)], we show how the Bellman-Krein formula provides us with a Cauchy system of the functional equations governing the resolvent and the scattering function. The invariant imbedding equations for the scattering function and the auxiliary function for a = 0 reduce to those given in a preceding paper [cf. Casti, Kalaba, and Ueno J. Quant. Spectry. Radiative Transfer 9, 537 (1969)], which treated with the diffuse reflection and transmission of radiation by a finite isotropically scattering atmosphere bounded by a specular reflector at the bottom.
Clebsch-Gordan coefficients for nonunitary groups
Authors: Aviran A. , Litvin D. B.
Published: February 2004

It is shown that calculating Clebsch-Gordan coefficients of a nonunitary group can be reduced to formulas containing only representations of the unitary subgroup and additional conditions due to the antiunitary symmetry. This is another example demonstrating that, in applications involving corepresentations of nonunitary groups, the analysis can be made mainly in terms of representations of its unitary part.
Thin-sandwich conjecture and a fifth initial value equation for the gravitational field
Authors: Pereira C. Martin
Published: February 2004

The thin-sandwich conjecture for Einstein's field equations of general relativity is discussed. Three of the four initial-value equations of general relativity are considered. This system of three equations is shown to have an integrability condition when the spatial metric, its time rate of change, and the lapse function N are given. The nature of this integrability condition is discussed in detail. It is also noted that this integrability condition can be expected to play a significant role in any proof of existence for a thin-sandwich problem in which the spatial metric and its time derivative are chosen arbitrarily. A local proof of existence is given for the first three thin-sandwich equations. The proof allows the spatial metric components, their time rate of change, and the lapse function N to be chosen arbitrarily. No coordinate conditions of any kind are used in the proof.
Depolarization of electromagnetic waves excited by distributions of electric and magnetic sources in inhomogeneous multilayered structures of arbitrarily varying thickness. Full wave solutions
Authors: Bahar E.
Published: February 2004

Full wave solutions to the problem of depolarization of electromagnetic waves excited by general three-dimensional distributions of electric and magnetic sources in inhomogeneous multilayered structures of arbitrarily varying thickness are derived. Generalized field transforms that provide an appropriate basis for the expansion of transverse electromagnetic fields are employed to convert Maxwell's equations into a set of coupled first order ordinary differential equations for the forward and backward, vertically and horizontally polarized wave amplitudes. The continuous parts of the complete wave spectrum correspond to the radiation and lateral wave terms while the discrete part of the wave spectrum corresponds to the surface wave or trapped waveguide modes. Exact boundary conditions are imposed at all the interfaces of the structure and the solution is not restricted by the surface impedance concept. When the bounding media of the structure are characterized by perfect electric or magnetic walls, the fields are expressed exclusively in terms of waveguide modes. On the other hand, if the electromagnetic parameters are functions of one coordinate variable, the solutions are expressed exclusively in terms of an infinite integral—the radiation term. The solutions are shown to satisfy the reciprocity relationships.
An analytic approximation method for the one-dimensional Schrödinger equation.II
Authors: Hecht W.
Published: February 2004

The problem with three classical turning points which must be solved in order to discuss ``orbiting'' collisions in molecular physics or ``quasimolecular states'' occurring in α-nucleus and heavy ion scattering is treated, using the approximation method already discussed in Paper I. The general statement of Paper I concerning complex conjugate turning points is thereby confirmed and the corresponding formulas known from Langer's method can be obtained as special cases.
Motion and expansion of wavepackets in periodic potentials
Authors: Weissman Y. , Sussmann J. A.
Published: February 2004

The motion and expansion of single band wavepackets in a three-dimensioanl periodic potential are studied. Explicit expressions are derived for the expectation values  and  of an arbitrary combination of time-dependent Bloch functions belonging to a given nondegenerate band. Special attention is paid to spatial expansion of a Wannier function. It is shown that in this particular case  =  + t2, where  is the average value of [▿kω(k)]2. This apparent generalization of the well known analogy between ▿kω(k) and velocity does not hold in the more general case, where we get an additional term which is linear in time. The expressions derived for  are an important element in the calculation of the diffusion coefficient when the intermediate state of the jumping process is a wavepacket.
Lie algebras connected with infinite momentum kinematics
Authors: Blasi A. , Collina R.
Published: February 2004

