bluuebunny/crossref_metadata_2025 huggingface dataset:
Timelike curves of limited acceleration in general relativity
Authors: Chakrabarti Sandip K. , Geroch Robert , Liang Can-bin
Published: March 2003

A simple result, restricting the behavior of a timelike curve under limitations on its integrated acceleration, is obtained and discussed.
A unified theory of the point groups. III. Classification and basis functions of improper point groups
Authors: Kim Shoon K.
Published: March 2003

This paper introduces a new system of classification of improper point groups which is most effective for describing their general irreducible representations. The complete set of the general angular momentum eigenfunctions is classified according to the general irreducible representations of the seven sets of the improper point groups corresponding to Cn(C∞) and Dn(D∞) for an aribtrary n.
Inverse problem for the reduced wave equation with fixed incident field. III
Authors: Weston V. H.
Published: March 2003

The inverse problem for the reduced wave equation Δu+k2n2(x)u=0, x∈R3, is examined for the case where measurements of the amplitude of the scattered field (produced by a fixed incident field at a single frequency) are obtained at a finite number of points. A strategy is given for the recovering of the phase data through the minimization of a quadratic form involving comparison data. The problem is then reduced to the problem treated in previous papers where the complex-valued quantities us(xl) are known at a finite number of points. A relationship between the smallest eigenvalue of the ‘‘measurement’’ matrix and ∥K∥2 is given.
The generalized anharmonic oscillator in three dimensions: Exact eigenvalues and eigenfunctions
Authors: Rampal Anita , Datta K.
Published: March 2003

We study the generalized anharmonic oscillator in three dimensions described by the potentials of the form ∑2m+1k=1bkr 2k. An asymptotic analysis of the Schrödinger equation yields the leading asymptotic behavior of the energy eigenfunctions in terms of the dominant (m+1) coupling constants bk, m+1≤k≤2m+1. Using an ansatz which incorporates this asymptotic behavior, we reduce the eigenvalue equation to an (m+2)-term difference equation. The corresponding Hill determinant may be made to factorize with a finite determinant as a factor if a set of constraints on the couplings is satisfied; an infinite sequence of such sets exists. The exact energy eigenvalues appear as the real roots of the finite factor of the Hill determinant; the corresponding wavefunctions are Gaussian weighted polynomials. We consider the potentials ∑31bkr 2k and ∑51bkr 2k explicitly; potentials of the form ∑2m1bjr j and ∑2m1bjr j+δ/r containing both even and odd terms are also considered. Finally, we show that this method of constructing exact solutions fails for anharmonic potentials of the form ∑2m1bkr 2k, of which the quartic anharmonic oscillator is the simplest example.
Geometrical interpretation of a generalized theory of gravitation
Authors: Kunstatter G. , Moffat J. W. , Malzan J.
Published: March 2003

The geometrical structure is developed for a theory of gravitation, based on a nonsymmetric metric in a four-dimensional real manifold. The local fiber bundle gauge group is GL(4,R), which contains the (local) homogeneous Lorentz gauge group SO(3,1) of general relativity.
Local symmetries in extended conformal gravity and conformal supergravity in superspace
Authors: Mansouri Freydoon
Published: March 2003

The extended conformal field theory of gravity is discussed, and its local symmetries are compared to those of Einstein and standard Weyl theories. It is then shown that the local symmetries of the extended conformal geometry are also natural for the construction of SU(N)-extended conformal supergravity theories in superspace. The natural superspace for the formulation of such theories is one with two sets of four-component fermionic variables which transform oppositely under scale transformations.
On a relation between percolation and phase transition in the gauge invariant Ising model
Authors: Marra Rossana
Published: March 2003

We point out a connection between the coexistence of phases in the Z2 lattice gauge model and the existence of infinite clusters for a suitable associated system of duplicate currents.
Orbit space and minima of Landau–Higgs potentials
Authors: Jarić Marko V.
Published: March 2003

We establish a connection between recent propositions for minimization of Higgs potentials in an orbit space and related treatments in the Landau theory of phase transitions. Starting from isotropy groups we give a simple and systematic procedure for determining a stratification in an orbit space. As an illustration we treat the point groups Oh and Td which occur in the Higgs mechanism for SO7 and SU4 adjoint representations.
Particle states and scattering theory in abelian gauge model with spontaneously broken symmetry
Authors: Bishop Garner , Haller Kurt
Published: March 2003

This is an exposition of the electrodynamics of the φ4 theory with a spontaneously broken U(1) symmetry. The Lagrangian in a manifestly covariant gauge is used to construct the Hamiltonian and canonical commutation rules. Part of the Hamiltonian is a ‘‘free-field’’ Hamiltonian which describes noninteracting massive spin-1 Proca bosons, Higgs bosons, and ghosts. The remainder of the Hamiltonian is a perturbation for which an interaction picture is developed and Feynman rules are systematically derived by the Dyson–Wick procedure. The choice of the ‘‘free-field’’ Hamiltonian is based on earlier work, in which the particle spectrum was identified and verified explicitly by implementing Lorentz boosts on particle states. It is shown that application of the subsidiary condition and inclusion of interactions in evaluating positive frequency parts of gauge fixing fields is not only essential for consistency, but in this case also of practical importance in the proper identification of the Proca bosons.
On the generalization of the ’t Hooft field strength in the Yang–Mills–Higgs model
Authors: Houston P.
Published: March 2003

