bluuebunny/crossref_metadata_2025 huggingface dataset:
Covariant n2-plet mass formulas
Authors: Davidson A.
Published: March 2003

Using a generalized internal symmetry group analogous to the Lorentz group, we have constructed a covariant n2-plet mass operator. This operator is built as a scalar matrix in the (n;n*) representation, and its SU(n) breaking parameters are identified as intrinsic boost ones. Its basic properties are: covariance, Hermiticity, positivity, charge conjugation, quark contents, and a self-consistent n2−1, 1 mixing. The GMO and the Okubo formulas are obtained by considering two different limits of the same generalized mass formula.
A critique of the major approaches to damping in quantum theory
Authors: Greenberger Daniel M.
Published: March 2003

We examine the two major approaches that have been suggested for the quantum mechanical treatment of the damped motion of a particle as a one-body problem. These are the linear, but time dependent, Kanai Hamiltonian, and the more recent nonlinear potentials which have been introduced to simulate the damping force. The most important criticism that has been leveled at the Kanai Hamiltonian is that its solutions seem to violate the uncertainty relations. We show that this Hamiltonian actually represents a particle of variable mass, whose classical behavior is identical to that of a damped particle of constant mass. But quantum mechanically, its changing mass does lead to unphysical behavior when misinterpreted as a constant mass particle. So this Hamiltonian cannot directly describe a constant mass damped quantum particle. The nonlinear model has been interpreted in terms of the hydrodynamical analogy of quantum theory, and a well behaved decaying wavepacket solution has been produced. However we generalize this result to produce solutions that ’’decay’’ to arbitrarily high energy. Thus it is not clear that this model specifically treats dissipation. Rather it seems to seek out any stationary state. At any rate, its physical interpretation is obscure at present. However we show, by analyzing the physical problem of damping at low energies, that one can modify the Kanai Hamiltonian to eliminate its unphysical features, so that this modified Kanai Hamiltonian can in fact be interpreted as representing a constant mass damped particle with physically reasonable solutions.
A new approach to the problem of dissipation in quantum mechanics
Authors: Greenberger Daniel M.
Published: March 2003

The usual treatment of damping forces in quantum mechanics starts from the introduction of the explicitly time dependent Kanai Hamiltonian, which actually represents a variable mass particle, and the misinterpretation of this Hamiltonian as representing a particle of constant mass leads to certain physical difficulties. However the Hamiltonian can be modified so that it can be reinterpreted as describing a constant mass particle. Here we explicitly introduce the mass as a new dynamical variable, which allows us to write a linear, time independent Hamiltonian for the system, which can be solved by conventional methods. The damped harmonic oscillator and damped free particle are treated in detail, both for the Kanai Hamiltonian and for our case, and the solutions are compared. Our solution can be reduced to the Kanai one in appropriate circumstances, but in general it has a much greater versatility, as a result of which it can be more easily reinterpreted as describing a constant mass particle subject to a damping force, which reinterpretation is of course necessary if the method is to have practical applicability. We also show how such a reinterpretation can be carried out in detail by introducing a ’’dissipation variable’’, in terms of which one may avoid the concept of a variable mass altogether.
Upper bounds for the many-channel Marchenko transformation operator and its derivatives
Authors: Rochus Pierre
Published: March 2003

We specify the class of perturbative complex matrix potentials for which the corresponding many-channel Marchenko type transformation operators are bounded and integrable. Our reference matrix potential contains Coulomb interactions, different threshold energies, and centrifugal potentials with different angular momenta. Estimates for the transformation operator and its derivatives are obtained; they enable us to improve our recent results and are necessary for the establishment of a unique solution to the ’’generalized Marchenko fundamental equation.’’ From the existence of an integrable transformation operator, the analyticity of the Jost solution as a function of k1 is deduced in the upper-half of the physical k1 plane.
On conserved quantities in general relativity
Authors: Ashtekar Abhay , Magnon-Ashtekar Anne
Published: March 2003

Recently, definitions of total 4-momentum and angular momentum of isolated gravitating systems have been introduced in terms of the asymptotic behavior of the Weyl curvature (of the underlying space–time) at spatial infinity. Given a space–time equipped with isometries, on the other hand, one can also construct conserved quantities using the presence of the Killing fields. Thus, for example, for stationary space–times, the Komar integral can be used to define the total mass, and, the asymptotic value of the twist of the Killing field, to introduce the dipole angular momentum moment. Similarly, for axisymmetric space–times, one can obtain the (’’z-component’’ of the) total angular momentum in terms of the Komar integral. It is shown that, in spite of their apparently distinct origin, in the presence of isometries, quantities defined at spatial infinity reduce to the ones constructed from Killing fields. This agreement reflects one of the many subtle aspects of Einstein’s (vacuum) equation.
The scaling limit of the φ2 field in the anharmonic oscillator
Authors: Marchesin Dan
Published: March 2003

We prove that the rescaled and renormalized q2 process for Hg=[p2+gq4+(1−g) q2]/2 tends to the Gaussian process for the Harmonic oscillator as g tends to infinity.
A general setting for reduction of dynamical systems
Authors: Marmo G. , Saletan E. J. , Simoni A.
Published: March 2003