In this paper we investigate the Lie algebras obtained from the infinite momentum limit of the Poincaré group. It will be shown that this limit depends upon a real, nonnegative number γ, and so do the structure constants of the resulting Lie algebra, which has three singular points γ = 1,0,∞. The last two singularities give algebras isomorphic to two different contractions of the algebra of the Poincaré group, while the case γ = 1 gives an algebra which cannot be obtained in this fashion. Suggestions are provided towards a physical interpretation of these results.
Continuum ambiguity in the construction of unitary analytic amplitudes from fixed-energy-scattering data
Authors: Bart G. R. , Johnson P. W. , Warnock R. L.
Published: February 2004

The problem of determining the scattering amplitude for a given fixed-energy elastic differential cross section is discussed in the spinless case. We show that when the energy is above the inelastic threshold, one may construct an infinte family of unitary scattering amplitudes, by appropriate variation of the elasticity parameters. These amplitudes are analytic in the cosine of the scattering angle throughout the Lehmann ellipse, and all correspond to the same cross section. Hence, even if the cross section is known exactly, there are infinitely many sets of phase shifts. Similar results have been obtained in earlier work, under conditions (on the cross section and elasticities) which seem to be physically unrealistic. In the present paper, the outstanding unrealistic assumptions are avoided. In particular, a finite number of zeros of the dispersive part are now allowed. Each zero reduces the continuum ambiguity by one elasticity parameter, but leaves infinitely many parameters to be varied independently.
Application of Kraichnan's direct interaction approximation to kinematic dynamo theory. II. Incompressible, helical velocity turbulence and a pair of coupled, singular, nonlinear integral equations
Authors: Lerche I.
Published: February 2004

Using Kraichnan's direct interaction approximation, we set up the equations governing the normal modes of the ensemble average magnetic field under incompressible, nonmirror symmetric velocity turbulence. We show that (i) the Green's stress tensor enjoys equipartition of its symmetric and antisymmetric parts at the normal mode frequencies of the ensemble average field, (ii) for static velocity turbulence, including helicity, there are no growing modes, (iii) the commonly used first order smoothing theory approximation is invalid when compared to the Kraichnan equations, for the Kraichnan equations do not satisfy Hammerstein's theorem while first order smoothing theory requires the satisfaction of Hammerstein's theorem, (iv) if there is to be any growth of the ensemble average magnetic field it must come from time dependent velocity turbulence, and when the velocity turbulence is time dependent we have so far been unable to solve the Kraichnan equations. We have done these calculations for two reasons. First to illustrate, by exact solution, the manner in which the normal modes of the ensemble average magnetic field depend on the helicity and Reynolds number of the turbulent velocity field. Second to show that approximate treatments of the hydromagnetic equation (like first order smoothing theory), rather than exact solution, are liable to give rise to substantial error in view of the fact that the Kraichnan equations do not satisfy Hammerstein's theorem.
Uniformly valid asymptotic solution to a Volterra equation on an infinite interval
Authors: Hanson F. B. , Klimas A. , Ramanathan G. V. , Sandri G.
Published: February 2004

A Volterra equation on the infinite interval with a logarithmic kernel multiplied by a small parameter is analyzed. A Laplace transform solution is found; also, an approximate solution is given and proved to be uniformly asymptotic as the small parameter tends to zero for all time. The solution has an algebraic-logarithmic decay for large times. The Volterra equation is a model for the transport of charged particles in a random magnetic field.
Quark structure and octonions
Authors: Günaydin Murat , Gürsey Feza
Published: February 2004

The octonion (Cayley) algebra is studied in a split basis by means of a formalism that brings outs its quark structure. The groups SO(8), SO(7), and G2 are represented by octonions as well as by 8 × 8 matrices and the principle of triality is studied in this formalism. Reduction is made through the physically important subgroups SU(3) and SU(2) ⊗ SU(2) of G2, the automorphism group of octonions.
Projective manifolds and projective theory of relativity
Authors: Evans G. T. , Sen D. K.
Published: February 2004

We present a global formulation of projective theories of relativity in the framework of projective manifolds, that is, manifolds based on the pseudogroup of homogeneous transformations in R5. Apart from formulating every previously considered geometric object and physical relation in an invariant manner, some new results, such as the theorem on the semidirect product structure of the invariance group of Einstein-Maxwell equations, and theorems on topological restrictions on the underlying five-dimensional projective manifold, etc. have been obtained. The relationship between space-time and the auxiliary 5-manifold is clarified and investigated in detail. A more general geometric definition of the electromagnetic field tensor and a geometric interpretation of the charge/mass ratio is given.
Gauge invariant canonical mechanics for charged particles
Authors: Torrence R. J. , Tulczyjew W. M.
Published: February 2004

