bluuebunny/crossref_metadata_2025 huggingface dataset:
Branching rules for U(N)⊃U(M) and the evaluation of outer plethysms
Authors: Butler P. H. , King R. C.
Published: February 2004

Littlewood's third method of evaluating plethysms is generalized by noting that plethysms determine the branching rules associated with the subgroup decomposition U(N)⊃U(M), and by making use of the well-known branching rule for U(M)⊃U(M−1). This generalization leads to recurrence formulas which are simpler than those due to Murnaghan and to a new method of evaluating plethysms which is free of the ambiguities inherent in the use of Littlewood's third method.
Projective representations of SL(3,C) in the Z-operator formalism
Authors: Bars Itzhak
Published: February 2004

An operator formalism, previously developed to discuss the Gel'fand-Naimark z-basis for the homogeneous Lorentz group, is now generalized to treat the projective representations of SL(3,C). We find the projective ``position'' operators Z1, Z2, Z3, as well as their canonical conjugate ``momenta'' II1, II2, II3 which form the building blocks of the generators of SL(3,C). The z-representation, the states in which the ``position'' operators Zi are diagonal, has very simple global transformation properties. This representation also leads to a Hilbert space endowed with an affine metric G, which relates the ``covariant'' and ``contravariant'' states. All unitary representations are unified by means of a single scalar product in which the matrix elements of G play the role of an intertwining operator.
Finite-contour dispersive inequalities
Authors: Celik Tarik , Palmer David R.
Published: February 2004

Finite-contour dispersive inequalities are derived for a function f(ξ) which is analytic in the ξ plane except for a right-hand cut. Inequalities are also derived for the derivative of the function. These inequalities are rigorous and the sharpest ones that can be derived using only analyticity.
Complex coordinate transformations and the Schwarzschild-Kerr metrics
Authors: Newman E. T.
Published: February 2004

Utilizing the fact that the Schwarzschild and Kerr geometries have an intrinsically defined Minkowski space associated with them, we show that these Minkowski spaces (as the Kerr parameter varies) can be viewed as ``real slices'' in a complexified Minkowski space. The complex Weyl tensor of each member of the family can then be viewed as a single complex field on the complex Minkowski space. Further, the degenerate principle null vectors associated with each geometry can be considered as projections into the ``real slices'' of a complex null vector field in the complex Minkowski space. These results may be considered as clarifying earlier work on obtaining the Kerr metric from the Schwarzschild metric by a complex coordinate transformation.
Hypercontractivity for fermions
Authors: Wilde Ivan F.
Published: February 2004

If T is a fermion one-particle operator, with ‖ T ‖ < 1, then T induces a bounded map from L2(C)→Lp(C), for some p > 2, where C is the fermion von Neumann algebra. The proof is an adaptation to the fermion case of the corresponding proof for bosons given by Nelson. This leads to a generalization of a theorem of Gross, inasmuch as T is not required to be self-adjoint.
The characteristic development of trapped surfaces
Authors: Demmie Paul N. , Janis Allen I.
Published: February 2004

Conditions are found that are sufficient to insure the development of trapped surfaces in space-times whose metrics satisfy the Einstein field equations in vacuum or in the presence of a massless scalar field. These conditions involve a topological requirement that a certain two-surface be compact and inequalities that must be satisfied by certain pieces of the characteristic data determining these space-times. It is shown that a particular piece of data playing an important role in these inequalities is related to angular momentum.
Dynamics for classical relativistic particles: Circular orbit solutions and the nonrelativistic limit
Authors: Cordero P. , Ghirardi G.-C.
Published: February 2004

This work consists of two parts. First we consider a general classical relativistic direct interaction theory (for two point particles) coming from an action principle such that the equations of motion have, at most, second-order derivatives of the position 4-vectors with respect to proper time. We introduce the general formalism, derive the explicit form of the conserved quantities, and discuss some particular cases which had previously been considered in the literature. We analyze in detail the circular orbit solutions of the general equations of motion, deriving in particular the constraints which the interaction function must satisfy in order that such solutions exist. In the second part we study in detail the nonrelativistic limit of the theory, showing that the limit is perfectly consistent. The obtained Newton equations contain an arbitrary potential that depends on the relative position and velocity.
Perturbation of the P(φ)2 quantum field Hamiltonian
Authors: Spencer Thomas
Published: February 2004

We consider local energy operators δH0 as perturbations of the P(φ)2 Hamiltonian. Our principal result is the estimate δH0≤ C[H(g) − E(g)+1] where C is a constant independent of the space cutoff g and E(g) is the infimum of the spectrum of H(g).
A note on Kato's perturbation theory
Authors: Schroeck F. E.
Published: February 2004

The results of T. Kato are expanded by generalizing the relative bound condition on the perturbation to determine the domain of powers of the perturbed operator and by exhibiting some useful relative bounds between the unperturbed operator, the perturbed operator, and the perturbation.
The transformation from a harmonic single-particle basis to the self-consistent harmonic approximation
Authors: Caron Laurent G.
Published: February 2004