The generalization to the gauge groups SU(n) and SO(n) of the ’t Hooft electromagnetic field is considered for finite energy configurations of the Yang–Mills–Higgs model, and it is shown how this results in the association of sets of integer charges with any closed surface. Differential inequalities satisfied by the Higgs invariants are presented, and their implications are discussed.
A particle representation for Korteweg–de Vries solitons
Authors: Bowtell Graham , Stuart Allen E. G.
Published: March 2003

In an earlier paper we established an equivalence between the dynamics of interacting sine–Gordon solitons and the motions of poles of the corresponding Hamiltonian density. In particular, we found analytic expressions for the forces acting between the solitons and used these to represent the N-soliton solution as an N-body interaction between classical particles. In this paper, we apply the methods of our previous analysis to obtain a dynamically equivalent particle representation for interacting Korteweg–de Vries solitons. The representation is faithful and a detailed analysis is present for the one- and two-soliton solutions. In these cases the particle motions accurately reflect the behavior of the solitons, giving, respectively, a uniform motion and a repulsive interaction. Furthermore, in the case of the two-soliton solutions, the phase shifts calculated from the particle trajectories are the same as those obtained from an asymptotic analysis of the waveforms. Because of the nature of the Korteweg–de Vries equation, there are important differences between the present analysis and that employed for the sine–Gordon equation and these are discussed in some detail. A comparison with related work on other solutions of the Korteweg–de Vries is also presented.
Lorentz transformation properties of nonconserved charges
Authors: Bender Carl M. , Williams David A.
Published: March 2003

If a current jμ( x) is conserved, then the charge Q defined as the three-space integral of j0( x) is a Lorentz scalar. In this paper we investigate the Lorentz transformation properties of Q assuming that jμ( x) is not conserved; that is, ∂μ jμ( x)≠0. We find that Q, which now depends on time, transforms as the infinite direct sum of the spin-0 parts of the (0,2j+1) finite-dimensional tensor representations of the Lorentz group plus the spin-0 component of an infinite-dimensional indecomposable representation of the Lorentz group, [(0,1)→(1,0)]:[(0,1)→(1,0)] ⊕∑∞j=0⊕ (0,2j+1), where we are using the Gel’fand, Milnos, and Shapiro notation. More simply, if T μ1μ2⋅⋅⋅μn(x) is an n-index traceless, symmetric tensor density and S(x) is a density transforming as the spin-0 component of the infinite-dimensional representation, we find that Q transforms as the infinite sum S(x)+T(x)+T00(x)+T0000(x) +T000000(x)+⋅⋅⋅ .
Some character theory for groups of linear and antilinear operators
Authors: Newmarch J. D.
Published: March 2003

Elementary group concepts are recast into a form applicable to finite magnetic groups of linear and antilinear operators. Analogs of useful definitions for linear groups such as the Frobenius–Schur invariant, commutator subgroups, and ambivalent classes are considered. These are applied to the 180 magnetic single and double point groups and it is shown that only seven require independent treatment of characters.
Canonical structure of the CPn−12 model in some noncovariant gauges
Authors: Gozzi Ennio , Guha Arunabha
Published: March 2003

The canonical structure of the CPn−12 model is derived in four different noncovariant gauges using the Dirac method for constrained Lagrangian systems. A suitable quantization scheme is proposed for all n.
On a class of synchronized observers attached to the Lorentzian structures
Authors: Coll Bartolomé , Moreno Carlos
Published: March 2003

The first-order evolution form for the Klein–Gordon equation is characterized by an operator T(t) which, for inertial observers in the Minkowski space–time, is skew-self-adjoint with respect to the energy product. This fact is essential for a rigorous treatment of the equation. We prove here that, in arbitrary Lorentzian structures, there always exists a class of ‘‘synchronized observers’’ (equivalence class of physically admissible local charts), here called adjoint systems, for which this property of T(t) remains true. They are completely determined by the Lorentzian structure, and, in this sense, they appear as a suitable generalization of the Killing vector fields. We obtain the definition equations for such observers and state some of their properties. A particular class of them, here called simple adjoint systems, has already been introduced by one of us (C.M.) for the study of the Klein–Gordon equation in arbitrary space–times, according with Lichnerowicz’s quantization program.
The partial-wave projected Coulomb T matrix for all l in closed hypergeometric form
Authors: van Haeringen H.
Published: March 2003

We obtain relatively simple closed expressions for the partial-wave projections of the off-shell Coulomb T matrix in the momentum representation, 〈 p‖Tcl(k2)‖p′〉, for all l=0,1,2,⋅⋅⋅ . These exact analytic expressions consist of three parts: (i) ℱl, simple combinations of the Jacobi polynomial P(iγ,−iγ)l and the hypergeometric function 2F1(1,iγ;1+iγ;⋅), with different arguments [γ is Sommerfeld’s parameter; the Coulomb potential is Vc(r)=2kγ/r]; (ii) a polynomial ℰl; and (iii) ℒl=a polynomial times ln[( p+p′)2/( p−p′)2]. The polynomials under (ii) and (iii) are given in terms of the Jacobi polynomials P(m,−m)l , m=0,1,...,l. We derive interesting relations, especially valuable for the theory of off-shell Coulomb scattering, and we present simple closed expressions for the special cases l=0, 1, and 2; p′→k, p′→p, p′→∞, and γ→ 0.
Production of tachyons from Schwarzschild black holes
Authors: Srivastava Sushil K.
Published: March 2003