The reduction of dynamical systems is discussed in terms of projecting vector fields with respect to foliations of the manifold on which the dynamics take place. Examples of established reduction procedures are presented and are shown to be special cases of the general procedure described in this paper. Instances of other types of analysis of dynamical systems related to our projection procedure are briefly discussed.
Generalized susceptibility of a solitary wave
Authors: Lee K. C. , Trullinger S. E.
Published: March 2003

We define a generalized susceptibility for solitary wave solutions of the nonlinear Klein–Gordon equation and obtain its expression in terms of the complete set of functions which arise in the linear stability analysis of the solitary wave. Explicit expressions are presented for the susceptibility of the sine-Gordon soliton and the φ4 kink. Plots are presented for the long-wave dynamic polarizability of the φ4 kink which have application to the response of ferroelectric domain walls to an oscillating external electric field.
Petrov type N vacuum metrics and homothetic motions
Authors: Halford W. D.
Published: March 2003

Petrov type N vacuum spaces which admit an expanding and/or twisting principal null congruence and a homothetic motion are considered. It is shown that there are no such spaces which admit two Killing vectors, or one Killing vector of special type. If there are no Killing vectors present, the form of the homothetic Killing vector is restricted to one possibility.
Time delay in N-body scattering
Authors: Bollé D. , Osborn T. A.
Published: March 2003

We extend the theory of time delay to N-body scattering. The known results relating time delay to the S matrix in the two-body and three-body problem suggest that these relationships are universal. Within the context of two-Hilbert space N-body scattering theory an abstract definition of time delay is provided. For all scattering processes initiated by the collision of two clusters a simple proof is constructed establishing the connection of time delay to the on-shell S matrix and its energy derivatives. The definition of time delay and method of proof given here are compared with earlier approaches used in the three-body problem.
The spectral properties of many-electron atomic Hamiltonians and the method of configuration interaction. III. Compactness proof associated with an infinite system of linear equations for n-electron atoms
Authors: Choudhury M. H.
Published: March 2003

An infinite system of linear equations is derived from the Schrödinger equation of an n-electron atomic system (n⩾3). The linear operator defined by this system of equations is then shown to be compact in a region of the complex energy plane which excludes the various bound state and multiparticle scattering cuts (i.e., the essential spectrum of the Hamiltonian of the n-electron atomic system). It is further shown that the method can be used to deal with the case of the diatomic molecule. The above result then permits one, both in the case of the n-electron atomic system and the diatomic molecule, to truncate the infinite system of equations in question with the assurance that as the size of the truncated system is increased, the energy eigenvalues computed from the truncated system will uniformly converge to those of the original infinite system.
Yet another formulation of the Einstein equations for stationary axisymmetry
Authors: Cox Dale , Kinnersley William
Published: March 2003

We rewrite Einstein’s equations for stationary axially symmetric gravitational fields, using a pair of noncanonical, intrinsically-defined coordinates. We show that both field equations of the Ernst formulation of this problem can be solved identically, by means of a new superpotential K. One more field equation remains to be satisfied, however. It can be expressed as a single fourth-order equation for K, or as a pair of coupled second-order equations. The approach works equally well for the wave metrics one can get from the stationary case via complex coordinate transformations. We illustrate our method by using it to derive a new class of wave solutions.
A relativistic Lee model
Authors: de Dormale Bernard M.
Published: March 2003

We construct a fully relativistic version of the Lee model in the S (1,1) sector.
Global properties of systems quantized via bundles
Authors: Doebner H. D. , Werth J. -E.
Published: March 2003

Take a smooth manifold M and a Lie algebra action (g action) ϑ on M as the geometrical arena of a physical system moving on M with momenta given by ϑ. We propose to quantize the system with a Mackey-like method via the associated vector bundle ξρ of a principal bundle ξ= (P,π,M,H) with model dependent structure group H and with G-action φ on P lifted from ϑ on M. This (quantization) bundle ξρ gives the Hilbert space ℋ=L2(ξρ,ω) of the system as the linear space of sections in ξρ being square integrable with respect to a volume form ω on M; the usual position operators are obtained; φ leads to a vector field representation D (φρ,ϑ) of g in ℋ and hence to momentum operators. So ℋ carries the quantum kinematics. In this quantization the physically important connection between geometrical properties of the system, e.g., quasicomqleteness of ρ and G maximality of φρ, and global properties of its quantized kinematics, e.g., skew-adjointness of the momenta and integrability of D (φρ,ϑ) can easily be studied. The relation to Nelson’s construction of a skew-adjoint nonintegrable Lie algebra representation and to Palais’ local G actions is discussed. Finally the results are applied to actions induced by coverings as examples of nonmaximal φρ on Eρ lifted from maximal ϑ on M which lead to direct consequences from the corresponding quantum kinematics.
Integral bounds for N-body total cross sections
Authors: Osborn T. A. , Bollé D.
Published: March 2003