The transformation rules between a harmonic single-particle basis and the self-consistent harmonic approximation in quantum crystal theory are deduced. In the process, the thermal renormalization of the phonon spectrum is calculated to all orders in the phonon-phonon interaction. The generalization of the transformation technique to a Hartree single-particle basis is speculated upon.
An algebra of the Yang-Mills field
Authors: Buoncristiani A. M.
Published: February 2004

It is shown how the classical Yang-Mills (and the Maxwell) field equations can be written in a simple form by introducing differential operators based on the split-Cayley algebra. As a result, a field algebra accommodating both space-time symmetry (Lorentz invariance) and internal symmetry evolves. The connection between the view of the Yang-Mills field as a split-Cayley algebra and the exceptional Jordan angebra M83, discovered by Jordon, von Neumann, and Wigner, is discussed.
Linear operators and transfer of radiation with spherical symmetry
Authors: Wang Alan P.
Published: February 2004

This paper is concerned the construction of linear-operator equations for transfer of radiation taking place on a spherical shell. A complete set of equations is obtained for inhomogeneous, anisotropically scattering media with internal or external illumination and with an arbitrary reflecting core. In application, linear-operator equations are reduced to a class of familiar functional equations. Our general result provides answers to a set of well-known problems in astrophysics.
Asymptotic solutions of integral equations with a convolution kernel. I
Authors: van Trigt C.
Published: February 2004

Homogeneous eigenvalue problems for integral equations with a kernel of the convolution type, defined on a finite volume in N-dimensional space, are discussed. It is shown that they can be reduced asymptotically to eigenvalue problems for simpler integral equations. The integral equations to be derived also yield the asymptotic solution of the inhomogeneous problem for the original integral equations.
On the solution of the partial differential equation Πi=1N(∇2+ki2)ψ=0
Authors: Agarwal G. S. , Devaney A. J. , Pattanayak D. N.
Published: February 2004

It is shown that the solution of the partial differential equation Πi=1N(∇2+ki2)ψ=0, (ki2≠kj2) subject to appropriate boundary conditions may be written as ψ=Σi=1Nαiψi where the ψi's are the solutions of the Helmholtz equation (∇2+ki2)ψi=0 and the αi's are constants. The explicit forms of the ψi's in terms of the boundary values are also given. It is also shown that the solution of the partial differential equation (∇2+k2)Nψ=0 is obtained by means of a certain limiting procedure from the solution of the nondegenerate problem.
Position operators in relativistic quantum theory: Analysis of algebraic operator relationships
Authors: Durand Bernice
Published: February 2004

This work is the first of a series of three papers examining different aspects of position operators in relativistic quantum theory. In this paper the properties of the position operator X and the velocity operator V are derived for single particle matrix elements in the context of the Poincaré generator algebra. Both the physical meaning and the mathematical implications of each property are discussed. The algebraic structure of the extended set of relationships including the Poincaré generators, X and V is examined. It is found that this set defines an infinite algebra which is intractable mathematically. The Casimir operators of the Poincaré algebra are required to be Casimir operators for X and V, a new condition on V is formulated, and a simple solution for K is constructed. These conditions, together with familiar position operator properties, give the constraints and solutions for the extended algebra.
Thermodynamics of an anisotropic boundary of a two-dimensional Ising model
Authors: Au-Yang Helen
Published: February 2004

We consider a semi-infinite two-dimensional Ising model with its spins on the boundary row having a different interaction energy E′1 from the ferromagnetic bulk. We find that the boundary specific heat has two divergent terms: one of which diverges linearly at the bulk critical temperature Tc, and the other, logaritmically. The linearly divergent term is independent of E′1, and the coefficient of the logaritmically divergent term is a decreasing function of E′1. There is a boundary latent heat at Tc, which is identical to McCoy and Wu's result. The boundary spins, which can be either ferromagnetic or antiferromagnetic, are aligned for temperature lower than Tc. The boundary spontaneous magnetization approaches zero in the form of A(E′1)(1−T/Tc)1/2, and the boundary zero field magnetic susceptibility diverges at Tc in the form −B (E′1)ln|1−T/Tc|, where A(E′1) and B(E′) are increasing functions of E′1.
Covariant disturbances and exceptional waves
Authors: Boillat Guy
Published: February 2004

The disturbances of a field are determined for each kind of wave by the hyperbolic field equations. In a space-time formulation one may consider tensors which also depend on the 4-normal to the wavefront. It is shown that the disturbance of such a tensor has a definite covariant form only when the wave is exceptional. For the sake of illustration a perfect fluid is considered. It appears that the sound waves are exceptional not only when the fluid is incompressible but also when a special equation of state is used. This relation between pressure and density corresponds in the nonrelativistic limit to a usual approximation for subsonic flow.
Properties of matrix representations of SU(3)
Authors: McDonald A. , Rosen S. P.
Published: February 2004