The mechanics of charged particle motion is presented in a five-dimensional form compatible with the five-dimensional Kaluza theory of the electromagnetic field. Gauge dependence is given an intrinsic geometrical interpretation and the role of generalized momenta is clarified. The theory is a new example of a mechanical system with constraints and offers an interesting exercise in canonical quantization with a nonstandard Poisson bracket.
Duffin-Kemmer-Petiau subalgebras: Representations and applications
Authors: Fischbach Ephraim , Nieto Michael Martin , Scott C. K.
Published: February 2004

A reduction of the Duffin-Kemmer-Petiau algebra to a direct sum of irreducible subalgebras for spin-0 and spin-1 bosons is presented. The subalgebras are defined by multiplication rules for the linearly independent basis elements. In the representations discussed the spin projection operators are independent basis elements of the subalgebras. The formal utility of these representations is demonstrated by obtaining the reduction of arbitrary operator products and trace theorems. The practical utility is demonstrated by application to the analysis of free and interacting boson field currents. Most importantly, one can understand the differences between DKP nonconserved currents and those obtained from second-order wave equations.
Kinetic equations for the quantized motion of a particle in a randomly perturbed potential field
Authors: Besieris Ioannis M. , Tappert Frederick D.
Published: February 2004

Within the framework of the first-order smoothing approximation and the long-time, Markovian approximation, kinetic equations are derived for the stochastic Wigner equation (the exact equation of evolution of the phase-space Wigner distribution function) and the stochastic Liouville equation (correspondence limit approximation) associated with the quantized motion of a particle described by a stochastic Schrödinger equation. In the limit of weak fluctuations and long times, the transport equation for the average probability density of the particle in momentum space which was reported recently by Papanicolaou is recovered. Also, on the basis of the Novikov functional formalism, it is established that several of the approximate kinetic equations derived in this paper are identical to the exact statistical equations in the special case that the potential field is a δ-correlated (in time), homogeneous, wide-sense stationary, Gaussian process.
Two-magnon bound states in Heisenberg ferromagnets
Authors: Sáenz A. W. , Zachary W. W.
Published: February 2004

A generalized theory of bound two-magnon states in three-dimensional isotropic Heisenberg ferromagnets is given and the passage to the limit in which the total number of spins tends to infinity is handled rigorously. Powerful methods, mostly of the trace-inequality type, are developed for determining upper and lower bounds to the number of such bound states in the latter limit. These methods constitute the central contribution of this paper. In the latter we apply them to investigate the existence of bound two-magnon states in body-centered Heisenberg ferromagnets whose nonvanishing exchange interactions are those of the nearest-neighbor type. In work reported elsewhere, we have employed these methods to study spin-wave impurity states in Heisenberg ferromagnets. They should be useful for determining bounds on the number of localized states in solids in many cases when interactions extending over several orders of neighbors are operative.
Deformations of inhomogeneous classical Lie algebras to the algebras of the linear groups
Authors: Boyer Charles P. , Wolf Kurt Bernardo
Published: February 2004

We study a new class of deformations of algebra representations, namely, i2so(n)⇒sl(n,R), i2u(n)⇒sl(n,C)⊕u(1) and i2sp(n)⊕sp(1)⇒sl(n,Q)⊕sp(1). The new generators are built as commutators between the Casimir invariant of the maximal compact subalgebra and a second-rank mixed tensor. These algebra deformations are related to multiplier representations and manifold mappings of the corresponding Lie groups. Behavior of the representations under Inönü-Wigner contractions is exhibited. Through the use of these methods we can construct a principal degenerate series of representations of the linear groups and their algebras.
Asymptotic behavior of atomic bound state wave functions
Authors: Ahlrichs Reinhart
Published: February 2004

In the present paper we investigate the asymptotic properties of an exact bound state wave function φ of an n-electron atomic system within the infinite nuclear mass approximation and neglecting relativistic effects. An explicit upper bound is derived for ‖riμφ‖, where ri denotes the distance of the ith electron from the nucleus and μ = 1,2,3,⋯. We are then able to derive upper bounds for expressions like ‖h(ri)φ‖, where h (x) is an exponentially increasing function. We finally indicate an exponentially decreasing pointwise bound for φ.
Energy eigenvalues of a bounded centrally located harmonic oscillator
Authors: Vawter Richard
Published: February 2004

