bluuebunny/crossref_metadata_2025 huggingface dataset:
Partial wave expansion of the RKKY indirect exchange interaction in metals
Authors: Larsen Ulf
Published: March 2003

Using the full partiall wave series for the exchange coupling constant J(k,k′)=∑iL=0 (2L+1) PL(k̂⋅k̂′ JL(k,k′), in standard notation, for an s-d type exchange interaction between a local spin (electronic or nuclear) and free conduction electrons in metals, the corresponding full partial wave series for the long range, indirect, exchange interaction (Ruderman–Kittel–Kusuya–Yosida, RKKY) between two such local spins is derived. In particular, the asymptotic long range form of the exchange coupling constant is ℱ (R)∼−(9πn2/EF) JRKKY2 cos(2kFR)/(2kFR)3, where JRKKY=∑∞L=0 (2L+1)(−1)L JL(kF, kF). For constant JL(k,k′)=JL the exchange coupling ℱ(R) is exactly calculated for all distances R in terms of standard functions. To obtain this result nonstandard indefinite integrals of spherical Bessel functions have been caLculated and the results are given in terms of recursion relations. Also, a closed form is obtained for the Cauchy principal value of the singular integral ℱ∞0 dy y2 JL(y)/(y2−x2). Results are given for the electron spin polarization due to a local spin.
Symmetries and metrics of homogeneous cosmologies
Authors: Melvin M. A. , Michalik T. R.
Published: March 2003

It is shown that an assumption of ’’historical homogeneity’’—or the persistence of spatial homogeneity in time—leads to the synchronous (time-orthogonal) form ds2=−dt2+γAB (t)εA⊗εB, of the metrics for general spatially homogeneous (Bianchi) cosmologies. The εA are group-representation 1-forms associated with the spatial symmetry group of the given cosmology, and are independent of any particular space–time theory; in particular they do not depend on Einstein’s equations and the local physics. Expressions for the εA in the canonical basis used by Estabrook, Wahlquist, and Behr (EWB) have been tabulated in the companion paper on ’’Spatially homogeneous neutrino cosmologies’’ (SHNC). In the present paper explicit expressions are given for the scale factors γAB(t). These do correspond to the choice of the canonical basis to describe the symmetry but, in contrast to the εA, they also depend on the space–time physical theory. Here the γAB(t) come out as observable geometric–kinematic quantities (generalized Hubble constants) which also appear in the solutions of Einstein’s equations for a given cosmology. Central to the discussion is the matrix C(t) which relates the time-independent canonical basis describing the symmetry to a time-dependent orthonormalizing basis. With the imposed requirement that the Riemannian geometry of the evolving spatial hypersurfaces retain its quasi-canonical form in time (’’quasi-canonical gauge’’) it is shown that C(t) is a product of a diagonal matrix D̀ and a rotation matrix R; and a table of these forms of C(t) for the various Bianchi types is given. The simple Hubble-constant expressions for the metric scale factors γAB(t) for all types come solely from the diagonal factor D̀ in C. The metric, then, in all cases takes the form ds2=−dt2+γABεA ⊗εB=−dt2 +(εI/α)2 +(εII/β)2 +(εIII/γ)2. Thus, the specializing assumption of Misner and of Ryan and Shepley, requiring C to be symmetric, does not limit the form of the metric but does restrict the relation between the invariant symmetry basis and the quasi-canonical orthonormal basis to the cases where the orthogonal factor R reduces to the identity, i.e., to those cases where the two bases remain parallel at all times. Thus, the gauge assumed by them is not compatible with the preservation of the quasi-canonical form of the spatial geometry in almost all cases where there is degeneracy involved in the spatial curvatures.
Spatially homogeneous neutrino cosmologies
Authors: Michalik T. R. , Melvin M. A.
Published: March 2003