We study the behavior of the total cross sections in the three- and N-body scattering problem. Working within the framework of the time-dependent two-Hilbert space scattering theory, we give a simple derivation of integral bounds for the total cross section for all processes initiated by the collision of two clusters. By combining the optical theorem with a trace identity derived by Jauch, Sinha, and Misra, we find, roughly speaking, that if the local pairwise interaction falls off faster than r−3, then σtot(E) must decrease faster than E−1/2 at high energy. This conclusion is unchanged if one introduces a class of well-behaved three-body interactions.
Internal Galilei group for a two-particle system
Authors: Daumens M. , Perroud M.
Published: March 2003

Two variable expansions of Galileian scattering amplitudes are proposed for a two-particle system with arbitrary spins. The barycentric decomposition of such a system permits, on the one hand, to realize the associated Hilbert space in the form ℋ=L2(R3)  ⊗ ℋINT, where ℋINT is the Hilbert space of the states of the system expressed in their CM frame, and, on the other hand, to introduce what we call the internal Galilei group G (3)INT as the maximal subgroup in G (3) ×G (3) which respects the barycentric decomposition. For this group we have a natural unitary representation acting on ℋINT induced by the PIUR of G (3) ×G (3) acting on ℋ. The reduction of this representation with respect to the chain of subgroups G (3)INT ⊆E (3)INT ⊆ SU(2) ⊆ SU(1) provides the usual one variable expansions while the reduction with respect to the chain G (3)INT ⊆G (3)0INT ⊆ SU(2) ⊆ SU(1) provides an example of a two variable expansion.
Conserved densities for nonlinear evolution equations. I. Even order case
Authors: Abellanas L. , Galindo A.
Published: March 2003

This paper is a first attempt to analyze in detail the number and structure of nontrivial polynomial conserved densities for a nonlinear evolution equation ut=P, P an arbitrary polynomial in the spatial derivatives of u. Our attention is here focused on the even order case, where stronger conclusions can be derived. Several criteria for nonexistence of conserved densities are afforded. The coexistence of conserved densities is shown to severely restrict both the evolution equation and the functional structure of such densities. Finally for the case of second order equations the problem is completely worked out.
Integral representation for the dimensionally regularized massive Feynman amplitude
Authors: Bergère M. C. , David F.
Published: March 2003

A convergent integral representation for the massive Feynman amplitude in complex dimension D is defined away from ReD equal to some rationals. The Feynman integrand is modified according to the technique of Zimmermann’s forests but each subgraph is subtracted at zero external momenta and zero internal masses; the order of the Taylor subtractions depends upon ReD. The so defined regularized Feynman amplitude is a meromorphic function of D with multiple poles at some rationals, which satisfies field equations and Ward identities. These amplitudes may be used in the construction of a bare Lagrangian field theory.
An algorithm to construct evolution equations with a given set of conserved densities
Authors: Galindo A.
Published: March 2003

This paper provides a simple formula to construct evolution equations ut=f (u,ui,uij,⋅⋅⋅) having a prescribed finite set {ρ(1), ρ(2),⋅⋅⋅,ρ(N)} amongst its conserved densities. Besides its usefulness as a constructive algorithm, such a formula can also yield valuable information on the structure of the set 𝒞 (f) of all conserved densities under a given evolution equation ut=f.
New expressions for the eigenvalues of the invariant operators of O(N) and Sp(2n)
Authors: Nwachuku C. O.
Published: March 2003

In the spirit of the recent work of Popov for u(n), we derive a direct expansion of the eigenvalues of the invariant operators Cp for the orthogonal and symplectic groups in terms of the power sums with completely specified coefficients βp(ν), which are easy to compute. The resulting expression, which is a complete analog of the u(n) results, is closed, simple and manifests the general structure of the Cp. It is now possible to say for what value of p a particular combination of the Sk’s begin to appear. Explicit applications of these results in computing the Cp for p<8 illustrate fully their simplicity. Thus our work simplifies and unifies the treatment of this aspect of the problem for the semisimple Lie groups.
Mayer equations for Bose field theoretical models
Authors: Gielerak Roman
Published: March 2003

We present a simple proof that volume and ultraviolet cutoff boson Hamiltonians with unbounded entire type self-interacting terms are essentially self-adjoint operators on the Fock space. We present the rigorous derivation of Mayer equations in the considered Bose field theoretical models. A new proof of the divergence of the Feynman perturbation expansion is presented.
Extension of KMS states and angular momentum
Authors: Loupias G. , Mebkhout M.
Published: March 2003

We present a description of β-KMS equilibrium states with respect to some one-parameter subgroup of (T×R3) ⧠K, over an asymptotically Abelian algebra of observables (here T×R3 is the group of time and space translations and K a compact group acting on R3). In the case where K=SO(3), the group of space rotations, we get a characterization of the angular momentum of such states as a parameter occurring in their description, similar to the chemical potential, and classify all of them according to their invariance group, a closed subgroup of T×R×SO(2).
Asymptotic eigensolutions of fourth and sixth rank octahedral tensor operators
Authors: Harter William G. , Patterson Chris W.
Published: March 2003

Qualitative and quantitative features of high quantum rotational spectra are discussed by appealing to geometrical and topographical representations of the tensor operators. Approximate formulas are derived for level-cluster energies. The approximate conditions for the occurrence of ’’anomalous’’ fourfold clusters are given.
Noncontinuous gauge potentials without magnetic monopoles
Authors: Doria Francisco Antonio
Published: March 2003