Matrices representing the Lie algebra of SU(3) can also serve as Clebsch-Gordan coefficients for the direct product of the basis states of the representation times their adjoints. This fact enables us to obtain a number of properties, both general and specific, of SU(3) matrices. To carry out our program we develop a general formula for constructing a symmetric tensor of rank (n + 1) from the product of a tensor of rank n times an octet. We then deduce some general properties concerning the multiplicity of representations contained in the direct product of a representation and its adjoint. In the specific cases of the six- and ten-dimensional representations we obtain the characteristic equation for the SU(3) matrices, and for the 27-dimensional representation we obtain other properties. We also compute the traces of products of two, three, and four matrices in any representation.
On the radial wave equation in Schwarzschild's space-time
Authors: Persides S.
Published: February 2004

The radial factor of a separable solution of the wave equation in Schwarzschild's space-time satisfies a second-order linear differential equation. This equation is studied in detail. The behavior of the solutions near the singular points (the origin, the horizon, and infinity) of the equation is analyzed. By an appropriate transformation two simpler differential equations are obtained corresponding to retarded and advanced solutions with characteristic asymptotic expansions. Their properties permit the expression of the general solution of the radial equation in terms of a single contour integral. Finally, through a ``matching'' technique, the behavior of a solution at the singular points is determined from its behavior at a single singular point.
Electromagnetic wave propagation in inhomogeneous multilayered structures of arbitrary thickness-Full wave solutions
Authors: Bahar E.
Published: February 2004

In this paper, we derive full wave solutions to the problem of electromagnetic wave propagation in inhomogeneous multilayered structures of arbitrarily varying thickness. To this end, we employ generalized transforms that provide an appropriate basis for the complete expansion of the transverse components of the electromagnetic fields. The continuous parts of the wavenumber spectrum are the radiation and the lateral wave terms while the discrete part is identified as the finite set of trapped waveguide modes (surface waves). When the bounding media are characterized by perfect electric or magnetic walls (μ/ε → 0 or ε/μ → 0, respectively) or surface impedances, the fields are expressed exclusively in terms of an infinite set of waveguide modes. These solutions are not restricted by the approximate surface impedance concept and the sources and observation point may be located in any of the nonuniform layers of the structure. Exact boundary conditions are imposed and the solutions satisfy the reciprocity relationships. Thus, the solutions are applicable to artificial layered structures as well as natural structures such as the inhomogeneous ionosphere and the earth's crust. These solutions can also be used to determine the scattering from objects of finite cross section in free space or embedded in the earth's crust.
On the necessity of nearly-best-possible methods for analytic continuation of scattering data
Authors: Miller K. , Viano G. A.
Published: February 2004

In the present paper we discuss some mathematical methods which are nearly-best-possible in order to extract as much as possible information from the numerical analytic continuation of the scattering data. All the questions related to the stability are analyzed; in this sense we explicitly show some cases where the continuity of the solutions on the data is very poor. Finally the error-bounds are extensively explored.
Perturbation solution of the Kirkwood-Salsburg equation
Authors: Klein William
Published: February 2004

A formal series solution to the Kirkwood-Salsburg equation and its radius of convergence are derived. This solution leads naturally to the establishment of an approximate hierarchy of equations for the distribution functions which needs no closure. The asymptotic behavior of the solutions to this approximate hierarchy is studied as well as the behavior of the derivatives of the pair function with respect to the interparticle distance.
Derivation of low-temperature expansions for Ising model. II. General theory
Authors: Sykes M. F. , Gaunt D. S. , Essam J. W. , Hunter D. L.
Published: February 2004

The enumeration problem that arises in the derivation of low-temperature and high-field expansions for the Ising model of a ferromagnet and antiferromagnet is studied. The method of partial generating functions (complete codes) is developed and a principle of complete code balance is explicitly stated. The detailed application of the method to a number of lattices is described and substitutions given that interpret the generating functions of certain lattices on the corresponding shadow lattice. It is shown that in zero-field and two dimensions some of these substitutions reduce to the well-known star triangle and magnetic-moment results.
Derivation of low-temperature expansions for Ising model. III. Two-dimensional lattices-field grouping
Authors: Sykes M. F. , Gaunt D. S. , Mattingly S. R. , Essam J. W. , Elliott C. J.
Published: February 2004

The derivation of series expansions appropriate for low temperatures or high applied magnetic fields for the two-dimensional Ising model of a ferromagnet and antiferromagnet is studied as a field grouping. New results are given for the high field polynomials for the triangular lattice to order 10, the simple quadratic lattice to order 15, and the honeycomb lattice to order 21.
Derivation of low-temperature expansions for Ising model. IV. Two-dimensional lattices-temperature grouping
Authors: Sykes M. F. , Gaunt D. S. , Martin J. L. , Mattingly S. R. , Essam J. W.
Published: February 2004

The derivation of series expansions appropriate for low temperatures or high applied magnetic fields for the two-dimensional Ising model of a ferromagnet and antiferromagnet is studied as a temperature grouping. New results are given for the ferromagnetic polynomials for the triangular lattice to order 16, for the ferromagnetic and antiferromagnetic polynomials for the simple quadratic lattice to order 11, and for the honeycomb lattice to order 16.
The density of a nonuniform system in the thermodynamic limit
Authors: Simmons Carver S. , Garrod Claude
Published: February 2004

