bluuebunny/crossref_metadata_2025 huggingface dataset:
Kinetic Description of an Inhomogeneous Plasma
Authors: Kuszell A.
Published: February 2004

The general description of a strongly inhomogeneous one-component plasma in the so-called ``ring'' approximation is derived. Using the general theory of inhomogeneous systems, the closed system of two equations in one-particle phase space is obtained. The additional equation for some function, which appears in the collisions term, has the form of a Vlasov equation linearized around the inhomogeneous one-particle distribution function. The meaning of the parameters which appear in this equation is discussed. This equation is solved in the hydrodynamic approximation. The collision operator in the Markoffian limit reduces to the well-known form. The velocity distribution function for the inhomogeneous state is discussed and some additional terms to the usual Balescu-Guernsey-Lenard equation, in the case of no square-integrable inhomogeneity factors, are obtained. The influence of initial correlation is discussed.
Solutions of the Zero-Rest-Mass Equations
Authors: Penrose Roger
Published: February 2004

By means of contour integrals involving arbitrary analytic functions, general solutions of the zero-rest-mass field equations in flat space-time can be generated for each spin. If the contour surrounds only a simple (respectively, low-order) pole of the function, the resulting field is null (respectively, algebraically special).
Many-Neighbored Ising Chain
Authors: Dobson J. F.
Published: February 2004

Using a method suggested by Montroll, we extend the well-known matrix formulation of the nearest-neighbor one-dimensional Ising problem to allow for interactions with an arbitrary finite range n, general spin l, and an applied magnetic field B. We exhibit the relevant matrix element explicitly and hence formally obtain the partition function via an eigenvalue problem of order (2l + 1)n. For the case B = 0, l = ½ we introduce a change of variable which simplifies the partition function while still allowing a matrix formulation. Using this approach we have computed specific-heat curves for infinite, ferromagnetic Ising chains with interactions of range n (n ≤ 7). We prove in an appendix that open and cyclic boundary conditions are equivalent for the system under consideration.
Comments on the Classical Theory of Magnetic Monopoles
Authors: Gamblin Rodger L.
Published: February 2004

The classical theory of electromagnetism including magnetic monopoles is formulated in terms of harmonic functions. The fact that there is no consistent action-integral formulation of the field that yields both particle and field equations for both electric and magnetic charges is discussed in detail. It is seen that a consistent formulation can be developed through an action integral, but, in such a development, a monopole does not have what has been considered to be an appropriate interaction with either an electric charge or another monopole.
Partially Alternate Derivation of a Result of Nelson
Authors: Federbush Paul
Published: February 2004

The result of Nelson that the total Hamiltonian is semibounded for a self-interacting Boson field in two dimensions in a periodic box is derived by an alternate method. It is more elementary in so far as functional integration is not used.
Dirac Formalism and Symmetry Problems in Quantum Mechanics. I. General Dirac Formalism
Authors: Antoine J.-P.
Published: February 2004

Dirac's bra and ket formalism is investigated and incorporated into a complete mathematical theory. First the axiomatic foundations of quantum mechanics and von Neumann's spectral theory of observables are reviewed and several inadequacies are pointed out. These defects then are remedied by extending the usual Hilbert space to a rigged Hilbert space as introduced by Gel'fand, i.e., a triplet Φ⊂H⊂Φ′ where H is a Hilbert space, Φ a dense subspace of H provided with a new (finer) topology, Φ′ the dual of Φ. It is shown that this mathematical structure, together with the Schwartz nuclear theorem, allows us to reproduce Dirac's formalism in a completely rigorous way, without losing its transparency; this makes the theory easier to handle. The temporal evolution of the system and the wave equation are considered. Finally the probabilistic interpretation and the physical aspects of the theory are discussed; Φ is identified with the set of all physically accessible states of the system, Φ′ with the set of all possible experiments (apparatus) to which it can be subjected; this provides a direct connection with Feynman's formulation of quantum mechanics.
Translational Invariance Properties of a Finite One-Dimensional Hard-Core Fluid Using the Grand Canonical Ensemble
Authors: Millard Kenneth
Published: February 2004

Translational invariance properties of the single-particle distribution function D1(x, L, z) of the grand canonical ensemble are investigated for a one-dimensional hard-core fluid. For a fluid of finite length L it is shown that D1(x, L, z) is nowhere constant. It is shown that, in the thermodynamic limit and for x far from either wall, D1(x, L, z) is a constant equal to the grand canonical density ρ.
Two-Variable Expansion of the Scattering Amplitude: An Application of Appell's Generalized Hypergeometric Functions
Authors: Charap John M. , Minton B. M.
Published: February 2004

Appell's polynomials in two variables orthogonal in a triangle are described and some of their properties and those of related generalized hypergeometric functions are given. An application to the expansion of the scattering amplitude is suggested, the equal-mass case being discussed in some detail. A simple crossing matrix is derived. Difficulties introduced by inequality of the particle masses are explained. A Neumann formula is presented which permits an analytic continuation in the parameters to be made of the expansion coefficients for parts of the amplitude: This is in analogy with the Froissart-Gribov continuation. A conjectured analog of the Sommerfeld-Watson transformation then suggests the existence of fixed cuts in the partial-wave scattering amplitude.
On Continuous Eigenvalues in Neutron Thermalization
Authors: Tokizawa Masamichi
Published: February 2004