We give examples for Abelian and non-Abelian gauge fields without magnetic Dirac-like monopoles and with essentially discontinuous potentials.
Toroidal black holes?
Authors: Peters P. C.
Published: March 2003

Recently Thorne presented a class of toroidal solutions which are cylindrically symmetric near the ring singularity. Although the class is a three-parameter family, there is a one-parameter constraint in order to eliminate an unwanted singularity. We show that for parameters satisfying a different one-parameter constraint, the ring singularity is replaced by a nonsingular toroidal horizon. We also show that such a constraint is inconsistent with Thorne’s constraint, by finding the latter constraint explicitly in the limit opposite to that considered by Thorne. We exhibit the two-parameter class of solutions with nonsingular toroidal horizons which do not violate the black hole uniqueness theorems, since there is a singularity outside the horizon.
Two-dimensional lumps in nonlinear dispersive systems
Authors: Satsuma J. , Ablowitz M. J.
Published: March 2003

Two-dimensional lump solutions which decay to a uniform state in all directions are obtained for the Kadomtsev–Petviashvili and a two-dimensional nonlinear Schrödinger type equation. The amplitude of these solutions is rational in its independent variables. These solutions are constructed by taking a ’’long wave’’ limit of the corresponding N-soliton solutions obtained by direct methods. The solutions describing multiple collisions of lumps are also presented.
Spacelike geodesics in the Nordström geometry
Authors: Dadhich Naresh
Published: March 2003

We study here the spacelike geodesics in the Nordström geometry. We show that (i) a radially falling tachyon can hit the singularity r=0 if either it is very energetic or the source is highly charged, (ii) nonradial orbits never end into r=0, and (iii) unstable circular orbits exist in the region which is bounded from below as well as from above. In the case of e2/m2=1, scattering cross sections are calculated.
Coupling coefficients: General theory
Authors: Dirl R.
Published: March 2003

Coupling coefficients for projective representations of finite groups are determined quite generally either by means of a general projection procedure, or as a linear combination of their corresponding Clebsch–Gordan coefficients. There we demonstrate that coupling— and Clebsch–Gordan coefficients are uniquely connected by special Clebsch–Gordan coefficients up to well-determined numerical factors.
Coupling coefficients for space groups
Authors: Dirl R.
Published: March 2003

Unitary matrices connecting coupling with their corresponding Clebsch–Gordan coefficients are determined quite generally for nonsymmorphic space groups which contain the inversion as point group operation. The matrix elements of these unitary matrices factorize into two independent parts where a special choice for the sets of the left coset representatives simplifies the calculations.
Coupling coefficients for P
n3n
Authors: Dirl R.
Published: March 2003

A general method for calculating Clebsch–Gordan coefficients is applied in order to compute for typical examples of Pn3n those unitary matrices which connect coupling—with their corresponding Clebsch-Gordan coefficients.
Successive observations in relativistic quantum theory
Authors: Srinivas M. D.
Published: March 2003

Relativistic quantum theory is formulated as a theory of successive local observations, consistent with all the fundamental requirements of relativistic invariance. Based on the causal structure of the space–time of special relativity, it is argued that the nonrelativistic notion of a ’’time-ordered sequence of instantaneous observations’’should be replaced in a relativistic theory by the notion of a ’’causally ordered sequence of local observations.’’ The fundamental statistical law of relativistic quantum theory is then formulated such that it provides an unambigous prescription for the statistical correlations between the outcomes of any causally ordered sequence of local observations. It is also shown that the fundamental statistical law of the theory is consistent with the so-called ’’principle of local causes’’ which essentially states that the probability connections between a set of local events do not depend on local observations carried out in space–time regions which lie outside of their causal past. Finally, an equivalent formulation of the theory in terms of a relativistically covariant generalization of the collapse postulate is presented.
Mass dependence of Schrödinger wavefunctions
Authors: Leung C. N. , Rosner J.
Published: March 2003

It is shown that for nonrelativistic central potentials of specific forms, the bound state wavefunctions u (r) have the property that G (r) ≡ℱ r0dx u (x)(∂u (x)/∂μ) ⩽0 for all r. Here μ is the reduced mass. Thus, for such potentials, the probability that a particle lies within a spherical shell of radius r is a monotonically increasing function of μ. The forms for which this property has been established are (a) V (r) =Crε, −2<ε<∞; (b) V (ir) =C lnr, and (c) S waves in the potential, V (r) =−V0 (0⩽r<a), V (r) =0 (a⩽r<∞). For all monotonically increasing potentials, G (r) ≳0 for nodeless states. It is shown explicitly that G (r) cannot be nonnegative for all bound states in an arbitrary monotonically increasing potential. The question remains open regarding the widest class of potentials for which G (r) is nonnegative for all bound states.
Equations for the propagation of finite local disturbances in vector fields of physics and mechanics
Authors: Costen Robert C.
Published: March 2003