In the study of the effects of finite boundaries on the magnetic properties of a solid, one encounters the problem of finding the energy eigenvalues of a one-dimensional harmonic oscillator located in a potential enclosure. Series expansion techniques are applied to solve this problem for a harmonic oscillator located at the center of an infinitely high potential well. An analytical expression for the energy eigenvalues is found as a function of the size potential enclosure L, the quantum state n, oscillator frequency ω, and the mass of the particle m. The first order approximation of this expression is given by E = Eosccoth(Eosc/Ebox) where Eosc = ℏ ω(n + 1/2) is the energy eigenvalues of an unbound harmonic oscillator and Ebox = (2m/ℏ2) (n + 1)2π2/L2 is the energy eigenvalues of a free particle in an infinitely high well. For the ground state this approximation is better than 1% for all values of L, ω, and m.
Integral equations for scattering in potentials of infinite range
Authors: Freeman D. F. , Nuttall J.
Published: February 2004

We show how, by finding an approximation to the exact Green's function, to obtain integral equations with compact kernels for two scattering problems involving potentials of infinite range. They are one particle scattering in a Coulomb potential for a given partial wave and one particle scattering in three dimensions in a potential having r−2 behavior at infinity. In the second case, we solve only an inhomogeneous version of Schrödinger's equation.
Symmetry mappings of constrained dynamical systems and an associated related integral theorem
Authors: Levine Jack , Katzin Gerald H.
Published: February 2004

By use of Lie derivatives symmetry mappings of constrained conservative dynamical systems are formulated in terms of continuous groups of infinitesimal transformations within the configuration space. Such symmetries are called ``natural trajectory collineations'' in that the total energy has the same fixed value along each trajectory of the natural family, this value being preserved by the symmetry. It is found that these natural trajectory collineations must be conformal motions subject to an additional restriction dependent upon the potential. The corresponding groups of natural trajectory collineations are obtained for a flat configuration space with potential energy functions with rotational invariance about a point. A specialization of the theory to an indefinite Riemannian space-time shows that homothetic transformations are necessary and sufficient to map a natural family of time (space)-like geodesics into itself. A related integral theorem for constrained dynamical systems admitting linear or quadratic constants of the motion is obtained and illustrated. This theorem shows that in general a new constant of the motion will be obtained by deformation of an existing constant of the motion under a natural trajectory collineation.
Scintillations of randomized electromagnetic fields. II
Authors: Taylor Leonard S. , Lekhyananda Danai
Published: February 2004

We study the propagation of an electromagnetic wave which has suffered changes of phase and amplitude in its passage through a randomizing medium such as a turbulent dielectric. General formulas are derived for the n th-order autocorrelation and spectrum of intensity fluctuations in terms of the 2n th-order mutual coherence function on the initial plane. Simple expressions are obtained when the wave is initially weakly phase distributed. The probability distribution of intensity fluctuations is shown to be Gaussian in the limit of vanishing phase perturbation.
Wigner and Racah coefficients for SU3
Authors: Draayer J. P. , Akiyama Yoshimi
Published: February 2004

A general yet simple and hence practical algorithm for calculating SU3⊃SU2×U1 Wigner coefficients is formulated. The resolution of the outer multiplicity follows the prescription given by Biedenharn and Louck. It is shown that SU3 Racah coefficients can be obtained as a solution to a set of simultaneous equations with unknown coefficients given as a by-product of the initial steps in the SU3⊃SU2×U1 Wigner coefficient construction algorithm. A general expression for evaluating SU3⊃R3 Wigner coefficients as a sum over a simple subset of the corresponding SU3⊃SU2×U1 Wigner coefficients is also presented. State conjugation properties are discussed and symmetry relations for both the SU3⊃SU2×U1 and SU3⊃R3 Wigner coefficients are given. Machine codes based on the results are available.
Infinite spin dimensionality limit for nontranslationally invariant interactions
Authors: Knops Hubert J. F.
Published: February 2004

A proof is presented that a nontranslationally invariant system of classical n -dimensional spins approaches in the limit n → ∞ a suitable generalized spherical model.
Probability density function and moments of the field in a slab of one-dimensional random medium
Authors: Lang R. H.
Published: February 2004

The problem of a plane wave normally incident on a slab of one-dimensional random medium is studied. The refractive index variations of the random medium are taken to be a stationary Gaussian-Markov process. By employing an invariant imbedding technique and by using the Markov property of the refractive index variations, two cascaded diffusion equations are obtained for the probability density function of the reflection coefficient and the field in the slab. These equations are then solved approximately for small refractive index fluctuations and an expression is obtained for mean intensity in the slab interior.
Proof of the strong subadditivity of quantum-mechanical entropy
Authors: Lieb Elliott H. , Ruskai Mary Beth
Published: February 2004