The continuous eigenvalue spectra of the linearized Boltzmann operator describing the energy distribution of neutrons in an infinite Einstein crystal are studied. This operator consists of two terms: a multiplication operator and an integral operator with δ-function-type singular kernel. The eigenvalue problem is transformed into the solution of an inhomogeneous integral equation by applying Case's method on the one-velocity transport equation. The existence of the solution of the integral equation is examined by the Neumann-series expansion. It is found that for sufficiently low temperature the range of numerical values of the multiplication operator forms the continuous eigenvalue spectra of the Boltzmann operator and the corresponding eigenfunctions are of δ-function type.
Particle-Hole Matrix: Its Connection with the Symmetries and Collective Features of the Ground State
Authors: Garrod Claude , Rosina Mitja
Published: February 2004

A detailed study is made of the properties of the ``particle-hole matrix''Gabcd≡〈g| (a†b−ρab)†(c†d−ρcd) |g〉,where |g> is a many-fermion ground state and ρab is the 1-body density matrix. It is shown that the zero eigenvalues of the particle-hole matrix are intimately and simply related to the one-body symmetries of the ground state. It is also shown that the large eigenvalues of Gabcd are closely related to the collective features of the ground state.
Diffusion in Nonlinear Multiplicative Media
Authors: Canosa José
Published: February 2004

The time-dependent behavior of the nonlinear distributions defined by the diffusion equation with several nonlinear source terms is studied. The nonlinear diffusion equation is solved by an eigenfunction-expansion method, which is in principle independent of geometry or number of dimensions. The qualitative time behavior of the distributions and their steady states can be ascertained from a simple analysis of the fundamental mode approximation only. Explicit solutions are presented in one- and two-dimensional geometries.
Observables for Massive Relativistic Particles of Arbitrary Spin
Authors: de Azcárraga J. A. , Oliver L.
Published: February 2004

The expressions for the dynamical operators corresponding to a Bargmann-Wigner particle of mass κ and arbitrary spin s are given, making use of the Foldy-Wouthuysen and Chakrabarti transformations for the Bargmann-Wigner equations given by Pursey, and Azcárraga and Boya, respectively. The operators selecting the positive and negative energy states are also given in the two representations. The operators for arbitrary spin are studied and a condition for an operator be constant of motion is given. Finally, the Newton-Wigner position operator and those obtained in the Foldy-Wouthuysen and Chakrabarti generalized representations are compared.
Properties of Generalizations to Padé Approximants
Authors: Common A. K.
Published: February 2004

The Padé-approximant method has recently been generalized in such a way that convergence of the new approximants can be proved for a larger class of functions than the series of Stieltjes and conditions can be obtained for these approximants to form sequences of converging upper and lower bounds. In this paper properties of these approximants to a class of functions, which correspond to a series of Stieltjes with nonzero radius of convergence, are considered. It is shown that under certain conditions they form only sequences of lower bounds to the exact function, but one can then define new approximants, which give upper bounds. Conditions are also obtained under which an upper bound can be put on the error of an approximant, using only the information necessary to calculate this approximant.
One More Technique for the Dimer Problem
Authors: Percus Jerome K.
Published: February 2004

The problem of counting the dimer coverings of a square lattice is recast as a counting of coverings by oriented closed loops. Thus the answer is expressed as the value of a suitable permanent. This permanent is transformed to a determinant, which on evaluation recovers the familiar result.
Plane-Symmetric Gauge Field
Authors: Uzes C. A.
Published: February 2004

Plane-symmetric solutions to the gauge field equations are considered on the classical level. The conditions of plane symmetry are gauge-invariantly defined in terms of the internal holonomy group. It is shown that, if analytic gauge fields satisfy the plane-symmetry conditions and if there exists at least one source-free region in event space, then the internal holonomy group is Abelian and a gauge exists in which the gauge field satisfies Maxwell's equations.
Representation Theory of SO(4, 1) and E(3, 1): An Explicit Spinor Calculus
Authors: Holman Wayne J.
Published: February 2004

The explicit spinor basis states for the irreducible unitary representations of the spinor covering group of the de Sitter group SO(4, 1) are obtained by analytic continuation from those of the compact group Sp(4). Some features of the contraction of these basis states to those of the Poincaré group are discussed; the explicit asymptotic form of the basis state of a continuous representation of SO(4, 1) in the limit of the contraction to a basis state of a finite-mass discrete-spin representation of E(3, 1) is investigated.
N-Representability Theorem for Reduced Density Matrices
Authors: Kiang Hsiao S.
Published: February 2004

A reduced density matrix representing a statistical mixture is shown to provide no definite information concerning its N-representability. A theorem about simultaneous N-representability and non-N-representability of a reduced density matrix is formulated and proved.
Quantum Harmonic Oscillator with Time-Dependent Frequency
Authors: Solimeno S. , Di Porto P. , Crosignani B.
Published: February 2004