The purpose of this theoretical investigation is to determine the propagation velocities of local disturbances that may occur in the curl and divergence of a vector field v that satisfies the equation ∂v/∂t+f=0, where f is a general vector field. Equations of this form frequently occur in physics and mechanics. A disturbance in the curl v (div v) field is defined by ∂curl v/∂t≠0 (∂div v/∂t≠0). Such a disturbance is termed a local disturbance if it is surrounded by a quiescent layer of finite thickness. Equations are derived for the velocity U(r,t) of curl v lines and the velocity W(r,t) of div v elements. These velocities conserve, respectively, the circulation of v about arbitrary circuits and the efflux of v through arbitrary closed surfaces. These conservation conditions are not sufficient to completely specify the two velocity fields, and each contains an arbitrary term. More convenient for three-dimensional applications than the circulation is the gyration G (spatial integral of curl v); and U is found to also conserve G in regions T where the curl v lines retain their individual shapes and orientations as they move, and our consideration of curl v disturbances is confined to such regions. The centroid of efflux is defined for arbitrary volumes, and the centroid of gyration for volumes in T. The movement of these centroids is linked to the velocities U and W by the conservation relations. Contributions from the arbitrary term in U (W) are suppressed by integration over a local curl v (div v) disturbance and by construction of a scalar potential field that satisfies Laplace’s equation in the interior of the disturbance with Dirichlet (Neumann) conditions related to f on the closed boundary. Formulas for the velocities of the centroids are thus obtained for local curl v and div v disturbances as functions of f, and these velocities are interpreted as propagation velocities of the disturbances. Only one type of disturbance need be localized for its formula to apply. These formulas enable us to calculate how such local disturbances will propagate without integrating forward in time; and in certain cases, only the fields outside a disturbance are required for this calculation. Applications to Maxwell’s electrodynamic equations are presented as examples.
Internal symmetries of the axisymmetric gravitational fields
Authors: Reina Cesare
Published: March 2003

The group H of the internal symmetries of the axisymmetric field equations in general relativity is known to be isomorphic to SO(2,1), which is the double covering of the conformal group of the hyperbolic complex plane ℋ. The Ernst potential ξ can then be geometrically understood as a map ξ:R3/SO(2) → ℋ. The fact that the hyperbolic plane is split into two connected components is used to introduce an algebraic invariant n∈Z+ for every axisymmetric solution. It is shown that under reasonable hypotheses this invariant is related to the number of S1 curves where the manifold is intrinsically singular.
Resolution of Fredholm equations with kernels K (z−z) by operational calculus
Authors: Si Do Tan
Published: March 2003

We show that the solutions of a Fredholm equation with kernels K (z−z0) is the transform of its second member in a transformation defined by a differential operator. The calculations of these solutions are then a matter of the powerful operational calculus.
Current responses of all orders in a collisionless plasma. I. General theory
Authors: Larsson J.
Published: March 2003

An arbitrary electromagnetic perturbation of a general solution of the relativistic Vlasov–Maxwell equations is considered. The nonlinear current responses are expressed in a form which in particular is an all order manifestation of the Manley–Rowe relations. A coordinate free formalism is used, starting with a representation of Minkowski space in terms of abstract linear algebra, and all formulas are intrinsically covariant. In the method used to derive the current responses the perturbation of particle orbits rather than of distribution functions is calculated.
Weak quantization in a nonperturbative model
Authors: Emch Gérard G. , Sinha Kalyan B.
Published: March 2003

The concepts of extended operator convergence and of spectral concentration are used to study rigorously a class of simple models for the tunnel effect and the laser. We compute exactly the asymptotic decay times of the eigenmodes, and we prove their link with the line width of the corresponding resonances.
Bifurcate Killing horizons
Authors: Miller J. G.
Published: March 2003

It is shown that an analytic spacetime with a bifurcate Killing horizon is locally symmetric with respect to the axis of rotation. It is also shown that if the surface gravity of a Killing horizon is a nonzero constant, then there exists a local prolongation (extension) of the spacetime that contains a bifurcate Killing horizon.
Decay of local correlations and absence of phase transitions
Authors: Messer Joachim
Published: March 2003

If the local truncated correlation functions of a system of statistical mechanics decay in a prescribed manner the limiting pressure becomes differentiable with respect to the activity. Criterions of clustering of the local truncated m-point correlation functions are shown to lead to a pressure being element of Cn for arbitrary n and m=1,...,n+1.
The application of group theory to generate new representability conditions for rotationally invariant density matrices
Authors: Erdahl R. M. , Garrod C. , Golli B. , Rosina M.
Published: March 2003

New linear conditions are derived which must be satisfied by a two-body density matrix. In the derivation, the ideas of Davidson and McRae are extended so that full use is taken of the symmetries of the system. The coefficients of the linear form are determined by means of reduction of a chosen group in a physically meaningful chain of its subgroups.
Segal quantization of dynamical systems
Authors: Gallone Franco , Sparzani Antonio
Published: March 2003

Segal quantization, usually thought of and used as a tool for quantizing kinematical frameworks, is extended to (finite-dimensional) dynamical systems, i.e., to kinematical frameworks plus dynamical motions applied to them. Such a procedure allows us to classify quantum dynamical systems, and to understand how physical inequivalence appears in spite of von Neumann unitary equivalence, for the former is also grounded on the evolution operators of the systems being different functions of the labeled observables of the systems. Second quantization is also examined and is shown to be just one possible procedure of quantization, which can only be used in a particular class of cases.
Static conformally flat solution in a scalar-tensor theory of gravitation
Authors: Reddy D. R. K.
Published: March 2003