We prove several theorems about quantum-mechanical entropy, in particular, that it is strongly subadditive.
Statistical theory of effective electrical, thermal, and magnetic properties of random heterogeneous materials. II. Bounds for the effective permittivity of statistically anisotropic materials
Authors: Hori Motoo
Published: February 2004

Upper and lower bounds are derived for the effective permittivity of random heterogeneous materials that are statistically homogeneous but not necessarily statistically isotropic. As trial functions in standard variational principles, we use modified perturbation expansions for the electric field and the electric displacement. The bounds are expressed in terms of the many-point correlation functions of the spatial variation of permittivity. For a wide class of random multiphase materials called cell materials, explicit calculation is performed taking account of the three-point correlation effects.
Invariant trilinear couplings involving both SU(2) and SU(1, 1) states
Authors: Patera J. , Winternitz P.
Published: February 2004

Multiplets |J M > transforming under irreducible representations of the algebra of S U(2) are constructed as infinite sums of products of two S U(1, 1) states |−pl> and |M+pj>. The ``generalized coupling coefficients'' figuring in the construction are shown to exist if the S U(2) label J and the S U(1, 1) labels j and l satisfy j = l + J - k, 0 ≤ k ≤ 2J. They are constructed explicitly and turn out to be analytic continuations of both S U(2) and S U(1, 1) Clebsch-Gordan coefficients. The constructed states |J M > are not normalizable in the usual sense. The ``generalized coupling coefficients'' can be applied, e.g., to study vertices, involving ordinary particles (with mass satisfying m2 > 0 and S U(2) spin) and tachyons (m2 < 0, S U(1, 1) spin).
On the transport properties of a van der Waals fluid. I. Formal theory
Authors: Piasecki J. , Resibois P.
Published: February 2004

We present a formal exact analysis of the autocorrelation formulas for transport coefficients in a van der Waals fluid. We show that the first correction due to the long range force is of order γ (γ = inverse range of the force) and the formal expression for this correction is displayed in terms of the Prigogine-Balescu graphs. The analysis crucially rests upon a generalization of hydrodynamical modes in a van der Waals fluid, valid for wave numbers smaller or of the order of γ.
Detection and ``emission'' processes of quantum particles in a ``chaotic state''
Authors: Benard Christine , Macchi Odile
Published: February 2004

We study the statistical properties of a chaotic beam of quantum particles (bosons or fermions) by using wavepacket formalism, which allows us to deal with bosons and fermions in a very symmetrical way. Our study is based on the definition and analysis of two different stochastic point processes consisting, respectively, of the ``emission'' time instants and detection time instants (or positions in a space) of the particles of the beam. The two processes are shown to be identical in the chaotic boson case and in the chaotic fermion case, respectively. The symmetry between the well-known results concerning the photon detection process and the new results concerning the fermion detection process is pointed out. And finally it is noted that in the chaotic case the bunching (or antibunching) effect is present already in the ``emission'' of the particles.
A spinor approach to the generalized singular electromagnetic field theory of Bel, Lapiedra, and Montserrat
Authors: Zund Joseph , Maher William
Published: February 2004

A spinor approach to the generalized singular electromagnetic field of Bel, Lapiedra, and Montserrat is presented. We include new proofs of the basis existence theorems of the field theory using the method of spin coefficients, and interpretations of these theorems in terms of the optical scalars associated with a null geodesic congruence. We also exhibit general classes of solutions of the generalized singular electromagnetic field equations and classify them according to the optical properties of their associated null geodesic congruences.
A note on vector-meson dominance and the compactness of current algebra
Authors: de Azcárraga J. A.
Published: February 2004

It is shown that for any semisimple inner symmetry group (compact or not) the Lee-Weinberg-Zumino procedure applied to a Yang-Mills type Lagrangian leads to field algebra. The exclusion of the noncompact case is analyzed.
On matrix superpropagators. I
Authors: Ashmore J. , Delbourgo R.
Published: February 2004

Given the free propagator of a matrix-valued field φαβ in the form <φαβ(x), φγδ (0)> = (1/2) (δαγδβδ +δαδδβγ − 2cδαβδγδ) Δ (x), we derive an integral representation for the matrix superpropagator <φαβN(x),φγδN(0)> for arbitrary N, and apply this to find the exponentially parametrized gravity superpropagator <|−g(x)|ωgαβ (x), |−g(0)|ωgγδ (0)> with gμν(x) ≡ [exp κφ(x)]μν. Other applications are also mentioned.
Exact bound states of some N-body systems with two- and three-body forces
Authors: Calogero F. , Marchioro C.
Published: February 2004