The temporal evolution of the state vector relative to a harmonic oscillator with time-dependent frequency is examined. The Schrödinger equation is solved by choosing the instantaneous eigenstates of the Hamiltonian as the basis, thus getting an infinite set of coupled linear differential equations. This formulation is particularly suitable for studying the cases in which the Hamiltonian undergoes a very slow or a sudden variation from an initial constant value into a final one. A rigorous proof of adiabatic invariance to all orders in the slowness parameter is given for the transition probabilities. An application to the evolution of an initially coherent state is made.
Relations between the Elements of the Phase Matrix for Scattering
Authors: Abhyankar K. D. , Fymat A. L.
Published: February 2004

The process of scattering of radiation is usually characterized by a 4 × 4 transformation matrix which relates the radiation field vector incident on the scatterer to the scattered field vector. The nine relations between the 16 elements of this phase matrix for scattering are derived explicitly for the three most commonly used representations of the intensity vector, viz., Wolf's coherency matrix formalism, Chandrasekhar's and Stokes's representations. The invariance of these relations under the action of any optical train containing one or more elements characterized by their Jones representation is demonstrated. These relations should be useful in the theory of polarization optics. The same relations are also shown to hold after rotation of the axes of reference for the electric vectors in the incident and scattered beams. Since such a transformation is required in the formulation of the theory of radiative transfer, the relations derived here may find use in multiple scattering problems as well.
Effective-Range Formula for Two-Body Scattering Coupled to a Closed Secondary Channel
Authors: Kermode Mark W.
Published: February 2004

The multichannel effective-range formulas are extended to the case of a closed secondary two-body channel in which there is a repulsive Coulomb potential.
Representation Functions for SU(3)
Authors: Mickelsson Jouko
Published: February 2004

``Euler'' decomposition for SU(3) has been found by analytic continuation from the ``Euler'' decomposition of SU(2, 1), which is based on the factorization SU(2, 1) = SU(2) × Au × A × SU(2) derived by Hillion [Au ∼ U(1) and A is one-parameter subgroup of the V-spin subgroup.] For the degenerate case the SU(3) representation functions can be found by transforming to a new basis where the V-spin subgroup is diagonal. The result is a sum of products, each product containing two D-functions, one d-function, and an exponential function exp [imχ]. As is well known, every representation D(p, q) can be reduced from the direct product D(p, 0) × D(q, q). The nondegenerate representation functions can then be directly written down using the SU(3) CG coefficients, which are relatively simple for the above-mentioned case.
Bounds for Effective Electrical, Thermal, and Magnetic Properties of Heterogeneous Materials
Authors: Miller Melvin N.
Published: February 2004

Determining the effective dielectric constant is typical of a broad class of problems that includes effective magnetic permeability, electrical and thermal conductivity, and diffusion. Bounds for these effective properties for statistically isotropic and homogeneous materials have been developed in terms of statistical information, i.e., one-point and three-point correlation functions, from variational principles. Aside from the one-point correlation function, i.e., the volume fraction, this statistical information is difficult or impossible to obtain for real materials. For a broad class of heterogeneous materials (which we shall call cell materials) the functions of the three-point correlation function that appear in the bounds of effective dielectric constant are simply a number for each phase. Furthermore, this number has a range of values 19 to ⅓ and a simple geometric significance. The number 19 implies a spherical shape, the number ⅓ a cell of platelike shape, and all other cell shapes, no matter how irregular, have a corresponding number between. Each value of this number determines a new set of bounds which are substantially narrower and always within the best bounds in terms of volume fraction alone (i.e., Hashin-Shtrikman bounds). For dilute suspensions the new bounds are so narrow in most cases as to be essentially an exact solution. There is a substantial improvement over previous bounds for a finite suspension and yet greater improvement for multiphase material where the geometric characteristics of each phase are known.
On Canonical SO(4, 1) Transformations of the Dirac Equation
Authors: Bracken A. J. , Cohen H. A.
Published: February 2004

Certain matrix transformations of the free-particle Dirac equation are described as momentum-dependent SO(4, 1) transformations. Such of these belonging to any one of five subgroups G(α) (α = 0, 1, 2, 3, 4) are canonical, preserving the Lorentz-invariant Dirac scalar product in a corresponding one of five modes of expression. The Dirac equation itself is linear in all five components pα[pμ (μ = 0, 1, 2, 3) is the four-momentum operator, and p4 = m] of the ``five-vector'' p̃, and a transformation in G(β) has the additional property that the component pβ appears linearly also in the transformed equation. The Mendlowitz and the Foldy-Wouthuysen-Tani transformation accordingly are in G(0), the SO(4) subgroup; and that proposed by Chakrabarti is in G(4), the SO(3, 1) subgroup associated with homogeneous Lorentz transformations. For any p̃′, obtained from p̃ by a momentum-dependent SO(4, 1) transformation, there is a corresponding transform of the Dirac equation. Where pα appears in the Dirac equation, pα′ appears in the transformed equation. The ambiguities which arise in the specification of the transformation leading to a given such equation are associated with the existence of a ``little group'' for any such p̃′.
Internal-Labeling Problem
Authors: Sharp R. T. , Lam C. S.
Published: February 2004