Vacuum field equations for the static spherically symmetric conformally flat metric are obtained in a scalar-tensor theory of gravitation proposed by Ross. It is observed that unlike in Brans–Dicke scalar-tensor theory the only spherically symmetric static conformally flat vacuum solution in this theory is simply the empty flat space–time of Einstein’s theory.
Moment-method in a hard-sphere problem on a lattice, and physical applications. I. Uniform chain
Authors: Gallinar J.-P.
Published: March 2003

An exact representation is obtained for the propagator of two ’’hard spheres’’ on a one-dimensional (uniform) lattice where only nearest-neighbor hops are considered. The problem is solved within a random-walk formulation, with a general expression for the nth moment of the spectral density being given. These formal results are then applied to the discussion of several physical applications in a unified manner. In particular, we show that within the framework of the Hubbard Hamiltonian one may obtain, from the appropriate generalized spectral density, the optical absorption spectrum of a strongly correlated one-dimensional band of electrons. This theory, as applied, for example, to magnetic insulators or to the TCNQ (tetra-cyanoquinodimethane) salts, predicts a logarithmic divergence of the optical spectrum, for which a novel interpretation is given here in terms of an equivalent ’’surface’’ problem, shown to be isomorphic to the one studied. This is the problem of a two-dimensional rectangular crystal which has been cleaved along a main-diagonal line ’’surface.’’ From this, we also indicate the effects of chain dimerization (or Peierls transition) in a simple case of the spectral density. A simple counter example is also given which shows the nonuniqueness of the moment-method reconstruction for functions of unbounded variation. The partition function is also obtained analytically, and from this follows the energy of the two holes one-dimensional spinless fermion band. Finally, a physical argument is presented which supports the spinless fermion prediction of infinite mobility (or d.c. conductivity) for the hard spheres.
Husimi–Temperley model under a random field
Authors: Horiguchi Tsuyoshi
Published: March 2003

The free energy of the Husimi–Temperley model under a random field is obtained in terms of the n-replica method. The interchangeability of various limits such as the thermodynamic limit, the limit n→0 where n is the number of replicas, etc., is justified on the usage of the n-replica method in the course of the evaluation of the free energy. A tricritical point is found for the model under the random field which takes on two values σ and −σ with equal probability.
On the coupling of self-conjugate systems with S̄L̄ (3̄,R) symmetry
Authors: Castilho Alcarás J. A. , Biedenharn L. C.
Published: March 2003

The coupling of unitary self-conjugate S̄L̄ (3̄,ℛ) multiplicity-free irreps is explicitly calculated. It is proven that pair-wise coupling of a finite number of these self-conjugate irreps never contains a continuum S̄L̄ (3̄,ℛ) irrep which is multiplicity-free. The significance of S̄L̄ (3̄,ℛ) symmetry in nuclear and hadronic systems is discussed, including implications for the coupling of quarkels.
Comment on the Wigner 9-j symbol
Authors: Chatterjee R. , Dixon J. M.
Published: March 2003

A number of errors in the algebraic formulas of Rotenberg et al’s The 3j and 6-j Symbols have been corrected. Attention is drawn to a few other simple new algebraic relationships.
Representation matrix elements and Clebsch–Gordan coefficients of the semisimple Lie groups
Authors: Klimyk A. U. , Gavrilik A. M.
Published: March 2003

We give a general theory of matrix elements (ME’s) of the unitary irreducible representations (UIR’s) of linear semisimple Lie groups and of reductive Lie groups. This theory connects together the following things, (1) MEUIR’s of all the representation series of a noncompact Lie group, (2) MEUIR’s of compact and noncompact forms of the same complex Lie group. The theory presented is based on the results of the theory of the principal nonunitary series representations and on a theorem which states that ME’s of the principal nonunitary series representations are entire analytic functions of continuous representation parameters. The principle of analytic continuation of Clebsch–Gordan coefficients (CGC’s) of finite dimensional representations to CGC’s of the tensor product of a finite and an infinite dimensional representation and to CGC’s of the tensor product of two infinite dimensional representations is proved. ME’s for any UIR of the group U(n) and of the group U(n,1) are obtained. The explicit expression for all CGC’s summed over the multiplicity of the irreducible representation in the tensor product decomposition is derived.
Singular spin harmonics
Authors: Weir G. J.
Published: March 2003

The definition of the spin-weighted spherical harmonics, sYlm, is extended so that all integral spin weights, s, are allowed. We then discuss a set of spin-weighted functions, sZlm, which are analogous to the spherical harmonics of the second kind.
Rigid body motions, space curves, prolongation structures, fiber bundles, and solitons
Authors: Lakshmanan M.
Published: March 2003

The dynamics of a nonlinear string of constant length represented by a helical space curve may be studied through a consideration of the motion of an arbitrary rigid body along it. The resulting set of compatibility equations is shown to result in the class of nonlinear evolution equations solvable through the two component inverse scattering phenomenology. A class of pseudopotentials and prolongation structures follow naturally due to the intrinsic group structure of the phenomenon. This leads to an identification of the underlying fiber bundle structure and connection forms. Thus a unified picture emerges for a class of soliton possessing evolution equations.
Markov fields in noncommutative probability theory on W* algebras
Authors: Ekhaguere G. O. S.
Published: March 2003