Gravitational effects of a c number neutrino field in spatially homogeneous geometries are analyzed. At the basis of the description of the geometries is an arbitrary timelike congruence with aligned tetrad reference frames, i.e., one basis vector of the tetrad frame at each point of space–time is aligned along the congruence. The remaining three basis vectors of the tetrad lie in orthogonal spacelike hypersurfaces, and for these there are three alternative choices: (1) invariant reference triads, i.e., which conform to the isometry group of the space with structure constants Gcgh; (2) orthonorm al reference triads simulating a Euclidean structure at each point; (3) holonomic coordinate triads in terms of which metrics are usually given. The relations between (1), (2), and (3) for all nine Bianchi–Behr types are reviewed. The relatively compact vector–dyadic formalism used by Estabrook, Wahlquist, and Behr is introduced; it has the advantage that it gives directly the Bianchi–Behr classification of cosmologic solutions, and represents these solutions in terms of the orthonormal frame components of interesting physical quantities such as shear rates, volume expansion rates, and rotation with respect to inertially stabilized directions. The coupled Einstein–Dirac equations for the gravitational neutrino field and the neutrino stress-energy tensor are derived, and the coupling equations are replaced by a set in which the neutrino amplitude is eliminated, and instead there appear the neutrino current (J, J0=‖J‖) (vector bilinear covariant) and the ’’eikonal momentum’’ P=∇ f, the gradient of the phase function f(x) which appears in the neutrino spinor amplitude ψ=χ(t)eif(x). Solutions for all nine Bianchi types are classified. Further, with the two assumptions: (1) axial symmetry of the geometry, (2) alignment of the neutrino momentum density t with the Bianchi vector n (in the symmetry direction), a new exact solution is found explicitly. It is of type VIIh. This solution goes over into a solution for type V when a parameter in the solution is set equal to zero. This is to be expected from the fact that type V may be regarded as a limiting case of type VIIh when a=b→0.
Simplified Bose description of para-Bose operators
Authors: Schmutz M.
Published: March 2003

A set of n para-Bose operators of order p is explicitly constructed in terms of n×p Bose operators.
N. Fröman’s phase-integrals versus JWKB: Documentation of the advantages of the former in higher-order approximations
Authors: Dammert Örjan , Fröman Per Olof
Published: March 2003

The purpose of the present paper is to clarify in a general way and to document the great advantage of using, instead of the higher-order JWKB-approximations, certain related but much simpler higher-order phase-integral approximations.
Construction of L2 dependent potentials
Authors: Hooshyar M. A.
Published: March 2003

Central and L2-dependent potentials, acting among spinless particles, are constructed from the knowledge of the phase shifts for all angular momenta at two different fixed values of energy. It is shown that the information on phase shifts at two fixed energies does not lead to a unique set of central and L2-dependent potentials and they will depend on an infinite number of parameters.
The Gel’fand–Levitan equation can give simple examples of non-self-adjoint operators with complete eigenfunctions and spectral representations. I. Ghosts and resonances
Authors: DeFacio B. , Moses H. E.
Published: March 2003

It is shown that the Gel’fand–Levitan equation for the radial and one-dimensional Schrödinger equations yield complex and singular potentials which support complete sets of eigenfunctions. Explicit examples are given involving complex point eigenvalues and/or complex or negative normalization for the corresponding eigenfunctions. Ghosts and other resonance phenomena thus appear as special cases of this more general inverse spectral theory. It is hoped that these explicit examples for simple situations will clarify ideas relating to non-self-adjoint operators occurring in field theory, scattering theory, and the use of inverse spectral transforms to solve certain classes of nonlinear equations. The treatment given here indicates that the Gel’fand–Levitan equation is a powerful tool in constructing operators with spectral decompositions, even when the operator is not self-adjoint.
The Jost solutions for Yukawa potentials
Authors: Trlifaj L.
Published: March 2003

Using a suitable Laplace transformation of the regular solution and the expansion of its Laplace transform in partial fractions we found new explicit expressions for the Jost solutions of the radial Schrödinger equation with complex wave numbers and angular momenta, in general, and for potentials of the exponential and, especially, Yukawa type, which were described by means of the Stiltjes integral with respect to a function μ(t) of bounded variation. Many other relations including those for the Jost functions were derived or rederived, which have their counterpart among relations for the Bessel functions.
Para-Fermi quantization in the representation of SO(n)
Authors: Maekawa T. , Noguchi N.
Published: March 2003