A method is proposed for labeling the bases of a compact group when reduced with respect to an arbitrary subgroup. The scheme is based on the observation that the heaviest state of a multiplet (subgroup irreducible representation) of an IR (group irreducible representation) can be labeled by a product of heaviest states of simpler ``elementary'' multiplets. Details are worked out for a number of group-subgroup combinations.
Short-Range Interactions and Analyticity in Momentum Transfer
Authors: Finley J. D.
Published: February 2004

We investigate possible characterizations of ``short-range'' interactions by means of conditions on the total transition probability ∥Tψ∥2. We desire to require that the total transition probability decrease exponentially as the displacement of the wavepacket ψ increases. It is shown that this can only be done for certain types of sequences of wavepackets, and a criterion is developed for selecting these ``proper'' wavepackets. We then show for all such interactions that what is essentially the square of the scattering amplitude is analytic, in the cosine of the scattering angle, in an ellipse which always includes the physical region. We then compare these results with the Schrödinger potential theory and thereby relate the type of the exponential decrease of a potential to the type of the exponential decrease of the corresponding transition probability. Finally, our results are compared with similar results previously obtained by others working on this problem.
V-Particle Decay in the Lee Model
Authors: Hammer C. L. , Weber T. A.
Published: February 2004

The formalism developed previously for scattering of wavepackets is applied to the N + θ sector of the Lee model. A single analysis suffices to discuss both the stable and unstable case. The rate at which N and θ particles are produced and the number of V particles produced are calculated as a function of time assuming that the incident wave is initially a semi-infinite, plane-wave train. An unstable V-particle state is constructed from the |N, θ〉 state by requiring agreement with the scattering analysis. Its dependence on the production process is explicitly shown. The state can be made independent of the production process by requiring normalization. The time dependence of each channel is also calculated for this case. It is shown that both the unstable and stable V-particle states can be generated from the mathematical V-particle state, the only difference being the location of the pole which describes the resonance state or the bound state.
Accidental Degeneracy in the Bethe-Salpeter Equation
Authors: Basu Debabrata , Biswas S. N.
Published: February 2004

The Bethe-Salpeter equation for the bound state of the pion-nucleon system has been studied in the ladder approximation; the propagation time of the exchanged nucleon is neglected. By using the two-component formalism, the spinor equation is first reduced to a pair of simultaneous integral equations in momentum space. Following Fock, we transform these equations into ones in a four-dimensional hyperspace and the solutions are obtained in terms of series of O(4) harmonics. As a simple illustration of our method, we have also considered the Bethe-Salpeter equation for the scalar-meson system. We find that the pion-nucleon Bethe-Salpeter equation shows an accidental degeneracy in the discrete-energy spectra similar to that in the solutions of the Dirac equation for the hydrogen atom, provided the coupling constant does not exceed a certain critical limit. The scalar problem exhibits at small binding energies a Schrödinger-type degeneracy. Convergence criteria for the pion-nucleon Bethe-Salpeter eigensolutions as series in O(4) harmonics have been discussed; it is found that no solution exists when the coupling constant exceeds a certain critical value. In our approximation scheme, there are no abnormal solutions as are encountered in the fully covariant treatment of the equation.
Internal Multiplicity Structure for the Chain SU(n)⊃SU(n−1)⊃…⊃SU(2)
Authors: Radhakrishnan D.
Published: February 2004

The partition function for SU(n) is given in terms of that for SU(n − 1) through a recursion formula which is derived using the method of generating series. The usefulness of the expression is demonstrated in the cases of specific values of the rank.
Wavefunctions on Homogeneous Spaces
Authors: Bacry Henri , Kihlberg Arne
Published: February 2004

The properties of a class of homogeneous spaces of the Poincaré group are discussed. An 8-dimensional space appears especially promising and the explicit unitary irreducible representations corresponding to physical particles are given using scalar wavefunctions on this space.
Quasiparticle Formalism and Atomic Shell Theory
Authors: Cunningham M. J. , Wybourne B. G.
Published: February 2004

The quasiparticle formalism developed by Armstrong and Judd for atomic shells is extended to expose the complete group structure of the quasiparticle eigenfunctions of the equivalent electron l shell. A simple method for relating quasiparticle states to determinantal states and for calculating quasiparticle matrix elements is developed. The need for fractional parentage coefficients in calculating these matrix elements is entirely eliminated.
Functional Integration and the Generalized Matthews-Salam Equations
Authors: Zimmerman Robert L.
Published: February 2004

Various properties of Feynman functional integrals that appear in quantum field theory are studied. An indefinite functional integral is constructed. For the indefinite functional integral we prove a relation which is analogous in ordinary Riemann integrals to integration by parts. A special case of this relation gives an integration-by-parts formula for the Feynman functional integrals. In addition, various relations for integrating over variationals and variational derivatives are obtained. Application of these relations gives, among other things, a set of generalized Matthews-Salam equations.
Application of Perturbation Theory to Many-Body Systems with Localized Particles
Authors: Rousseau C. C. , Saylor D. P.
Published: February 2004