Many important results in ordinary probability theory do not have extensions in noncommutative probability theory. Here we consider Markov fields, and we prove that new Markov fields may be generated from old ones by means of multiplicative measurable operators. There is an analog of this result in ordinary probability theory involving multiplicative functionals. It is envisaged that the result established here would be of use in the study of interacting Fermion quantum fields.
The spectrum of the multigroup neutron transport operator for bounded spatial domains
Authors: Larsen Edward W.
Published: March 2003

The spectrum of the multigroup neutron transport operator A is studied for bounded spatial regions D which consist of a finite number of material subregions. Our main results provide simple conditions on the material cross sections which guarantee that (1) A possesses eigenvalues in the finite plane; (2) A possesses a ’’leading’’ eigenvalue λ0 which is real, not less than the real part of any other eigenvalue, and to which there corresponds at least one nonnegative eigenfunction ψλ0; and (3) A possesses a ’’dominant’’ eigenvalue λ0 which is real, simple, greater than the real part of any other eigenvalue, and whose eigenfunction ψλ0 satisfies ψλ0⩾0 and ∫ψλ0d2Ω≳0. We give examples to illustrate the results and to show that a leading eigenvalue need not be simple, nor its eigenfunction(s) positive.
On the problem of existence of quantum field theory
Authors: Chaichian M. , Hayashi M. , Nelipa N. F. , Pukhov A. E.
Published: March 2003

Existence of quantum field theory is considered for the four-dimensional φ3 model. The mathematical tool of contraction mapping principle is used to investigate the question of existence of solution for the infinite system of coupled equations for the Green functions of the theory in the Euclidean region. Formulation of the problem for this model with one divergent part is interesting in itself and provides the first attempt towards the study of other renormalizable quantum field theory models with an infinite number of divergent graphs. For sufficiently small values of coupling constant, the theory has a unique solution for the truncated system of equations for the Green functions. However, for the complete, infinite set of equations, the Banach fixed point theorem admits a solution only when the coupling constant tends to zero. Possible reasons for such a result are discussed.
Scalar quantum field in an external gauge field
Authors: Dimock J.
Published: March 2003

Let G be a compact complex Lie group with Lie algebra G′ and let Aμ∈C∞0(R4,G′) be a gauge potential. We construct a gauge covariant local quantum field operator φ which solves the equation [(∂μ+iAμ)(∂μ+iAμ)+ m2]φ=0 and is a free field in the distant past or future. The associated scattering theory is described by a unitary gauge-invariant S operator.
On a common property of gravitational and chiral exponential Green functions
Authors: De Meyer H. E.
Published: March 2003

The dependence of gravitational and chiral exponential Green functions on a ’’gauge’’ parameter which enters the free propagation function of the basic matrix field, is analyzed. It is proven that by an appropriate choice of this parameter, the Green functions can be made ambiguity-free.
Theory of temporal pump stochasticity in stimulated Raman scattering in dispersionless media
Authors: Eimerl D.
Published: March 2003

A diagrammatic formalism is presented which gives exact results for the forward Stokes wave in dispersionless media in the field of a temporally stochastic pump. Both pump and Stokes waves are assumed to be plane waves, but transient effects are treated exactly. Results are derived in the Bourret approximation for the n-point functions (n≳2) but are exact to all orders in the mean pump field and its two-point function. The generalization to treat general n-point functions within this formalism is possible and the method of doing so is indicated. The partial summation of diagrams corresponding to previous treatments is identified and the next order terms are evaluated. It is found that for high gain systems, approximations made in previous work may be quite poor.
Remarks on a theorem by G. Epifanio, ’’On the matrix representation of unbounded operators’’ [J. Math. Phys. 1
7, 1688 (1976)]
Authors: Epifanio G. , Trapani C.
Published: March 2003

We give a generalization of a theorem concerning the change of basis for the matrix representation of unbounded operators defined in a scalar product space. We introduce for the proof a suitable structure which can be useful when one has to make operations with operators defined between different scalar product spaces.
A scale limit of φ2 in φ4 Euclidean field theory. I
Authors: Haba Z.
Published: March 2003

It is shown that a scale limit (appropriately defined) of the Wick square of the free Euclidean field in d<4 dimensions with mass m0 exists and is a random field with values independent at every point. When m0→0 a stable distribution is obtained. The same limit is then calculated in φ4 cutoff field theory. After taking the scale limit the regularization can be removed. The limit field is again independent at every point but with different density and mean different from zero. The interpretation of the results in lattice approximation is given. The problem of restoring the correlations between different points is considered as a perturbation around an independent-value field.
Neutrino, Maxwell, and scalar fields in the cylindrical magnetic or plasm universe
Authors: Cattell David F. , Melvin M. A.
Published: March 2003