The exact wavefunctions and the corresponding binding energies are exhibited, for some N-body systems with long-range two-body and three-body forces. These results may also be used to obtain upper and lower bounds for the binding energies of certain many-body systems with two-body forces only.
The class sum operator approach for the point group O and D4
Authors: Killingbeck J.
Published: February 2004

The class sum operator approach to the representation theory of the point groups O and D4 is described and illustrated by means of several examples. Modified character tables are given for both groups, together with the class multiplication table for O. The construction of tensor operators within the group algebra of each group is discussed, using a modified version of traditional character analysis, and it is found that no E type tensor operator appears in the D4 group algebra.
Mathieu function solutions to the radial Schrödinger equation for the −f2/r4 interaction
Authors: Holzwarth N. A. W.
Published: February 2004

We describe the Mathieu function solutions to the radial Schrödinger equation for the −f2/r4 potential with reference to adiabatic elastic scattering of electrons from neutral atoms. By an appropriate choice of boundary conditions, the total scattering phase shift δl decomposes into two parts: δl = γl + ρl. The ``polarizability phase shift'' ρl depends solely on parameters of the interaction and is easily calculated. The ``polarizability extracted phase shift'' γl contains information of the core interaction. We suggest that such a parametrization of this scattering problem is convenient for data analysis or for potential scattering calculations. We find that the Mathieu function solutions are characterized by a ``polarizability range'' rt=√f/k For r > rt, the functions resemble spherical waves with phase shift ρl with respect to the free particle wavefunctions; while for r < rt they deviate strongly from spherical wave forms. The relationship of rt with respect to the atomic radius grossly determines the behavior of the scattering phase shifts.
Space-times with a future projective infinity
Authors: Eardley D. , Sachs R. K.
Published: February 2004

We use a projective structure to make precise the concept of ``future timelike infinity'' for certain space-times. We apply our definitions to many exact and approximate solutions of the Einstein equations. Some physical restrictions are necessary.
Closed-form Glauber cross sections in p-H and e−-H collisions. I
Authors: Thomas Brian K. , Gerjuoy E.
Published: February 2004

The Glauber predicted integrated (over scattering angle) cross section for the elastic scattering of charged particles by ground state atomic hydrogen is evaluated in closed form. The asymptotic form of the Glauber cross section for large incident particle momenta is obtained and compared with the exact first Born approximation result. The present analytic results, together with previous numerical results, indicate that (neglecting exchange) the Glauber integrated elastic scattering cross section is well represented, for both incident electrons and incident protons, by σelastic = (7/3)νi−2πa02 at essentially all incident particle speeds νi.
Measure theoretic convergences of observables and operators
Authors: Gudder Stanley P. , Mullikin Harry C.
Published: February 2004

Definitions of different types of measure theoretic convergence for observables and operators are given. In particular we define convergence in measure, almost everywhere, everywhere, almost uniformly, and uniformly. These types of convergence are compared and characterized. Furthermore, our theory is compared to that of Segal-Stinespring. Convergence theorems such as a bounded convergence theorem, Fatou's lemma, and a special case of Egoroff's theorem are proved. We show that the general Egoroff's theorem does not hold.
Vector space models of abstract quantum logics
Authors: Deliyannis Platon C.
Published: February 2004

A representation theorem for a class of logics is established in which the elements of the logic are represented as subspaces of some real vector space. A partial converse is also proved, which allows the systematic construction of various kinds of logics.
Description of a system of interacting linear chains by means of the electron network model
Authors: Weger M. , Alexander S. , Della Riccia G.
Published: February 2004

The electron network model of Coulson and Della Riccia is applied to describe a simple lattice consisting of two families of linear chains, coupled together. It is shown that the model displays resonances, at which the wavefunction is preferentially situated at one or the other family of chains, and that at these resonances, there is a 1/√E divergence in the electronic density of states.
The Nagel-Moshinsky operators for U(p,1)⊃U(p)
Authors: Patera J.
Published: February 2004

It is shown that the operators of Nagel and Moshinsky which lower and raise the irreducible spaces of U(n-1) contained in an irreducible space of U(n) are also the operators which lower and raise the irreducible spaces of U(n-1) contained in an irreducible space of U(n-1, 1). The validity of this conclusion is demonstrated for all discrete, and continuous principal and supplementary series of representations of U(n-1, 1).
Algebraically special perturbations of the Schwarzschild metric
Authors: Couch W. E. , Newman E. T.
Published: February 2004

Algebraically special perturbations of the Schwarzschild metric are found and expressed in a simple form. They become singular on the event horizon.
The bounding properties of the multipoint Padé approximant to a series of Stieltjes on the real line
Authors: Barnsley Michael
Published: February 2004