We discuss the existence, continuity, and other properties of the canonical and grand canonical density distributions in the thermodynamic limit for nonuniform classical mechanical systems. For an external potential φ defined on a domain Λ the free energy per unit volume for fixed temperature is given by F(ρ0,φ) = min ∫Λ[ρ(x)φ(x) + f(ρ(x))]dx/V(Λ) where the minimum is over all density distributions satisfying the restriction of fixed average density ρ0, and f(ρ0,β) is the free energy per unit volume in the thermodynamic limit when φ = 0. We prove that if φ is not constant over any region of finite volume then the density distribution which minimizes is unique, and also that the density is the functional derivative of F(ρ0,φ) with respect to φ. We also show that the density distribution of an infinite nonuniform system is the limit of density distributions associated with finite systems of increasing size.
Equivalent variational functionals in potential scattering
Authors: Robinson Peter D.
Published: February 2004

The equivalence is established between dual pairs of variational functionals (Kohn type) derived from the differential equation description of potential scattering and other dual pairs of variational functions (Schwinger type) derived from the integral equation description. Apparent differences are resolved by suitable choice of trial vector. The Kohn functional and minus the Schwinger functional are shown to be duals of each other.
On analytic nonlocal potentials. I. A forward dispersion relation
Authors: Yao Te Hai
Published: February 2004

We propose a class of analytic short-ranged nonlocal potentials, and we obtain dispersion relations for the forward scattering amplitude. We use the Fredholm method for the Lippman-Schwinger equation for the scattering solution, and contour rotation in the analytic continuation of the forward scattering amplitude.
The symmetric group: Characters, products and plethysms
Authors: Butler P. H. , King R. C.
Published: February 2004

It is demonstrated following the work of Murnaghan and Littlewood that the symmetric group may with advantage be considered as a subgroup, albeit finite, of the general linear group. This approach involves in a natural way the use of a reduced notation for the specification of irreducible representations of Σn and leads to the determination of closed formulas for the dimension, characters, and Kronecker products of such representations. The relationship between the characters and S functions is discussed in detail and some results on symmetrized Kronecker squares are obtained.
Duality of a Young diagram describing a representation and dimensionality formulas
Authors: Murtaza G. , Rashid M. A.
Published: February 2004

We discuss the standard dimensionality formulas for irreducible representations of continuous Lie groups SU(n), O(n), and Sp(n). Every Young diagram describes not only an irreducible representation of any of the groups SU(n), O(n), and Sp(n) of dimension n, but it also describes an irreducible representation of the symmetric group SN, where N is the number of boxes in the diagram. This property of a Young diagram leads to the factorization of the dimensionality formulas for irreducible representations of any of these continuous groups into two factors. One factor which depends upon the dimension n of the group appears as a polynomial (with integral roots) of degree N. If we choose the leading coefficient of this polynomial as unity, the other factor turns out to be just 1/N! times the dimensionality of the associated irreducible representation of the symmetric group on N symbols. The polynomial depends upon the type of the group under study, i.e., whether it is an SU(n) or O(n) or Sp(n). We also give simple recipes to read the dimensionality of the representations of these groups from the Young diagram following our formulas.
Matter symmetries in general relativistic kinetic theory
Authors: Berezdivin R. , Sachs R. K.
Published: February 2004

It is shown that a surface forming matter symmetry for collision-free general relativistic kinetic theory gives rise to an isometry on the space-time. Specific solutions are given, and it is shown that limiting the surface forming conditions to the mass subbundle does not alter the results. A possible method for solving more general cases is given.
Natural basis expansion of functions of the distance between two points: Generalization of Laplace's and Neumann's expansions
Authors: Matcha Robert L. , Daiker Kenneth C.
Published: February 2004

A method of obtaining expansions of functions of r12 utilizing solutions of separable differential operators which annihilate the functions is presented. Expansions of r12 n in spherical polar and confocal elliptic coordinates are obtained in terms of solutions of a generalized Laplace operator.
KS-related f-g couples as exact vacuum solutions of Salam's two-tensor theory
Authors: Urbantke Helmuth K.
Published: February 2004

The exact solutions of the vacuum field equations of the two-tensor theory of gravitation proposed by Salam et al. are determined for the case that the two tensors differ only by the tensor product of a null vector field with itself. It is found that this null vector field must be geodesic with vanishing shear, expansion, and twist, and represents a field of multiple principal null directions for both Weyl tensors. As a consequence, the solutions can be derived from the results of a paper by Kundt.
Invariant imbedding and the resolvent of Fredholm integral equations with variable parameters
Authors: Bellman R. , Ueno S.
Published: February 2004

In recent years Bellman and Krein have given independently a geometrical invariant imbedding of the resolvent K(t, y, x) (0 ≤ t, y ≤ x) of Fredholm integral equations with continuous kernels. In the case of symmetric kernels and constant parameters, the Cauchy systems for the symmetric resolvents have been discussed by several authors. In this paper, when the parameter depends upon the independent variable, we show how to solve exactly the Fredholm integral equation with the aid of invariant imbedding. In other words, by reducing the kernel to symmetric kernel, the Bellman-Krein formula for the Fredholm resolvent permits us to reduce the two-point boundary value problem to the initial value problem.
On the approach to equilibrium in kinetic theory
Authors: Grmela Miroslav
Published: February 2004