Inside the Schwarzschild surface the line element becomes spacelike. Hence, in the present paper, the Schwarzschild black hole is considered as a spherical world of tachyons. It is assumed that tachyons are present in this world in a superdense state. In this framework a spacelike line element for this world is derived. Moreover, the scalar wavefunction of a tachyon is obtained which satisfies the Klein–Gordon equation. Expressions for transmission and reflection coefficients of a scalar tachyon wave from a Schwarzschild surface are obtained. It is found that transmission and reflection coefficients are equal. Expressions for energy and momentum of a tachyon, emitted from a Schwarzschild black hole, are also obtained.
Eigenvalues of the Chandrasekhar–Page angular functions
Authors: Suffern Kevin G. , Fackerell Edward D. , Cosgrove Christopher M.
Published: March 2003

The Chandrasekhar–Page angular functions for the Dirac equation in the Kerr–Newman background are expanded as series of hypergeometric polynomials, and a three-term recurrence relation is derived for the coefficients in these series. This leads to a transcendental equation for the determination of the separation constant which is obtained initially as a power series and is then iterated by the method of Blanch and Bouwkamp.
SU(2)×SU(2) shift operators and representations of SO(5)
Authors: Hughes J. W. B.
Published: March 2003

SU(2)×SU(2) shift operators analogous to the SU(2) shift operators developed and used by the author for the classification and analysis of representations of Lie algebras in an SU(2) or SO(3) basis are obtained for the SU(2)×SU(2) Lie algebra in the case where one has an additional set of operators forming an irreducible four-dimensional tensor representation of SU(2)×SU(2). The shift operators obtained are used to treat the representations of SO(5) in an SU(2)×SU(2) basis.
On the relations between irreducible representations of the hyperoctahedral group and O(4) and SO(4)
Authors: Baake M. , Gemünden B. , Oedingen R.
Published: March 2003

In this paper we describe the relations between the irreducible representations of the hyperoctahedral group in four dimensions and irreducible, low-dimensional representations of the orthogonal groups O(4) and SO(4).
The general theory of R-separation for Helmholtz equations
Authors: Kalnins E. G. , Miller W.
Published: March 2003

We develop the theory of R-separation for the Helmholtz equation on a pseudo-Riemannian manifold (including the possibility of null coordinates) and show that it, and not ordinary variable separation, is the natural analogy of additive separation for the Hamilton–Jacobi equation. We provide a coordinate-free characterization of variable separation in terms of commuting symmetry operators.
Some infinite series of products of Legendre and gamma functions
Authors: van Haeringen H.
Published: March 2003

We derive closed expressions for some infinite series of products of Legendre functions and gamma functions. A particular series has been used to obtain the partial-wave projected quantum mechanical Coulomb transition matrix in closed analytic form for all partial waves, l=0, 1,⋅⋅⋅.
Expression for y
L
M[(r1Λr2)Λr3]
Authors: Antone T. A.
Published: March 2003

The solid harmonic yLM[(r1Λr2)Λr3] is expressed in terms of the spherical harmonics YL1M1(r̂1) , YL2M2(r̂2), and YL3M3(r̂3). The calculation of the coefficients in the given expansion in terms of 9−j symbols explicitly justifies the form given by yLM[(r1Λr2)Λr3] 𝒥L1L2L12L3LM1M2 A(L1,L2,L12,L3,L) ×〈L1,M1;L2,M2‖L1,L2,L12M12〉 ×〈L12,M12;L3,M3‖L12L3LM〉 ×YL1M1(r̂1)YL2M1(r̂2) ×YL3M3(r̂3).
Can poles change color?
Authors: Tafel Jacek , Trautman Andrzej
Published: March 2003

The definition of the total nonabelian charge (‘‘color’’) in a classical Yang–Mills theory is shown to require a careful analysis of the boundary conditions at infinity imposed on the potentials and on gauge transformations. The color current of a nonabelian plane wave is found to be different from zero in the transverse gauge, though it vanishes in the null gauge. The color charge of a single pole, described by the Liénard–Wiechert potentials, is constant by virtue of the Yang–Mills equations. An approximate computation indicates that the total color charge of a system of particles may change in time, as a result of radiation. To make this result meaningful, it is necessary to find a method of fixing the allowed gauge transformations to those having a direction-independent limit at infinity.
Inverse scattering for the reflectivity function
Authors: Gray Samuel H.
Published: March 2003

An inverse method for elastic, electromagnetic, or acoustic waves in a stratified half-space is presented. Rather than transforming the wave equation to one for which quantum inverse scattering methods can be applied in solving for a potential q(τ), we transform to one where it is suitable to solve for a ‘‘reflectivity function,’’ or local reflection coefficient, γ(τ). We show that γ(τ) can be discontinuous, thus improving a result of Balanis, and that discontinuities of γ(τ) match those of the impulse response R(t). We also show the relationship between the scattering kernel of this method and the scattering kernel of the quantum inverse scattering theory.
Cycle statistics of steady states for master-equation systems
Authors: Nakagomi Teruaki
Published: March 2003