The multipoint Padé approximants to a series of Stieltjes and the corresponding complementary approximants are defined. Their bounding properties are established, and those of the usual [n,n−1] and [n,n] Padé approximants are shown to be special cases. It is further shown how information in the form of the first few terms in the expansion of the series of Stieltjes in inverse powers of x may be incorporated into the multipoint Padé approximant and its complement, thereby tightening the bounds supplied by the approximants. The usual ``two-point'' Padé approximant occurs as a special case of following this procedure. Physically occurring series of Stieltjes can often be written in the form G(x)=Σk = 1K Vk/(Ek+x)+H(x), where G(x) is a series of Stieltjes with radius of convergence R > 0, H(x) is a series of Stieltjes with radius of convergence R′ > R, R⩽E1<E2<…<EK<R′, and 0 < Vk < ∞ (k = 1,2,…, k). In addition to the bounds supplied by the multipoint Padé approximants for X ∈ (−R, ∞), it is shown that the approximants also exhibit interesting bounding properties for X ∈ (−R′, −R). A theorem on these bounding properties is proved. It is further shown that the multipoint Padé approximants yield best possible upper bounds on the Ek and on V1, but, in general, do not yield straightforward bounds on V2, V3, …, VK. Finally, the effect of fixing the locations of the poles of the multipoint Padé approximant and its complement at the correct values x = −Ek (k = 1,2,…,K) is considered. The resulting approximants then impose a complementary pair of bounds on G(x) for −R′ < x < ∞, which in most cases will be the best possible. In particular, one can now usually obtain best possible upper and lower bounds on V1, V2,…, VK.
Solution of the Hamilton-Jacobi equation for certain dissipative classical mechanical systems
Authors: Denman Harry H. , Buch Lawrence H.
Published: February 2004

Recent developments have shown that the pure Lagrange-Hamiltonian formalisms can be extended to problems (chiefly, classical systems involving dissipative forces) previously regarded as outside such theories. The Hamilton-Jacobi equations corresponding to certain such systems are given here, and the structure, separability, and solution of these equations are studied. Examples treated here include a particle moving freely and under a constant force in a viscous medium, the damped-harmonic oscillator in one and three dimensions, and a particle moving in one dimension with quadratic friction in an arbitrary potential. In all cases, the Hamilton-Jacobi equation separates into time and space components, and the complete solution is obtained.
The solution of the moment equations associated with a partial differential equation with polynomial coefficients
Authors: Miller Marvin , Steinberg Stanly
Published: February 2004

In this paper it is shown that the moment equations associated with a partial differential equation with polynomial coefficients possess formal power series solutions which are easily computed. An application is made to an equation which arises in the quantum theory of the laser. A simple example is given which illustrates the fact that although the original differential equation may not be solvable by power series methods, the related moment equations are always solvable.
The renormalized projection operator technique for linear stochastic differential equations
Authors: LoDato Vincent A.
Published: February 2004

A method for deriving an approximation to the equation [L0(r,t)+L1(r,t,ω)]Ψ(r,t,ω)=g(r,t) is discussed. Two criteria for the truncation of the series are shown. The nearest neighbor equation is derived via a diagram method and the Kraichnan equation is derived.
On the convergence of separable expansions for the † matrix
Authors: Osborn T. A.
Published: February 2004

We obtain theorems on the convergence of separable approximations for t matrices which derive from local potentials. We prove that convergence is impossible in the operator norm and the Hilbert-Schmidt norm. This result is universal and independent of the particular method used to construct the separable approximation.
Completeness of the wave operators in the repulsive N-body problem
Authors: Lavine Richard
Published: February 2004

Completeness of the wave operators is proved for N equal mass quantum mechanical particles interacting by repulsive forces given by pair potentials Vij (|xi − xj|) = O (|xi−xj| −1−ε), ε>0, which also satisfy certain regularity conditions. In a previous paper an incorrect derivation of this result for the two-body problem was given, which we correct and adapt to the N-body situation.
Nth rank tensor representations of U(n) symmetry adapted to subgroups of the symmetric group S
N
Authors: Sullivan John J.
Published: February 2004

Representations of the symmetric group SN symmetry adapted to subgroup sequences ⊗SNj↗        [SE pointing arrow]    SN             ⊗SiNj[SE pointing arrow]        ↗⊗SiN are considered using double-coset decomposition. The matrix elements of the double-coset representatives are given and their group theoretical properties are discussed. The matrix elements are identified with the recoupling transformations of the unitary group by considering the tensor representations of the latter. The orthogonality and completeness relations of the symmetric group expressed in terms of double-coset representative matrix elements are used to establish general relations that must be satisfied by the coupling coefficients of the unitary group.
On stochastic scattering
Authors: Bassanini Piero
Published: February 2004