Definition, existence and properties of the equilibrium states, existence and uniqueness of the approach to the equilibrium states, the Onsager reciprocity relations, and existence of hydrodynamic stage in the approach to the equilibrium states are the problems which are discussed in this paper for dynamics defined by the family of kinetic equations of the Enskog-Vlasov type. A modification of the Chapman-Enskog method for quantitative calculations involving the kinetic equations considered is suggested.
Lienard-Wiechert fields and general relativity
Authors: Newman E. T.
Published: February 2004

An analogy is established between the Lienard-Wiechert solutions of the Maxwell equations and the Robinson-Trautman solutions of the Einstein equations by virtue of the fact that a principal null vector field of either the Maxwell or Weyl tensor in each case satisfies the following four conditions: (1) The field is a geodesic field, (2) it has nonvanishing divergence, (3) it is shear free, and (4) it is twist (or curl) free.
Classical SU(3) gauge field equations
Authors: Wu Alfred C. T. , Wu Tai Tsun
Published: February 2004

Admissible forms of the static solutions to the SU(3) gauge field equation are examined. It is shown that by a proper choice of the form of solutions which extricate the SU(3) indices, the set of nonlinear partial differential equations is reducible to nonlinear ordinary differential equations for the radial functions.
The Lie algebra s o (N) and the Duffin-Kemmer-Petiau ring
Authors: Fischbach Ephraim , Louck James D. , Nieto Michael Martin , Scott C. K.
Published: February 2004

An explicit expression is given for the unit element E of the ring generated by the Duffin-Kemmer-Petiau (DKP) operators βμ. The relation of E to the unit operator I (unit matrix in a matrix representation) is also derived. It is pointed out that one must be careful to distinguish E from I. Bhabha's observation that one may use the irreducible representations (irreps) of the Lie algebra s o (5) to obtain the irreps of the Dirac, DKP, and other algebras is given a concise and general setting in terms of a relation between the Lie algebra s o (n + 1) and a family of semisimple operator rings. We emphasize that for the case n + 1 = 5 this means that there is an underlying relationship between the physical DKP and Dirac algebras and wave equations.
Zeroes of the partition function for the Ising model in the complex temperature plane
Authors: Brascamp H. J. , Kunz H.
Published: February 2004

For special boundary conditions, the zeroes of the partition function of the square Ising model are shown to lie on Fisher's two circles in the complex exp(− 2βJ) plane. For some more general boundary conditions, the zeroes distribute asymptotically on these circles.
Statistical mechanics for velocity dependent interactions
Authors: Srinivas M. D. , Prahalad Y. S.
Published: February 2004

The quantum corrections to the phase space distribution function are obtained for general velocity dependent interactions. It is noted that a study of the thermodynamic properties of bulk nuclear matter may settle the question of velocity dependence of nucleon-nucleon interaction.
On a complex representation of Lorentzian random variables
Authors: Eggarter T. P.
Published: February 2004

A Lorentzian random variable X is characterized by its mean value a and its width γ. We point out some interesting properties of the map X↝a+iγ. We illustrate the usefulness of this map by solving a particular problem in the theory of disordered materials.
General expressions for the position and spin operators of relativistic systems
Authors: Lorente M. , Roman P.
Published: February 2004

Some general assumptions based on the physical properties of elementary and of composite quantized systems lead in a natural way to general expressions for the position and spin operators of massive particles. All previously proposed position and spin operators, defined in the enveloping algebra of the Poincaré group, appear as special cases. By algebraic arguments a general local position operator is obtained which is proved to coincide under special conditions with the Pryce-Newton-Wigner position operator.
Nonrelativistic current algebra in the N / V limit
Authors: Goldin G. A. , Grodnik J. , Powers R. T. , Sharp D. H.
Published: February 2004

The case of a noninteracting infinite Bose gas at zero temperature is studied in the formalism of local current algebras, using the representation theory of nuclear Lie groups. The class of representations describing such a system is obtained by taking an ``N / V limit'' of the finite case. These representations can also be determined uniquely from the solutions of a functional differential equation, which follows in turn from a condition on the ground state vector. Finally a system of functional differential equations is formulated for a theory with interactions, using a proposed definition of indefinite functional integration.
The recursive perturbation method and its application to the study of nuclear shell models
Authors: Hioe F. T.
Published: February 2004

The recursive perturbation method given previously by the author is generalized and applied to the calculation of the energy levels of nuclear shell models. Specifically, we consider a numerically exactly soluble model of interacting fermions with S U(3) symmetry studied by Li, Klein, and Dreizler. The method can be obviously extended to the study of more general models with S U(n) symmetry.
Local bounded perturbations of KMS states
Authors: Presutti E. , Scacciatelli E.
Published: February 2004