A systematic graph theoretical treatment of steady-state master-equation systems is presented, in order to give a general formulation to Hill’s theory of cycle fluxes which characterizes the cyclic-action structure of open systems in nonequilibrium steady states accompanied by nonzero steady flows of energy or materials between the systems and their environments, such as laser actions or enzymatic reactions. In our formalism, a steady state is described by an ensemble of cycles C’s with each of which a probability current ω(C) and an occurrence probability u(C) are associated. A steady flow is expressed as an average over the cycles with ω(C), i.e., ∑C ω(C) ×(elementary flow generated in C). A similar cycle-average formula by u(C) is also given to state quantities. The Kirchhoff formula for steady states is also referred to.
Two-dimensional, steady-state diffusion of a passive scalar in a flow field
Authors: Turner Leaf , Bender Carl M.
Published: March 2003

The two-dimensional, steady-state equation governing the diffusion of a passive scalar field Ψ, ∇⋅(uΨ)=η∇2Ψ, is shown to yield a set of analytic solutions for η-independent flows u. For the case of vorticity flow, this equation can be reduced to an equation solved by Darboux. For the case of potential flow, a special class of solutions is found, of which that demonstrated by Matthaeus and Montgomery is a special case.
The problem of physical coordinates in predictive Hamiltonian systems
Authors: Iranzo V. , Llosa J. , Marqués F. , Molina A.
Published: March 2003

In the Hamiltonian formulation of predictive relativistic systems, the canonical coordinates cannot be the physical positions. The relation between them is given by the individuality differential equations. However, due to the arbitrariness in the choice of Cauchy data, there is a wide family of solutions for these equations. In general, those solutions do not satisfy the condition of constancy of velocities’ moduli, and therefore we have to reparametrize the world lines into the proper time. We derive here a condition on the Cauchy data for the individuality equations which ensures the constancy of the velocities’ moduli and makes the reparametrization unnecessary.
Homogeneous quadratic invariants for one-dimensional classical homogeneous quadratic Hamiltonians: Some properties of the auxiliary equation
Authors: Wollenberg L. S.
Published: March 2003

Using a previously derived characterization of the homogeneous quadratic invariants for an arbitrary one-dimensional classical homogeneous quadratic Hamiltonian we obtain various ‘‘nonlinear superposition laws.’’ We establish a close connection between one of these (the quadratic superposition law) and the original characterization.
Normal forms of elements of classical real and complex Lie and Jordan algebras
Authors: Djoković D. Ž. , Patera J. , Winternitz P. , Zassenhaus H.
Published: March 2003

Elements of the classical complex and real Lie and Jordan algebras with involutions are classified into conjugacy classes under the action of the corresponding classical Lie group. Normal forms of representatives of each conjugacy class are chosen so as to resemble the Jordan normal forms of n×n complex matrices. For completeness similar results are given for gl(n,C), gl(n,R), and gl(n,H).
Large coupling behavior of the energy eigenvalues of two anharmonic oscillators
Authors: Isaacson David
Published: March 2003

We give two methods for calculating the behavior of the energy levels of H≡(1/2){−∂2x−∂2y +g[(x2−a2)2+(y2−a2)2]+b(x−y)2} as the coupling constant g goes to infinity.
Time delay for long-range interactions
Authors: Bollé D. , Gesztesy F. , Grosse H.
Published: March 2003

We discuss the concept of time delay and its relation to the S matrix for quantum mechanical scattering with potentials of the form V(r)=γ/r+(α− 1/4)/r2 +Vsc (r). The spherically symmetric interactions Vsc (r) are allowed to be O(r−2−ε) at infinity and O(r−2+ε) at zero. This improves considerably the existing results in the literature where the total V(r) is required to be O(r−5/2−ε) at infinity. We study pure Coulomb time delay, relative time delay with respect to the long-range part γ/r+(α− 1/4)/r2 of the interaction, and total time delay. The corresponding results in classical scattering are also derived.
Time-dependent vector constants of motion, symmetries, and orbit equations for the dynamical system r̈=îr{[Ü(t)/U(t)]r −[μ/U(t)]r−2}
Authors: Katzin Gerald H. , Levine Jack
Published: March 2003

The most general time-dependent, central force, classical particle dynamical systems (in n-dimensional Euclidean space, n=2 or 3) of the form (a) r̈=îr F(r, t), (r2≡r ⋅ r, r=îkxk, k=1,...,n), which admit vector constants of motion of the form (b) I=U(r, t)(L×v)+Z(r, t)(L×r) +W(r, t)r (L≡r×v, v≡ṙ) are obtained. It is found that the only class of such dynamical systems is (c) r̈=îr(ÜU−1r−μ0U−1r−2), for which the concomitant vector constant of motion (b) takes the form (d) I=U(L×v)−U̇(L×r)+μ0r−1r, where in (c) and (d) U=U(t) is arbitrary (≠0). The dynamical system (c) includes both the time-dependent harmonic oscillator and a time-dependent Kepler system. Based upon infinitesimal velocity-independent mappings the complete symmetry group for the dynamical system (c) is obtained. This complete group of [2+n(n−1)/2] parameters contains a complete Noether symmetry subgroup of [1+n(n−1)/2] parameters. In addition to the n(n−1)/2 angular momenta, there is an energy-like constant of motion also associated with the Noether symmetries. By means of the vector constant of motion (d), the orbit equations of the dynamical system (c) are obtained. A one-dimensional procedure for obtaining constants of motion developed by Lewis and Leach is applied to the effective one-dimensional system concomitant to (c). Relations between constants of motion so obtained and those mentioned above are determined.
Deformation of Hamiltonian dynamics and constants of motion in dissipative systems
Authors: Taborda Duarte J. , Vilela Mendes R.
Published: March 2003