We investigate the possibility of using perturbation theory to compute the binding energy for infinite systems in which the particles are localized. For the case of the linear chain of coupled harmonic oscillators, we prove that the perturbation series for the ground-state energy per particle is convergent. Exact expressions for the generalized Padé approximants are derived. The generalized approximants provide a manifestly convergent sequence of approximations to the energy.
Ground State of a One-Dimensional N-Body System
Authors: Calogero F.
Published: February 2004

The problem of N quantum-mechanical equal particles interacting pairwise by inverse-cube forces (``centrifugal potential'') in addition to linear forces (``harmonical potential'') is considered in a onedimensional space. An explicit expression for the ground-state energy and for the corresponding wavefunction is exhibited. A class of excited states is similarly displayed.
Self-Consistent Approximations in Many-Body Systems. II
Authors: Shlidor O. , Revzen M.
Published: February 2004

A stationary property of the grand-canonical potential is introduced. This stationary property is used to define a class of self-consistent approximations. The class of self-consistent approximations is shown to be particularly suitable for the random-phase approximation (RPA). The conditions for self-consistency are only sufficient.
Canonical States in Quantum-Statistical Mechanics
Authors: Kvarda Robert E.
Published: February 2004

The quantum-mechanical analog of the classical Gibbs canonical density is characterized by considering a large collection Q of noninteracting quantum systems, each in an equilibrium statistical state. The set Q, the Hamiltonian operator for each system, and the statistical states are assumed to have certain properties which are given as axioms. It is shown that these assumptions imply that each member of Q is in a canonical state at a temperature which is the same for all systems. The possibility of zero absolute temperature is included.
Kinematic Interaction for the Heisenberg Antiferromagnet at Low Temperature
Authors: Herbert D. C.
Published: February 2004

The general theory of antiferromagnetic spin waves is examined from a new viewpoint and the nature of the antiferromagnetic ground state is clarified. It is shown that the Anderson canonical transformation to free spin waves is nonunitary with the magnon state vectors having large nonphysical projections, and a projection technique which restores unitarity at low temperatures is developed. The nonphysical projection of the state vectors is shown to give a large kinematic interaction even at zero temperature.
Statistical Average of Product of Phase Sums Arising in the Study of Disordered Lattices. I
Authors: Sah Priyamvada
Published: February 2004

A recurrence formula is established to evaluate the statistical average 〈S(k1)S(k2) … S(kn)〉 in the limit of N → ∞, where S(k)=∑j=1Neikxj, x1,x2,…,xN, denotes the position of atoms in a disordered lattice, under the condition that interatomic distances are statistically independent and have the same probability distribution s(r).
Analytic Properties of a Class of Nonlocal Interactions. II
Authors: Gutkowski D. , Scalia A.
Published: February 2004

A definition is given for the function Sl(k) in the complex l plane for a class of nonlocal interactions, called F, which has been considered in a previous paper [J. Math. Phys. 9, 588 (1968)]. The definition is obtained by means of a new class of nonlocal interactions, called G, for which the definition of Sl(k) in the l plane can be determined by a ``dynamical interpolation.'' The analytic properties of potentials of class G are studied. Then a suitable approximation is defined which allows us to approximate any potential of class F by means of potentials of class G. Comparing the analytic properties of potentials of class G which sufficiently approximate any given potential of class F, it is shown that their total scattering amplitudes can be made as near as we please to each other and that there exist Regge trajectories which can be made as near as we please to each other. With the given definition, Sl(k) turns out to be an analytic function in the complex l plane, but for a finite number of poles. Some general properties of the Regge trajectories are discussed and some examples are given.
Wave Propagation and Other Spectral Problems in Kinetic Theory
Authors: Sirovich Lawrence , Thurber James K.
Published: February 2004

A rigorous discussion of the spectrum of the linear Boltzmann equation and kinetic models is presented. Particular attention is given to plane-wave propagation for a general class of kinetic models. These models in general have a velocity-dependent collision frequency ν(ξ). The main results of this paper concern the relationship between the complex wavenumber and complex frequency for a plane wave. It is shown that the question of analyticity of this relation is reduced to considering ν in the neighborhood of infinity. Specifically, if lim lim ξ→∞v/ξ=0,the relationship is not analytic. Otherwise, analyticity is obtained. (Although not specifically considered here, analyticity is closely connected to the convergence of the Chapman—Enskog procedure.) In a general discussion it is shown how the question of analyticity is closely connected with (i) the continuous spectrum of the underlying operator, (ii) the behavior of solutions at large distances from boundaries, and (iii) the nature of the cutoff in an intermolecular interaction.
Inner and Restriction Multiplicity for Classical Groups
Authors: Delaney R. M. , Gruber B.
Published: February 2004