The Schrödinger equation for two-particle scattering with random potential is considered, including both the cases of a local and a nonlocal potential with convolution kernel. It is shown that the statistical fluctuations of the potential give rise to additional terms which increase the scattering cross section, and an evaluation of the additional terms in the Born approximation is given. A brief discussion about analyticity properties of the scattering amplitude under suitable assumptions is included.
On the phase velocity and group velocity of guided waves
Authors: Eaves R. E.
Published: February 2004

Relations between the phase velocity and group velocity of guided waves in homogeneous media and the restrictions under which they can be generalized to inhomogeneous media are discussed. Dirichlet, Neumann, and mixed boundary conditions are considered, including the case of frequency dependent media and boundary conditions.
Hamiltonian orderings and functional Integrals
Authors: Mayes I. W. , Dowker J. S.
Published: February 2004

The factor ordering problem is discussed using functional integrals and the nonuniqueness of the quantum Hamiltonian is more closely investigated. Systems whose Hamiltonians are quadratic in the momenta are considered in detail and the equivalence of the canonical and Lagrangian approaches is explicitly confirmed by an averaging procedure. It is important that the integrand be in an averaged form if formal manipulations such as partial integrations are to be performed. This is probably significant for perturbation calculations.
The representation theory of SU(4) and Sp(4)
Authors: Holman Wayne J.
Published: February 2004

Basis states of irreducible representations of SU(4) in its Sp(4) basis are explicitly constructed in the boson calculus by the method of lowering operators. Expressions are derived for the Wigner coefficients of internal coupling and for the most general matrix which transforms an irreducible representation of SU(4) from its Sp(4) basis to a U(3) basis.
General scaling method for electromagnetic fields with application to a matching problem
Authors: Mo Tse Chin , Papas C. H. , Baum Carl E.
Published: February 2004

A scaling method that reduces an electromagnetic problem described by a complicated geometry in a complicated medium to one described by a simple Cartesian geometry in a simple medium is explored and developed. This method creates and identifies an equivalent class of problems and their solutions from the Cartesian simple medium problem. We illustrate the usefulness of the method by applying it to the design of a reflectionless, distortionless, loaded matching section connecting a cylindrical and a conical coaxial waveguide, with the TEM fields being explicitly found everywhere.
Extension of a compact Lorentz manifold
Authors: Miller J. G. , Kruskal M. D.
Published: February 2004

For a certain geodesically incomplete, compact Lorentz manifold T, we construct an analytic non-Hausdorff extension in which no geodesic bifurcates. The extension is geodesically incomplete, but is a maximal analytic Lorentz manifold in the sense that any further analytic extension has bifurcating geodesics. We also obtain a maximal analytic Hausdorff extension of the universal covering space of T. The latter extension is geodesically complete.
A generalization of the equations governing the evolution of a particle distribution in a random force field
Authors: Newman C. E.
Published: February 2004

The problem of a system of charged particles moving in a random force field and its application to the study of turbulent plasmas are discussed. We point out the inapplicability of existing formalisms to many cases of astrophysical interest. A generalization of this formalism is developed from two different points of view—a Fokker-Planck approach and a quasilinear approach. Both approaches lead to the same equation for the evolution of the particle distribution; this equation has the form of a Fokker-Planck equation, but the terms describing the effects of the random field do not retain the interpretation which they have in usual Fokker-Planck development. It is shown that this equation reduces to a quasilinear diffusion equation when the random field is electromagnetic.
A computable expansion for multiparticle propagators
Authors: Galas D. J. , Jensen C. A. , Sahlin H. L.
Published: February 2004

A formulation of the propagator for a quantum system is constructed to simplify computation for multiparticle systems. The propagator is manifested in terms of any complete set on the Hilbert space of physical states of the system. In the short-time limit a particularly simple matrix expression is obtained using an energy eigenstate basis. This formulation is shown to contain all orders of perturbation theory in an approximate form. Identical particle exchange is handled in a straightforward manner in which only the number of terms, but not the complexity, of expressions is affected. The number of terms is held to manageable proportions by approximating multiple-particle exchange with repeated operations containing only two-particle exchange. Three-particle exchange is represented exactly by this approximation in the limit of infinitesimal time steps. An argument is presented that indicates that this is also true for an arbitrary particle number.