Local bounded perturbations of an infinite equilibrium state are studied in the C*-algebraic framework. It is assumed that for the unperturbed state the pressure exists in the thermodynamic limit and that the Dubin-Sewell hypotheses are fulfilled. The following is then shown: At constant temperature the perturbed state is analytic in the perturbation Q, the infinite volume pressure does not depend on Q, and the new state is KMS with respect to the time evolution corresponding to the adiabatic perturbation, as treated in a previous paper.
Mathematical theory of the R matrix. I. The eigenvalue problem
Authors: Narcowich F. J.
Published: February 2004

This is the first paper in a two part series aimed at placing the theory of Wigner's R matrix on a mathematically rigorous footing. In Paper I of the series, we will show that the eigenvalue problem associated with the R matrix can be solved for a large class of potentials, including Coulomb-like potentials. We will do this for the case in which the boundary of the internal region is a smooth surface—although the results remain true for a much larger class of surfaces. In Paper II of the series, we will show that the R matrix exists for the class of potentials mentioned, is a compact operator, and can be approximated uniformly (i.e., normwise) by the usual expansions associated with the R matrix.
Multiregion criticality in general geometries
Authors: Sheaks O. J. , Schnatz T. W.
Published: February 2004

A general transform technique is developed for multiregion critical problems. The equivalence of a replication procedure and a derived boundary condition approach is demonstrated for the general multiregion geometries. An exact representation for the particle density may be obtained using this approach in the form of singular integral equations or equivalent Fredholm equations for expansion coefficients which arise from the superposition of the normal modes representing the particle density. The method is specifically demonstrated in the determination of solutions to the two-region critical cylinder problem.
Lattice gas with nearest-neighbor interaction in one dimension with arbitrary statistics
Authors: Lai C. K.
Published: February 2004

We define a quantum lattice gas with arbitrary statistics. For a one-dimensional system with nearest-neighbor interaction, we show that the problem is exactly soluble by use of Bethe's hypothesis when the interaction Δ=±1. The ground state energy is then obtained for the fermions of spin 1/2. Two phases are found in the case Δ=-1.
Must quantum theory assume unrestricted superposition?
Authors: Bernstein Herbert J.
Published: February 2004

A conjecture that the (n −1)2 independent moduli and (2n −1) unphysical phases completely specify all n-dimensional unitary matrices is shown to be true in two and three dimensions, but false in four or more. The implications for quantum theory are discussed.
Spectrality, cluster decomposition and small distance properties in Wightman field theory
Authors: Truman A.
Published: February 2004

We apply the results of a previous paper by Screaton and Truman to the truncated vacuum expectation values in Wightman field theory and, using spectrality, translational invariance, and Lorentz invariance, we derive the best bounds for the truncated vacuum expectation values at the real Jost points. In a local field theory these bounds include as a special case Araki's result on the exponential decrease of the truncated vacuum expectation value for large spacelike separations and the cluster decomposition property. The bounds also establish a connection between the small distance and high energy behaviors of the theory. In addition we evaluate the bounds in a nonlocal field theory and discuss some of their ramifications.
A general method for obtaining Clebsch-Gordan coefficients of finite groups. I. Its application to point and space groups
Authors: Sakata Isao
Published: February 2004

A general method is developed for obtaining Clebsch-Gordan coefficients of finite groups. With this method Clebsch-Gordan coefficients are obtained in a matrix form, whereas the so-called basis-function generating machine generates these coefficients one by one. The method is applied to double point group D̄3, the point group T, and the nonsymmorphic space group D̄4h14. It will be shown that the method can be simplified by the conservation law of the reduced wave vectors when applied to space groups.
A general method for obtaining Clebsch-Gordan coefficients of finite groups. II. Extension to antiunitary groups
Authors: Sakata Isao
Published: February 2004

A general method is presented for obtaining Clebsch-Gordan coefficients, in a matrix form, of finite antiunitary groups, as a direct extension of a general method for unitary groups. It is shown that there is an essential difference as well as apparent similarities between two methods for unitary and antiunitary groups.
Phase transitions of a multicomponent Widom-Rowlinson model
Authors: Runnels L. K. , Lebowitz J. L.
Published: February 2004

We study a multicomponent version of the ``A−B'' model of Widom and Rowlinson, generalized in a symmetric way: There is an infinite repulsive interaction between any two unlike particles. We consider both lattice and continuum versions of the model and show that the ``demixing'' transition occurs for any finite number M of components, all having the same activity. No conclusion can be drawn about this transition in the limit M→∞. It is shown, however, that another transition, in which the density is greater on one of the sublattices, appears at a finite value of M which persists for all larger M at any fixed value of the activity. In the limit M→∞, z→0, M z=ζ, const, this system apparently becomes ``equivalent'' to a one-component system with activity ζ in which there is an exclusion for occupancy of nearest neighbor sites. The latter transition then becomes the ``hard square'' transition.
A remark on the connection between stochastic mechanics and the heat equation
Authors: Albeverio Sergio , Ho/egh-Krohn Raphael
Published: February 2004