For the classical compact Lie groups G, a formula for the multiplicity of weights (called inner multiplicity) is given. This formula relates the inner multiplicity of a group G to the inner multiplicity of a naturally embedded subgroup G′. For the SU(n) groups the formula can be brought into a particularly simple form—namely, a sum over Kronecker symbols—by choosing the group SU(2) for G′. The multiplicity of irreducible representations of a subgroup G′ into which an irreducible representation of a group G decomposes if G is restricted to G′—called restriction multiplicity of G with respect to G′—is related to the inner multiplicity of the group G.
De Sitter Symmetric Field Theory. I. One-Particle Theory
Authors: Bakri Mahmoud M.
Published: February 2004

The formal structure and the free-particle solutions of the field equations (Sμνpν + mγμ)ψ = pμψ, derived recently by the author [Nuovo Cimento 51A, 864 (1967)] for realizations of the inhomogeneous de Sitter group are discussed. The enveloping algebra of the group is developed, and the covariance of the field equations under the five-dimensional rotations C, P, and T is proved. Bhabha's representation of the matrices γμ is completed. Observables, expectation, values and the scalar product are defined, and classical conservation laws are derived. The field equations are derived from a variational principle for the usual Lagrangian density ψ̄(−iγμ∂μ+m)ψ under a certain restriction. The free-particle solutions of the field equations are obtained in the canonical and the extreme relativistic representations. The connections between the wavefunctions in these representations, and also in the Foldy-Wouthuysen representation, are derived.
Inversion Problem with Separable Potentials
Authors: Mills Robert L. , Reading John F.
Published: February 2004

The problem of finding a potential, expressible as the sum of a finite number of separable terms, to fit a given phase shift at all energies is solved quite generally for nonrelativistic scattering within a single channel. The most general solution is found, and the necessary restrictions on the phase shift and the role of bound states are studied. The minimum number of separable terms needed to fit a given phase shift in a given channel is found to be determined, normally, by 1+max lim x2>x1{[δ(x2)/π]−[δ(x1)/π]},where x1 and x2 range through all positive energies, and [y] is the largest integer less than or equal to y. Our method differs from that of Kh. Chadan [Nuovo Cimento 10, 892 (1958); 47, 510 (1967)] who has solved what is, in essence, the same problem, in that it involves spherical Bessel transforms throughout, rather than the use at each stage of a representation determined by the solution of a previous stage.
Perturbation Theory of Nonlinear Boundary-Value Problems
Authors: Millman Martin H. , Keller Joseph B.
Published: February 2004

A systematic perturbation theory is presented for the analysis of nonlinear problems. The lowest-order result is just that obtained by linearizing the problem, and the higher-order terms are the solutions of inhomogeneous linear problems. The essential feature of the method is the procedure for avoiding secular terms, which is based on the Lindstedt-Poincaré technique employed in celestial mechanics. The method is applied to the following nonlinear boundary value problems: (1) temperature distribution due to a nonlinear heat source or sink; (2) self-sustained oscillations of a system with infinitely many degrees of freedom; (3) forced vibrations of a ``string'' with a nonlinear restoring force; (4) superconductivity in a body of arbitrary shape with external magnetic field; (5) superconductivity in an infinite film with parallel magnetic field; (6) comparison of solutions of the Hartree, Fock, and Schrödinger equations for the helium atom. The results in each case are different both qualitatively and quantitatively from those of the linear theory.
Experimental Confirmation of the Applicability of the Fokker-Planck Equation to a Nonlinear Oscillator
Authors: Morton J. B. , Corrsin S.
Published: February 2004

A traditional derivation of the Fokker-Planck equation is examined with emphasis on assumptions, especially sufficient inequalities between excitation and response characteristic times in a ``real'' system, i.e., a system with finite correlation time of the excitation. Comparison with experiment for an electronic ``cubic spring'' oscillator gives good agreement in both second and fourth moments of the response.
Generalization of Green's Theorem
Authors: Goldberg Joshua N. , Newman Ezra T.
Published: February 2004

For a system of field equations which is derivable from a Lagrangian whose density is (i) homogeneous quadratic in the first derivatives of the field variables yA,μ and (ii) homogeneous of degree n in the undifferentiated field variables yA, one has the identity (n+1)zALA(y)−yAMA(y,z)≡tρ,ρ,where MA(y, z) is the first-order change in the field equations LA(y) = 0 under the mapping yA → yA + zA. The specific example of general relativity is discussed.
Physical-Region Discontinuity Equations for Many-Particle Scattering Amplitudes. I
Authors: Coster Joseph , Stapp Henry P.
Published: February 2004

The discontinuity equations are derived for all singularities of multiparticle scattering functions that enter the portion of the physical region lying below the four-particle threshold. These equations, which are the precise statements of the Cutkosky formulas, are calculated directly from the unitarity equations. The only analyticity properties used are those obtained from the S-matrix macroscopic-causality condition. That is, the scattering functions are taken to be analytic in the physical region except on positive-α Landau surfaces, around which they continue in accordance with the well-defined plus-iε rule.
Functional Integration Theory for Incompressible Fluid Turbulence. II
Authors: Rosen Gerald , Okolowski J. A. , Eckstut Gene
Published: February 2004