A necessary condition for the existence of arcs of vector fields with constants of motion is found. The result is applied to arcs obtained by deformation of Hamiltonian dynamics and illustrated in the Van der Pol and Lorenz models.
The initial value formulation of higher derivative gravity
Authors: Noakes David R.
Published: March 2003

The initial value problem is considered for the conformally coupled scalar field and higher derivative gravity, by expressing the equations of each theory in harmonic coordinates. For each theory it is shown that the (vacuum) equations can take the form of a diagonal hyperbolic system with constraints on the initial data. Consequently these theories possess well-posed initial value formulations.
The local nonsingularity theorem
Authors: Geroch Robert
Published: March 2003

It is proven that, for a certain class of hyperbolic systems (a class which includes Einstein’s equation), sufficiently small initial data on a bounded patch of initial surface generates a solution nonsingular in the region determined by that initial data. This theorem is virtually a corollary of the boost theorem. Various consequences and possible generalizations are discussed.
The occupation statistics for indistinguishable dumbbells on a 2×2×N lattice space
Authors: Hock J. L. , McQuistan R. B.
Published: March 2003

A 20-term recursion relation is derived that describes exactly the occupation statistics for indistinguishable dumbbells (which occupy two nearest neighbor sites) distributed on a 2×2×N lattice space. On the basis of this recursion, the normalization, expectation, dispersion, and continuous representation of the statistics are also developed. When the lattice space is completely filled, the recursion relationship reduces to four terms, permitting a calculation of the orientational degeneracy of a completely filled 2×2×N lattice space.
Field theory models in the scattering picture
Authors: Farrukh M. O.
Published: March 2003

We propose general schemes for constructing quantum field theory models in the scattering picture. Our models include two types: those which are related to classical pure potential theories and those which are related to conventional quantum field theories. We also discuss the problem of symmetry breaking, and show how to avoid ultraviolet divergencies.
Splitting of the connection in gauge theories with broken symmetry
Authors: Fulp R. O. , Norris L. K.
Published: March 2003

We obtain a fully geometric analog of the Higgs mechanism whereby a symmetry-breaking Higgs field is used to impart mass to gauge fields. We do this by showing that under fairly general hypotheses a symmetry-breaking Higgs field φ on a ‘‘principal bundle with connection’’ (P,ω) allows the decomposition of the connection ω into a pair (ω′,τ) where ω′ is a connection on P that reduces to a φ-subbundle of P and where τ is a tensorial field on P. The gauge fields that remain massless are identified with the components of ω′ while the gauge fields that acquire mass are identified with the components of τ. This decomposition of the connection is exploited in the case where the group of the bundle is the conformal group which scales some fixed metric of arbitrary signature. The geometry of such a bundle with connection generalizes Weyl geometry and provides a bundle setting for conformal gauge theories. We then show that the Weinberg–Salam electroweak theory can be recast as a conformal gauge theory. A primary feature of our conformal version of the Weinberg–Salam theory is that it provides a geometrical interpretation of the surviving component of the Higgs scalar field as an infinitesimal conformal factor.
Casimir invariants, characteristic identities, and tensor operators for ‘‘strange’’ superalgebras
Authors: Jarvis P. D. , Murray M. K.
Published: March 2003

We define a class of (super) subalgebras of gl(m/n) realized as the set of fixed points of a (graded) endomorphism of gl(m/n). This class includes the superalgebras gp(m) and gq(m) [related to the so-called ‘‘strange’’ simple superalgebras p(m) and q(m)], as well as osp(m/n). General covariant, contravariant, and mixed tensor operators are defined for this class in terms of appropriate module homomorphisms. Traces of certain tensors give the usual sequence of Casimir invariants. For gp(m), these are shown to vanish identically, while for gq(m), eigenvalues of the quadratic and cubic Casimir invariants are derived in terms of highest weights and a polynomial characteristic identity is exhibited.
On the group structure, GKS and FKG inequalities for Ising models
Authors: Baumgartner Bernhard
Published: March 2003

The FKG inequality is applied to a lattice of states of the Ising model which are related to subgroups of the group of spin variables. The resulting correlation inequalities ar exactly the GKS inequalities.
A generalization of the proof of the triviality of scalar field theories
Authors: Hattori Tetsuya
Published: March 2003

The proof of the triviality of φ4 theory in d>4 dimensions is generalized. We show that the triviality of scalar field theories holds for a wide class of potentials.
Static conformally invariant scalar field
Authors: Accioly A. J. , Vaidya A. N. , Som M. M.
Published: March 2003

For a massless conformally invariant scalar field, a class of solutions is obtained to the Einstein equations for which the geometry of the space-time admits one timelike and two spacelike Killing vectors. The class of solutions admit plane-symmetric and conformally flat solutions as special cases. The metrics can be interpreted as static cylindrically symmetric solutions if one of the spacelike Killing vectors is associated with the rotational motion.
Application of nonlinear operator theory to the Edwards–Freed equations in the theory of polymer solutions
Authors: Yoshimura Tetz
Published: March 2003