We prove that the solution of Nelson's stochastic mechanics equation associated with any stationary solution ψ of the Schrödinger equation is the homogeneous Markov process of the heat equation with Dirichlet boundary condition on the hypersurface ψ=0.
Separation of tensor equations in a homogeneous space by group theoretical methods
Authors: Hu B. L.
Published: February 2004

Details of the group-theoretical method for the separation of tensor equations in a homogeneous space are given. As illustrations, the vector and tensor harmonics in a SO(3)-homogeneous space are constructed, with applications to the study of electromagnetic and gravitational perturbations in the mixmaster universe.
Proper dynamics of a rigid point particle
Authors: Hestenes David
Published: February 2004

A spinor formulation of the classical Lorentz force is given which describes the precession of an electron's spin as well as its velocity. Solutions are worked out applicable to an electron in a uniform field, a plane wave, and a Coulomb field.
Some topological and graphical aspects of phase contours
Authors: Shafee A.
Published: February 2004

Using the topological properties of phase contours, the phase contour diagram of a function in the complex plane is reduced to the simpler form of a bichromatic multigraph, which contains all the combinatorial characteristics regarding links between zeros and singularities of the function. It is found that the saddle points of the phase play an essential role in any such qualitative global description of the function, as can be anticipated from Morse theory. In the case of the scattering amplitude, constraints from symmetries, periodicity, or unitarity are seen to yield simplifications with interesting results concerning factorization and asymptotic behavior.
Limits in systems exhibiting a one-dimensional phase transition
Authors: Truex William L. , Strecker Joseph L.
Published: February 2004

Recent spherical Ising models by Strecker and Gersch which exhibit one-dimensional phase transitions have shown that at the critical temperature ε → γ⅔, whereas inside the one phase region ε→γ2. The models were unable to shed light on the behavior of this function as it passed through the vapor dome. Speculation might lead one to believe that a new type of singularity is present. Instead, we show that the exponent continuously changes from ⅔ to 2. A simple cubic polynomial controls the behavior of the ε function.
Zeros of the partition function for higher-order spin systems
Authors: Millard K. Y. , Viswanathan K. S.
Published: February 2004

A theorem is proved which is useful in determining information regarding the location of zeros of the partition function for lattice models with arbitrary spin. This theorem is a generalization to higher-order spin systems of a theorem for spin-1/2 systems proved by Ruelle. The total partition function for the system can be constructed by contracting (a generalization of the Asano contraction procedure) a set of lower-order ``partition function-like'' polynomials. The theorem presented relates information regarding the location of zeros of the lower-order polynomials to the location of zeros of the partition function. This theorem is then used to establish the Lee-Yang unit circle theorem for several higher-order spin models.
Exact next nearest neighbor degeneracy
Authors: McQuistan R. B.
Published: February 2004

It is shown that A [n11, n101, n111, q, N], the arrangement degeneracy arising when q indistinguishable particles are placed on a one-dimensional lattice of N equivalent compartments so that n11 occupied nearest neighbors, n101 next nearest neighbors of the 101-type, and n111 next nearest neighbors of the 111-type are created, is given by A[n11, n101, n111, q, N]=(N−2q+n11+2q−n11−n101)(q−n11−1n101)(q−n11n11−n111)(n11−1n111). The normalization and first moment of the next nearest neighbor density are determined. Similar results for the vacant next nearest neighbor degeneracy are also presented.
Quantumlike formulation of stochastic problems
Authors: Santos Emilio
Published: February 2004

It is shown that a stochastic process can be viewed as a set of states (normalized positive linear functionals) over an Abelian C*-algebra. Alternatively, the stochastic process can be associated with a set of representations of the algebra as a subalgebra of the (noncommutative) C*-algebra of bounded operators in a Hilbert space. Then, an operator equation can be associated with every stochastic equation in some general conditions. The formalism is applied to Brownian motion. Then, we study the nonrelativistic motion of a single particle in stochastic electrodynamics, a theory which has been proposed as a possible alternative to quantum mechanics. The equations of motion, which are derived, coincide with the basic ones of quantum mechanics. The differences between this theory and quantum mechanics are summarized.
Radio wave propagation in nonuniform multilayered cylindrical structures-Generalized field transforms
Authors: Bahar E.
Published: February 2004

Bessel type transforms, formulated recently, provide suitable bases for the expansion of the electromagnetic fields due to line sources in the vicinity of cylindrical structures of variable curvature. However, these expansions are restricted to open structures with convex cylindrical boundaries that are characterized by surface impedances which are independent of excitation. In this paper, we derive transforms that are suitable for the expansion of electromagnetic fields in multilayered cylindrical structures with both concave and convex boundaries. The innermost medium of the structure is assumed to be a good conductor. These field transforms are shown to be related to Fourier-type transforms derived for parallel layered structures. They can be used to obtain rigorous, full wave solutions, to problems of propagation in irregular waveguide ducts in the earth's crust, the ionosphere, and in the cavity between the earth and the ionosphere.
On the spectrum of the linear transport operator
Authors: Larsen Edward W. , Zweifel Paul F.
Published: February 2004