Two iterative solutional procedures are reported for the nonlinear integro-differential dynamical equation obtained previously by the stationary functionality method and supplemented here by a subsidiary dynamical condition. Rapidly convergent for grid Reynolds numbers between about 100 and 300, both methods yield general expressions for the two-point equal-time velocity-correlation tensor in approximate agreement with experiment for the initial period of decay.
Negative Finding for the Three-Dimensional Dimer Problem
Authors: Hammersley J. M. , Feuerverger A. , Izenman A. , Makani K.
Published: February 2004

The dimer problem can be solved if one can evaluate the permanent of P = (pij), the incidence matrix of the lattice. All known methods of solving the two-dimensional case consist (explicitly or implicitly) in finding another matrix Q = (qij), such that pij = |qij| and per P = |det Q|, and then computing the determinant of Q. We show that in the three-dimensional case no such matrix Q exists for any choice of elements qij, whether real or complex numbers, or quaternions. A stronger negative result of an asymptotic character seems to be true, but this rests upon a plausible but unproved conjecture.
Approach to the Mode Conversion Problem in Nonuniform Acoustic Waveguides
Authors: Wait James R.
Published: February 2004

A method is described for treating wave propagation in a waveguide structure whose cross section varies in the direction of propagation. Special attention is given to the conversion of energy between waveguide modes of different order. For simplicity, the waveguide is bounded by impedance-type walls and the lateral height variation is assumed to have circular symmetry. This is considered to be an idealized model of an atmospheric waveguide for acoustic-wave propagation in the case when there is a localized depression.
Hermite's Reciprocity Law and the Angular-Momentum States of Equivalent Particle Configurations
Authors: Wybourne B. G.
Published: February 2004

Hermite's reciprocity law is applied to the calculation of the angular-momentum states of equivalent particle configurations. Connections between boson and fermion states are considered and a method is given for determining the number of times a given term appears in l3 without requiring a complete term analysis. A succinct expression for the number of S-states arising in the [22] representation of R2l+1 under R2l+1 → R3 is developed.
Complementary Bounds for Ground-State Energies
Authors: Robinson Peter D.
Published: February 2004

Complementary upper and lower bounds are derived for the ground-state energies of Hamiltonians H = h + V, where V is positive-definite, by considering the Schrödinger equation in an integral form. Some simple applications are presented.
Theoretical Study of Finite Dielectric-Coated Cylindrical Antenna
Authors: Ting Chung-Yu
Published: February 2004

A finite cylindrical antenna which is imbedded in a concentric dielectric rod has been investigated by employing a rigorous formulation. When the antenna is relatively short, a numerical method is used; when the antenna is long, the Wiener-Hopf technique is applied. In both cases the input admittance and the current distribution are obtained. It is found that the input conductances are larger than for the corresponding free-space antennas, the field patterns tend to be more broadside and, as the antenna gets longer and longer, the locus of the input admittance becomes a circle instead of converging to one point as it does for a bare cylindrical antenna. The first method is applicable regardless of the thickness of the antenna and the dielectric rod; the second method can be applied only to a sufficiently long antenna. The minimum length is determined by the thickness of the dielectric rod. This study is limited to thin antenna in rather thick dielectric cylinders. However, the dielectric rod is still not thick enough to support a transverse magnetic (T.M.) mode.
High-Energy Scattering Cross Section for Singular Potentials at Large Angles
Authors: Spector Richard M.
Published: February 2004

For scattering off singular repulsive potentials at high energy, the large-angle scattering is shown to be classical. For nonrelativistic singular potentials of the form V(r) = gr-n (g > 0, n > 2), we give the explicit form of the differential cross section for large angles at high energy as a power series in (π - θ). The coefficients of the linear through cubic terms in (π - θ) are obtained.
Mean Ergodic Theorems in Quantum Mechanics
Authors: Moyal J. E.
Published: February 2004

An application of the abstract mean ergodic theorems to quantum systems is described, which is rather closely analogous to the application of these same theorems in classical statistical mechanics.
Second-Order Dispersion-Energy Series for Axially Symmetric Molecules
Authors: van der Merwe Johannes H. , van der Merwe Alwyn J.
Published: February 2004

With the aid of a model representing each molecule as a set of semi-isotropic dipole oscillators, the London-van der Waals interaction energy of a pair of unexcited axially symmetric molecules is calculated, in the second order of perturbation theory, as an infinite series in negative powers of the intermolecular separation.
S-Matrix Singularity Structure in the Physical Region. II. Unitarity Integrals
Authors: Bloxham M. J. W. , Olive D. I. , Polkinghorne J. C.
Published: February 2004

The general techniques developed in an earlier paper [J. Math. Phys. 10, 494 (1969)] are applied to evaluate the singularities and discontinuities of unitarity integrals. The results are conveniently expressed in terms of what we call mechanism (or M) diagrams.
Group-Theoretic Approach to the New Conserved Quantities in General Relativity
Authors: Carmeli Moshe
Published: February 2004