In this paper we discuss the solutions of the c-number quantum-mechanical equations of neutrino, Maxwell, and scalar fields in the background metric of a static, cylindrically symmetric magnetic or plasm universe. The magnetic universe consists of a parallel magnetic field distribution held together by the gravitational field of its own energy and stress. It is an exact solution of the Einstein–Maxwell equations for the gravitational field associated with a stationary source-free cylindrically symmetric magnetic field. The solution does not depend specifically upon the assumption that the seat of the energy-stress distribution is an electromagnetic field. A ’’plasm of index 2’’ would have the same metric. The main instrument of the present perturbation theory, valid in all algebraically special spacetimes, is the Cohen–Kegeles (CK) scalar wave equation for test fields of helicity h (or s). This equation, written in the updated Geroch–Held–Penrose (GHP) formalism, is made explicit for the chosen null tetrad by determining the spin coefficients and the operators of that formalism. Exact solutions of the CK wave equation are obtained for the case of zero orbital angular momentum. For the case of nonzero orbital angular momentum the JWKB approximation is used to obtain the quadratures for the orbits in the magnetic universe. It is shown that the neutrino orbits precess about the magnetic (or plasm) universe axis in a manner different from orbits of particles with helicity zero and helicity one. The expression for the neutrino precessional frequency (due to nonvanishing helicity) is given explicitly. The photon precessional frequency is twice that for neutrinos. Finally, the CK procedure is compared with that of Teukolsky for finding the neutrino and Maxwell fields in type D spacetimes.
Expansions of the affinity, metric and geodesic equations in Fermi normal coordinates about a geodesic
Authors: Li Wann-Quan , Ni Wei-Tou
Published: March 2003

Fermi normal coordinates about a geodesic form a natural coordinate system for the nonrotating geodesic (freely falling) observer. Expansions of the affinity, metric, and geodesic equations in these coordinates in powers of proper distance normal to the geodesic are calculated here to third order, fourth order, and third order, respectively. An iteration scheme for calculation to higher orders is also given. For generality, we compute the affinity and the geodesic equations in an arbitrary affine manifold, and compute the metric in a Riemannian manifold with arbitrary signature.
Euclidean and Minkowski space formulations of linearized gravitational potential in various gauges
Authors: Lim S. C.
Published: March 2003

We show that there exists a unitary map connecting linearized theories of gravitational potential in vacuum, formulated in various covariant gauges and noncovariant radiation gauge. The free Euclidean gravitational potentials in covariant gauges satisfy the Markov property of Nelson, but are nonreflexive. For the noncovariant radiation gauge, the corresponding Euclidean field is reflexive but it only satisfies the Markov property with respect to special half spaces. The Feynman–Kac–Nelson formula is established for the Euclidean gravitational potential in radiation gauge.
The classification of all ℋ spaces admitting a Killing vector
Authors: Finley J. D. , Plebański J. F.
Published: March 2003

We show that all ℋ spaces (self-dual solutions of the complex Einstein vacuum equations) that admit (at least) one Killing vector may be gauged in such a way as to be divided into only five types, characterized by the type of equation which determines their potential function. In four of these types we show that this knowledge is sufficient to reduce the requirement of being an ℋ space to a linear equation whose solutions are well known. The fifth case is reduced considerably and a large class of special solutions is given.
Bures distance and relative entropy
Authors: Gudder Stanley , Marchand Jean-Paul , Wyss Walter
Published: March 2003

We have previously constructed an entropy functional which characterizes statistical inference from partial measurement by maximum relative entropy. Here we discuss the mathematical properties of this concept in greater detail and establish its relation to the Bures distance and the Uhlmann transition probability.
Singular potentials and analytic regularization in classical Yang–Mills equations
Authors: Bollini C. G. , Giambiagi J. J. , Tiomno J.
Published: March 2003

The class of instaton solutions with ’’extension’’ parameter λ2 positive is extended to λ2 negative. The nature of the singular sphere of radius ‖λ‖ is analyzed in the light of the analytical regularization method. This leads to well defined solutions of the Yang–Mills equations. Some of them are sourceless (’’±i o’’ and ’’Vp’’), others correspond to currents concentrated on the sphere of singularity (’’+’’ and ’’−’’). Although the equations are nonlinear, the ’’Vp’’ solutions turn out to be the real part of the ’’±i o’’ solutions. The ansatz of the t’Hooft for the superposition of instantons is used to sum the contributions corresponding to λ2 with positive and negative signs. A subsequent limiting process allows then the construction of solutions of the ’’multipole’’ type. The general situation of potentials having a denominator D, with a corresponding surface of singularity at D=0, is also considered in the same light.
A double angle sum formula for Gegenbauer polynomials
Authors: Shebalin John V.
Published: March 2003

A formula is given by which a Gegenbauer polynomial whose argument is the cosine of twice an angle can be equated with a finite, alternating series of products of Gegenbauer polynomials whose arguments are all cosines of the angle.
On the applicability of the variation of action method to some one-field solitons
Authors: Laedke E. W. , Spatschek K. H.
Published: March 2003

The applicability of the widely used method of variation of action is discussed by investigating the transverse stability of the kink solution of the nonlinear Schrödinger equation and the bell solution of the Kadomtsev–Petviashvili equation. An exact calculation shows that neither instability nor stability can be predicted correctly by the variation of action method. The reasons for that defect are discussed and the correct stability regions are presented.