In this paper, spectral properties of the time-independent linear transport operator A are studied. This operator is defined in its natural Banach space L 1(D × V), where D is the bounded space domain and V is the velocity domain. The collision operator K accounts for elastic and inelastic slowing down, fission, and low energy elastic and inelastic scattering. The various cross sections in K and the total cross section are piecewise continuous functions of position and speed. The two cases ν0>0 and ν0=0 are treated, where ν0 is the minimum neutron speed. For ν0=0, it is shown that σ(A) consists of a full half-plane plus, in an adjoining strip, point eigenvalues and curves. For ν0>0, σ(A) consists just of point eigenvalues and curves in a certain half-space. In both cases, the curves are due to purely elastic ``Bragg'' scattering and are absent if this scattering does not occur. Finally the spectral differences between the two cases ν0>0 and ν0=0 are discussed briefly, and it is proved that A is the infinitesimal generator of a strongly continuous semigroup of operators.
Choquet simplexes of states in physical systems
Authors: Chen Etang
Published: February 2004

Two extreme types of Choquet simplexes, prime and Bauer, are shown in the states of some physical systems.
Weyl conform tensor for stationary gravitational fields
Authors: Ernst Frederick J.
Published: February 2004

Our formulas for the Weyl conform tensor components generalize results published earlier by Z. Perjés for vacuum fields. We also offer an abstract version of these equations which may shed some light upon their structure. The expressions for the Weyl conform tensor are specialized to the case of small perturbations from a stationary axially symmetric background geometry. The resulting formulas supplement the expressions which Chandrasekhar and Friedman have developed for the components of the Ricci tensor. We anticipate that this will facilitate the comparison of the CF perturbation theory with the recent studies of perturbations of the Kerr metric by Press, Teukolsky, and Wald. In this connection we identify in terms of the CF field variables the fields which are involved in Teukolsky's separable field equations.
Dynamics of a multilevel Wigner-Weisskopf atom
Authors: Davies E. B.
Published: February 2004

We study the dynamics of an atom with a finite number of discrete energy levels weakly coupled to a continuum of energy levels, showing that any bound state undergoes a decay into the continuum which, in the limit as the coupling constant goes to zero, becomes rigorously exponential.
Asymptotic solutions of second-order linear equations with three transition points
Authors: Nayfeh Ali H.
Published: February 2004

A uniformly valid asymptotic expansion is obtained for the regular solution of a class of second-order linear differential equations with three transition points-a turning point and two regular singular points. The solution is found by matching three different solutions obtained using the Langer Transformation. The matching yields the eigenvalues and the eigenfunctions.
A geometric interpretation of classical relativistic electrodynamics
Authors: Petti Richard
Published: February 2004

A solution is offered for this problem: Describe the observables of classical electrodynamics with connections on fiber bundles without using nonobservable entities, either in computations or in conceptual development. The solution employs a connection on the affine frame bundle of space-time. Comparisons are made with other geometric interpretations of electrodynamics.
Phase properties of some photon states with nonzero energy density
Authors: Provost J. P. , Rocca F. , Vallee G. , Sirugue M.
Published: February 2004

We describe some photon states with nonzero energy density in the whole space; these states are obtained by taking a finite number of photons within a finite box and letting the volume and the number of photons go to infinity according to usual procedure in statistical mechanics. In such a limit we describe an observable phase operator; we investigate its properties both in the case of free field and in the case of coupling with prescribed classical sources. Finally we give a quantum description of uniform static field.
The semiclassical fermion μ-space density in three dimensions
Authors: Balazs N. L. , Zipfel G. G.
Published: February 2004

An approximation is constructed to the phase-space, or Wigner, distribution function for a three-dimensional, dense Fermi gas in a spherically symmetric potential well. Near the surface separating the classically forbidden region from the classically allowed region, quantum oscillations occur. The oscillations are expressed in terms of a universal function.
Baker-Campbell-Hausdorff formulas
Authors: Gilmore R.
Published: February 2004

Baker-Campbell-Hausdorff formulas can be constructed simply by matrix multiplication. Examples are given.
On the existence of weakly retarded and advanced Green's functions
Authors: Capri Anton Z.
Published: February 2004

By considering a model field equation that contains the acausal propagation features of a spin 3/2 field we show that depending on the ``external field'' one can either have weakly retarded fundamental solutions or not.
The algebra and group deformations Im [SO(n)⊗SO(m)]⇒SO(n,m), Im [U(n)⊗U(m)]⇒U(n,m), and Im [Sp(n)⊗Sp(m)]⇒Sp(n,m) for 1⩽m⩽n
Authors: Wolf Kurt Bernardo , Boyer Charles P.
Published: February 2004

We discuss a class of deformations of the inhomogeneous classical algebras im [k(n)⊕k(m)] to k(n,m) for 1 ≤ m ≤ n. This generalizes the previously known expansions i k(n)⇒k(n,1). As the title indicates, this is done explicitly for the orthogonal, unitary, and symplectic cases. We construct the corresponding deformed groups K(n,m) as multiplier representations on the space of functions over the rank m coset space K(n - m)\K(n). This method allows us to build a principal series of unitary representations of K(n,m). The contractions of the deformed algebras and groups are considered.