The result of the representation theory of SO(n) is applied to the quantization of f para-Fermi oscillators, and it is shown that a special irreducible representation of SO(2f+1) is realized in the quantization of the field with order p when the condition of vacuum is used. The group theoretical meaning of the quantities such as vacuum, order p, and the space of the state in the para-Fermi quantization is made clear, and it is seen that the space of the state vectors corresponds to that of the single- or double-valued representations according to p even or odd.
Perturbation expansion of multichannel Regge poles
Authors: Bosanac S.
Published: March 2003

A perturbation method for the complex angular momentum poles of the multichannel S-matrix is developed. The inelastic residues of the S-matrix are also treated in a similar fashion. It is shown that the poles and residues are the second order in coupling between the channels. The closed channel Regge poles are also discussed and it is shown that their contribution in the perturbation series is finite, regardless of the asymptotic behavior of potential.
The asymptotic behavior of the generalized Einstein–Maxwell field theory
Authors: Horndeski Gregory Walter
Published: March 2003

It is shown that the Einstein–Maxwell and generalized Einstein–Maxwell field theories essentially agree to first order at null and spatial infinity.
Extended objects in quantum field theory
Authors: Matsumoto H. , Semenoff G. , Umezawa H. , Umezawa M.
Published: March 2003

A general formulation for treatment of extended objects in a quantum field system is presented. It is shown how to construct the solutions of the Heisenberg equation when static extended objects are present. A detailed study of the quantum coordinate is presented. The Hamiltonian for the quantum mechanical object, which comes out of the quantum field theory, is obtained. It is shown that creation of extended objects does not upset the renormalizability.
On the local simultaneity in general relativity
Authors: Olivert J.
Published: March 2003

In this paper the existence of simultaneous points, in the Landau sense, in the neighborhood of an observer P is studied. It is shown that the set of such points has the structure of a regular submanifold of the space–time manifold.
Diffusion in a periodic wind-tree model
Authors: Hardy J. , Weber J.
Published: March 2003

In this paper we study a two-dimensional wind-tree model where the diffusors are rectangles periodically disposed. One shows that the motion of the light particle depends strongly on the arithmetic properties of a number α. The light particle returns near its departure position at times which are in geometrical series; it is proved the particle escapes to infinity, but not faster than logt loglogt, where t is the time.
Stochastic electrodynamics of nonlinear systems. I. Partial in a central field of force
Authors: Marshall T. W. , Claverie P.
Published: March 2003

We treat the motion of a charged particle in a central field plus a stochastic field corresponding to the zero-point field of quantum electrodynamics as a quasi-Markov process in the classical action variables. As special cases we consider the rigid rotator, the harmonic oscillator, and the Kepler system. We show that in the first two cases, but not in the third, the quasi-Markov process satisfies the detailed balance condition, which expresses the invariance of the process under time reversal. We consider the implications of this last result, and argue that it shows the possibility of a mechanical system being in equilibrium with respect to the radiation field, while the radiation field itself is not in equilibrium.
Wigner–Eckart theorem for an arbitrary group or Lie algebra
Authors: Agrawala Vishnu K.
Published: March 2003

Circumstances sufficient for the validity of the Wigner–Eckart theorem are analyzed and the theorem is proved under very mild assumptions. The proof is purely algebraic and shows the theorem to be a direct consequence of Schur’s lemma and complete reducibility of tensor product of irreducible representations.
On Gel’fand states of representations of U(n) and the Gel’fand lattice polynomials
Authors: Henrich Christopher J.
Published: March 2003

Three theorems are proved concerning the Gel’fand lattice polynomials (GLP) introduced by Gazeaux, Dumont-Lepage, and Ronveaux. In these theorems, subdeterminant initial conditions are assumed. (1) The Gel’fand states are linear combinations of GLP corresponding to left Gel’fand lattices. (2) The set of all GLP is a basis for the space of polynomial functions of the elements of a matrix. (3) If the left Gel’fand lattices are arranged in a natural order, then each Gel’fand state is a linear combination of the corresponding GLP and earlier ones in the same order. Finally, a formula is given for computing individual GLP.
Solutions of the sine-Gordon equation in higher dimensions
Authors: Leibbrandt George , Morf Rudolf , Wang Shein-shion
Published: March 2003