Mathematical structure of nonlinear integral equations for ‘‘screened hydrodynamic interaction’’ and ‘‘self-energy’’ in the static version of Edwards and Freed’s theory of polymer solutions with finite concentrations are analyzed and it is shown that algorithms developed by Lika and Altman for nonlinear operator equations without Fréchet differentiability are applicable. Recipes for successive approximations are presented and questions to be investigated by those techniques are proposed.
The asymptotic evaluation of a class of path integrals. II
Authors: Luttinger J. M.
Published: March 2003

The asymptotic behavior of a class of Wiener-like path integrals (functions of the ‘‘local time’’) is determined. These integrals are of interest in themselves and also arise very naturally in the theory of disordered systems. We show that by making use of a Grassman algebra (i.e., a set of anticommuting variables), the earlier treatment of this problem can be greatly simplified. In particular, the previous use of ‘‘replica trick’’ (which involves a difficult to justify analytic continuation in the number of field components) is thus avoided.
Tensorial analysis of the hyperfine interaction operator by extensive use of Racah algebra and of translational invariance
Authors: Bréhamet Lionel
Published: March 2003

S t r i c t application of Racah algebra gives an efficient way of deriving the tensorial form of the hyperfine interaction one-electron operator involved in NMR spin coupling effects. In particular, this procedure avoids the use of classic explicit arguments of integration around the origin to find the Fermi-contact term. The linear momentum is retained in its explicit translationally invariant form as long as possible during the calculations. This allows the tensorial expansion of the operator to be obtained rapidly at any origin of coordinates. The reduced matrix elements of interest are given by new general closed expressions in the j−j coupling scheme.
A new approach to perturbation theory: star diagrams
Authors: Houard J. C. , Irac-Astaud M.
Published: March 2003

Perturbation theory for first-order nonlinear differential equations with source is developed in a new way, and associated with diagrams that we call star diagrams. In some cases the method allows one to express the n-point functions in explicit form.
A simple proof of a particular case of C. Siegel’s center theorem
Authors: de la Llave R.
Published: March 2003

We give an elementary proof of a particular case of C. Siegel’s center theorem, based on a method of M. Herman. Even if the proof has less generality than the standard one, it is simpler and provides sharper bounds.
Measure for measure: Covariant skeletonizations of phase space path integrals for systems moving on Riemannian manifolds
Authors: Kuchař Karel
Published: March 2003

We define phase space path integrals for systems moving on a Riemannian manifold and subject to a generalized potential by a skeletonization procedure which is manifestly covariant under point transformations. We achieve this goal by introducing a natural analog S(x″,t″‖x′,p′,t′) of the Hamilton principal function with phase space initial data. One class of such functions is based on the parallel transport of momentum, a second class is obtained by a modification of the first class, and a third class is based on the geodesic deviation transport of momentum. The third class of principal functions is geometrically privileged. We skeletonize the canonical action integral by replacing it by a manifestly covariant chain of phase space principal functions. Different functions lead to the same functional as we infinitely refine the skeletonization along a smooth path. Our phase space path integral is always taken with the natural Liouville measure, but the integration over momentum variables brings down a nontrivial measure to the remaining configuration space path integral. Because nondifferentiable rather than smooth paths dominate the path integral, different phase space principal functions generate different configuration space path measures. Such measures lead to quantum propagators which satisfy Schrödinger’s equations with all possible scalar curvature terms ∼ℏ2R. The geometrically privileged phase space principal function (based on the geodesic deviation transport) leads to the Schrödinger equation without any curvature term.
The Gel’fand–Levitan equation on a finite interval
Authors: Moses Harry E. , Prosser Reese T.
Published: March 2003

It is shown here, by using the methods of Gel’fand and Levitan, that one may alter in certain ways the spectral data (eigenvalues and normalizations) of the Schrödinger equation for a finite interval, by suitably altering the potential. These alterations include the deletion and insertion of a finite number of eigenvalues and/or renormalization of a finite number of eigenfunctions. The deletion of an eigenvalue requires the addition of a singular potential, while the insertion of an eigenvalue requires an adjustment of the boundary conditions resulting in a non-self-adjoint operator. Similarly the insertion of a continuous spectrum leads to non-self-adjoint operators. The non-self-adjoint operators have, nevertheless, complete sets of eigenfunctions and a corresponding spectral decomposition in a suitable subspace.
A new approach to permutation group representations. II
Authors: Zhu Cheng-Jiu , Chen Jin-Quan
Published: March 2003

The formula for the Yamanouchi matrix elements is rederived by the eigenfunction method in a simple fashion.
The geometric theory of deformation and linearization of Pfaffian systems and its applications to system theory and mathematical physics. I
Authors: Hermann Robert
Published: March 2003

Many physical and engineering problems lead to the study of the qualitative and geometric properties of differential equations and their solutions as a function of exogeneous parameters. The theory of deformation of geometric structures and pseudogroups initiated by K. Kodaira and D. C. Spencer deals with the common mathematical structure underlying these problems. This series of papers will adapt the work in the pure mathematics literature to the needs of the applications, with the emphasis on the theory of deformations of Pfaffian systems. The applied area to be emphasized in this first part is the theory of nonlinear input–output systems. I will also present the abstract algebraic structure which seems to underlie the theory of Pfaffian systems, which I call Cartan–Vessiot filtrations of Lie algebras.
Operators for the two-dimensional harmonic oscillator in an angular momentum basis
Authors: Òdúndún Olúwolé
Published: March 2003