The Newman-Penrose formalism for obtaining the recent conserved quantities in general relativity is discussed and a group-theoretic interpretation is given to it. This is done by relating each triad of the orthonormal vectors on the sphere to an orthogonal matrix g. As a result, the spin-weighted quantities η become functions on the group of three-dimensional rotation, η = η(g), where g ∈ O3. An explicit form for the matrix g is given and a prescription for rewriting η(g) as functions of the spherical coordinates is also given. We show that a quantity of spin weight s can be expanded as a series in the matrix elements Tsmj of the irreducible representation of O3, where s is fixed. Infinite- and finite-dimensional representations of the group SU2 are then realized in the spaces of η's and Tsmj. It is shown that the infinite-dimensional representation is not irreducible; its decomposition into irreducible parts leads to the expansion of η in the Tsmj, the latter providing invariant subspaces in which irreducible representations act.
Electron in a Given Time-Dependent Electromagnetic Field
Authors: Capri Anton Z.
Published: February 2004

The theory of a quantized Dirac field interacting with a classical electromagnetic field is considered. The resulting q-number problem is reduced to a closely related c-number problem. The theory is then shown to be without divergences. The interpolating field is shown to exist and is local. Also, the S matrix is shown to be unitary.
Method for the Evaluation of Certain Time-Dependent Thermal Averages
Authors: Howgate David W.
Published: February 2004

A simple method is presented for the evaluation of time-dependent thermal averages relating to the Debye-Waller form.
Curvature Collineations: A Fundamental Symmetry Property of the Space-Times of General Relativity Defined by the Vanishing Lie Derivative of the Riemann Curvature Tensor
Authors: Katzin Gerald H. , Levine Jack , Davis William R.
Published: February 2004

A Riemannian space Vn is said to admit a particular symmetry which we call a ``curvature collineation'' (CC) if there exists a vector ξi for which £ξRjkmi=0, where Rjkmi is the Riemann curvature tensor and £ξ denotes the Lie derivative. The investigation of this symmetry property of space-time is strongly motivated by the all-important role of the Riemannian curvature tensor in the theory of general relativity. For space-times with zero Ricci tensor, it follows that the more familiar symmetries such as projective and conformal collineations (including affine collineations, motions, conformal and homothetic motions) are subcases of CC. In a V4 with vanishing scalar curvature R, a covariant conservation law generator is obtained as a consequence of the existence of a CC. This generator is shown to be directly related to a generator obtained by means of a direct construction by Sachs for null electromagnetic radiation fields. For pure null-gravitational space-times (implying vanishing Ricci tensor) which admit CC, a similar covariant conservation law generator is shown to exist. In addition it is found that such space-times admit the more general generator (recently mentioned by Komar for the case of Killing vectors) of the form (−g Tijkmξiξjξk);m=0, involving the Bel-Robinson tensor Tijkm. Also it is found that the identity of Komar, [−g(ξi;j−ξj;i)];i;j=0, which serves as a covariant generator of field conservation laws in the theory of general relativity appears in a natural manner as an essentially trivial necessary condition for the existence of a CC in space-time. In addition it is shown that for a particular class of CC,£ξK is proportional to K, where K is the Riemannian curvature defined at a point in terms of two vectors, one of which is the CC vector. It is also shown that a space-time which admits certain types of CC also admits cubic first integrals for mass particles with geodesic trajectories. Finally, a class of null electromagnetic space-times is analyzed in detail to obtain the explicit CC vectors which they admit.
Massive Vector Meson Interacting with the Gravitational Field. I. General Formalism
Authors: Tauber G. E.
Published: February 2004

Starting from the covariant field equations for a vector meson, the energy-momentum tensor entering in Einstein's field equations is derived. It is shown that its most general algebraic form involves two vector fields and two scalars. Specifying the formalism to the special cases for which the fields are either parallel or perpendicular to each other, it is found that the vector field cannot be described in terms of a perfect fluid involving only density and pressure, but includes an additional term involving the stresses. The conservation laws are given, which, in addition to the ones of relativistic hydrodynamics, also include the ones describing the streaming of the vector field.
Asymptotic Fields in Some Models of Quantum Field Theory. II
Authors: Ho/egh-Krohn Raphael
Published: February 2004

A quantum field with nonlocal but translation-invariant interaction is considered. We prove that, with a proper smoothness condition on the interaction, the asymptotic limits of the annihilation-creation operators exists. The asymptotic limits are then used to prove that the state space decomposes as a tensor product of an incoming (outgoing) Fock space and a zero-particle space.
Some Analytic Properties of Scattering Amplitudes for Long-Range Forces
Authors: Ross William R. , Taylor John R.
Published: February 2004

We examine the properties of the partial-wave amplitude a(l, k) and the full amplitude A(k, cos θ) for scattering by a long-range potential made up of a Coulomb part 2α/r and a short-range part V(r). The properties of a(l, k) as an analytic function of l and k are shown to be quite similar to those of the usual short-range amplitude, except in the neighborhood of the threshold k = 0, which point we examine in detail. The full amplitude is treated as a function of cos θ for fixed physical momentum k; using the Sommerfeld-Watson transformation, we show that A(k, cos θ) is analytic in the cut plane of cos θ.