The forms of the operators ν°, ν, λ°, λ, which enable one to write the Hamiltonian of the two-dimensional isotropic harmonic oscillator in the form H=ℏω(2ν°ν+λ°⋅λ+1), are presented. Here ν° and ν are, respectively, the raising and lowering operators for ν°ν, the ‘‘radial’’ quantum number operator, while λ° and λ are, respectively, the raising and lowering operators for M, the magnitude of the angular momentum operator. Corresponding to this decomposition of H in the angular momentum basis are the energy eigenvalues Ekm=ℏω(2k+‖m‖+1) with k=0, 1, 2, ⋅⋅⋅ and m=0, ±1, ±2, ⋅⋅⋅. Here k is a ‘‘radial’’ quantum number, and m is a ‘‘magnetic’’ quantum number. The commutation relations satisfied by the operators ν°, ν, λ°, and λ are also presented.
Symmetric Hadamard series
Authors: Brown M. R.
Published: March 2003

In a general curved space–time, the requirements that the Feynman Green’s function be symmetric and have the Hadamard form are shown to result in specific constraints on the local behavior of the function. These constraints are solved yielding a general form for the function.
Twenty-four optimal inequalities and several new representations for the Coulomb T matrices in momentum space
Authors: van Haeringen H.
Published: March 2003

We derive new series and integral representations for the Coulomb transition matrix in momentum space, 〈p‖Tc‖p′〉, and for its partial-wave projections, 〈p‖Tcl‖p′〉 (l=0,1,...), to be denoted by Tc and Tcl, respectively. We also consider hypergeometric-function representations for Tc and Tcl and discuss their analytic continuation to the whole complex k plane (k2 is the energy). The new integrals are essentially ∫π0 cosh γt (ρ−cos t)−1 dt for Tc and ∫π0 cosh γt ×Ql(uu′+vv′ cos t)dt for Tcl, where γ is Sommerfeld’s parameter and ρ,u,u′,v, and v′ are variables depending on the energy and the momenta; related integrals follow from these. A well-known and convenient series representation for Tc consists essentially of the sum ∑nyn(n2+γ2)−1, where y depends on the energy and the momenta. We derive its analog for Tcl, the corresponding sum being ∑n(n2+γ2)−1Qnl(u) P−nl(u′), 1<u′<u. This sum is a new member of the family of sums of products of Legendre functions that can be evaluated in a relatively simple closed form; other members of this family have been recently obtained by the author. With the new representations for Tc and Tcl we derive a set of twenty-four optimal inequalities (containing two conjectured inequalities) for these Coulomb T matrices, presumably covering all cases relevant for physics. For the proof of these inequalities several different representations, and in particular the newly derived ones, would appear to be indispensable. Many of the inequalities are new. They are valid for fixed real Coulomb strength and fixed real energy≠0. Because of the complexity of exact closed forms for Tc and Tcl, approximations are needed for numerical calculations; the most natural one consists of replacing the Coulomb T matrix by the Coulomb potential. Our inequalities are useful for estimating the accuracy of this approximation.
New inequalities for the Coulomb T matrix in momentum space
Authors: van Haeringen H. , Kok L. P.
Published: March 2003

We present and prove new inequalities for the momentum representation (i) of the full Coulomb transition operator Tc, and (ii) of its partial-wave projections, Tcl, for all l=0, 1, ... . Also, a previously conjectured inequality is proved: ‖Tc/Vc‖>1, under certain conditions. These inequalities are useful for gaining insight into the—very convenient, and often proposed in the context of three-particle calculations—approximation in which the Coulomb transition operator is replaced by the Coulomb potential operator. Such an approximation is obviously not accurate at any zero of the T matrix. We investigate the zeros of 〈p‖Tc‖p′〉 for positive energy, and we give simple approximation formulas for these zeros.
Static spherically symmetric solutions in a general class of scalar tensor theories
Authors: Banerjee A. , Dutta Choudhury S. B. , Banerjee N.
Published: March 2003

The problem of the gravitational field due to a point mass, charged or uncharged, is completely solved within the framework of a general class of scalar tensor theories proposed by Nordtvedt. In Nordtvedt’s theory the parameter ω can be an arbitrary function of the scalar field. Different exact solutions are obtained for different functional forms of ω both in the presence and absence of charge. All these solutions including a few already existing in the literature are given in a systematic manner and their asymptotic behavior is studied.
An equivalence class of quantum field theories at finite temperature
Authors: Matsumoto H. , Nakano Y. , Umezawa H.
Published: March 2003

It is shown that there exists a certain equivalence class of quantum field theories at finite temperature each of which produces the same statistical averages. The theories in this equivalent class are classified by multiplicities of field degrees of freedom and have a one to one correspondence with the choices of the path in the real-time path-ordered formulation of the statistical average. Among them, thermo field dynamics is found to be the most convenient theory.
Eigenvalues and degeneracies for n-dimensional tensor spherical harmonics
Authors: Rubin Mark A. , Ordóñez Carlos R.
Published: March 2003

Symmetric transverse traceless tensor harmonics of arbitrary rank are constructed on spheres Sn of dimensionality n≥3, and the associated eigenvalues of the Laplacian are computed. It is shown that these tensor harmonics span the space of symmetric transverse traceless tensors on Sn and are eigenfunctions of the quadratic Casimir operator of the group O(n+1). The dimensionalities of the eigenspaces of the Laplacian are computed for harmonics of rank 1 and rank 2.
The shift operator technique for SO(7) in an [SU(2)]3 basis. II. Applications
Authors: De Wilde P. , Van der Jeugt J.
Published: March 2003

Reduced matrix elements of the tensor operator which forms part of SO(7) generator basis are calculated for the three respective classes of SO(7) representations [v,0,0], v∈N0, [v,0,1], v∈N0, [0,0,v], v∈N0. The calculation is based on the relations between quadratic products of shift operators, established in a previous paper by the same authors.
Chain models and their effective Hamiltonians
Authors: Znojil M.
Published: March 2003

We develop a new formalism suitable for diagonalization of Hamiltonians with 2t+1 nonzero diagonals (chain models). In a systematic perturbation-like way, we get the expansions of Green and/or wave functions. They are generated by solution of a sequence of ‘‘fixed-point‘‘ quadratic equations for (t×t)-dimensional matrices. For t=1 and t=2, this solution is feasible by elementary means, so that the respective tridiagonal and pentadiagonal chain models may be considered exactly solvable in this context. In an alternative first-order variational-perturbation formulation, the method may provide the simultaneous upper and lower energy bounds for any t.
Application of double Gel’fand polynomials to the symmetric group and spin–isospin wave functions of cluster systems
Authors: Fujiwara Y. , Tang Y. C. , Horiuchi H.
Published: March 2003

The theory of double Gel’fand polynomials is applied to irreducible representations of the symmetric and SU4 groups with the aim to treat spin–isospin wave functions of nuclear cluster systems. Multiplicity-free recoupling coefficients of the symmetric group are connected with special types of Clebsch–Gordan coefficients of the unitary group. The standard phase conventions of the Yamanouchi basis and of the multiplicity-free recoupling coefficients are proved to be derivable from natural phase conventions of double Gel’fand polynomials and these special Clebsch–Gordan coefficients. By extending the concept of double Gel’fand polynomials, useful expansion formulas are derived with respect to the determinant associated with a matrix tensor product. A simple example of their application is given for normalization kernels of two-body systems composed of s-shell clusters and for SU4 Clebsch–Gordan coefficients in the spin–isospin representation needed therein.
Some integrals involving three Bessel functions when their arguments satisfy the triangle inequalities
Authors: Gervois A. , Navelet H.
Published: March 2003

We calculate definite integrals involving three Bessel functions of the form ∫∞0xJμ(ax)Jν(bx) Jμ+ν(cx)dx and ∫∞0xYμ(ax)Jν(bx) Jμ+ν(cx)dx, which appeared in some absorption calculations. Results are given for all relative positions of lengths a, b, c. They complete formulas outside the triangle case and correct some misprints given in tables.
Electrodynamics of memory-dependent nonlocal elastic continua
Authors: Eringen A. Cemal
Published: March 2003

Balance laws and constitutive equations are given for elastic continua with memory of past motions and electromagnetic fields. Nonlinear, finite-linear, and linear constitutive equations are obtained and restricted by the second law of thermodynamics. Memory-dependent nonlocal piezoelectricity, piezomagnetism, heat and electric conduction, viscoelasticity, and other allied physical phenomena are in the domain of the general theory. The theory is applied to discuss infrared dispersion and lattice vibrations, natural optical activity, anomalous skin effect, and superconductivity, indicating the power and the potential of the nonlocal theory.
Anisotropic fluids and conformal motions in general relativity
Authors: Herrera L. , Jiménez J. , Leal L. , Ponce de León J. , Esculpi M. , Galina V.
Published: March 2003

We study the consequences of the existence of a one-parameter group of conformal motions for anisotropic matter, in the context of general relativity. It is shown that for a class of conformal motions (special conformal motions), the equation of state is uniquely determined by the Einstein equations. For spherically symmetric and static distributions of matter we found two analytical solutions of the Einstein equations which correspond to isotropic and anisotropic matter, respectively. Both solutions can be matched to the Schwarzschild exterior metric and possesses positive energy density larger than the stresses, everywhere within the sphere.
Probability measures and Hamiltonian models on Bethe lattices. II. The solution of thermal and configurational problems
Authors: Peruggi Fulvio
Published: March 2003

In a previous paper we introduced a method for the construction of rotationally and translationally invariant probability measures generated by one-step Markov Hamiltonian models on q-state-site Bethe lattices. Here, the corresponding thermal problems are solved by finding the relative free energy, which gives complete information on the properties of the models under study. Configurational problems also can be solved with the present tools. As an example, the solution of polychromatic correlated-site/random-bond percolation models is found.
Structure and representations of the hyperoctahedral group
Authors: Baake M.
Published: March 2003

In this paper, the main properties of the symmetry group of the n-dimensional cube are reviewed and formulated with respect to possible applications in lattice theories. The connection between the hyperoctahedral group Wn and the orthogonal group O(n) is investigated by means of the canonical representation.
Color analysis, variational self-adjointness, and color Poisson (super)algebras
Authors: Trostel Robert
Published: March 2003

After stating some facts concerning the calculation with ‘‘color variables’’ we cite some recent results of the author with respect to the color analytic extension of variational principles, self-adjointness, and Heisenberg commutation relations. As an apparent novelty, we then present the color analytic version of the Hamiltonian formalism including the construction of color Poisson brackets leading to a color (super)algebra with color derivation property.