Exact solutions are derived for the three-dimensional and four-dimensional sine-Gordon equation [∇2−∂2/(c2∂t2)]χ =sinχ. The principal tools in the derivation are a new Bäcklund transformation and the appropriate generating formulas which allow us to generate an infinite number of real classical solutions. Three-dimensional computer plots depicting the time evolution are presented (a) for the two-soliton and four-soliton solutions of the sine-Gordon equation, and (b) for the three-wave interaction of the associated sine-Gordon equation.
Unidirectional wave propagation in one-dimensional first-order Hamiltonian systems
Authors: van Groesen E. W. C.
Published: March 2003

Defining the velocity of a conserved density to be the velocity of the center of gravity of this density, it is shown that for linear equations this velocity equals the weighted group velocity (with the density as weight function). For nonlinear equations, expressions for the centrovelocity of several conserved densities are derived. In particular, for a class of nonlocal equations, the centrovelocity of the energy density turns out to be some weighted average of the group velocity of the corresponding linearized equation. For a specific equation of this type, viz, the BBM equation, it is shown that upon restricting it to solutions whose initial form represents a long, low wave, the centrovelocity of the energy density is positive for all positive time.
Symmetries and vacuum Maxwell’s equations
Authors: Steeb W.-H.
Published: March 2003

A new class of infinitesimal symmetries are given for Maxwell’s equations in the absence of sources.
High-energy behavior of renormalized Feynman amplitudes. II
Authors: Manoukian Edward B.
Published: March 2003

The high-energy polynomial and logarithmic behavior of renormalized Feynman amplitudes, involving subtractions, is studied with total generality when some or all of the external momenta of the graphs in question become large in Euclidean space nonexceptionally for theories which on experimental grounds may contain zero mass particles. Initially, all the propagators are defined to have nonzero masses in their denominators. The vanishing masses are led to vanish, and in general, at different rates. Rules are given for applications and examples are then worked out to demonstrate the application of these rules.
Coulomb scattering as the limit of scattering off smoothly screened Coulomb potentials
Authors: Goodmanson David M. , Taylor John R.
Published: March 2003

We examine the amplitude f ρ(cosϑ) for scattering off a screened Coulomb potential V ρ(r) =VC(r)α ρ(r), where VC(r) is the Coulomb potential γ/r. We prove that, for a wide class of smooth screening functions α ρ(r), the screened amplitude f ρ(cosϑ) approaches the pure Coulomb amplitude f C(cosϑ), times a phase factor, as the screening radius ρ→∞. This limit is pointwise and uniform in angle and energy (excluding arbitrarily small neighborhoods of ϑ=0 and E=0), and therefore implies that the corresponding cross sections become equal as ρ→∞.
Symmetries of the stationary Einstein–Maxwell field equations. VII. Charging transformations
Authors: Kinnersley William
Published: March 2003

The group B of transformations which preserve asymptotic flatness is enlarged to include ’’charging’’, and other electromagnetic transformations. The new group B′ can be applied to the Tomimatsu–Sato solution to produce an Einstein–Maxwell solution with nine free parameters.
On a new solution of Einstein’s equations
Authors: Hoenselaers C.
Published: March 2003

An analysis of a stationary axisymmetric solution of Einstein’s equations recently derived by Hoenselaers, Kinnersley, and Xanthopoulos is given. We derive the metric of the full space–time, the invariants of the Weyl tensor, the first few multipole moments, and discuss the stationary limit surfaces and the axis.
A note on the good cut equation
Authors: Lind Robert W.
Published: March 2003

The good cut equation (F2 Z=σ) is the link between a physical asymptotically flat space–time (characterized by σ) and its associated H-space (characterized by Z and interpreted by Penrose as a nonlinear graviton). In this work a class of regular, nontrivial (σ≠0) solutions to the good cut equation is obtained by writing σ in terms of a potential function φ.
Kerr-like neutrino-gravitational solutions
Authors: Lun Anthony W. -C.
Published: March 2003

Two distinct stationary axisymmetric Kerr-like neutrino-gravitational space–times are presented. They reduce to the Kerr solution when the neutrino field vanishes. In addition, the first solution possesses physical line singularities along the axis of symmetry; whereas the second solution is asymptotically flat and its locally bounded Riemann tensor is discontinuous at the equatorial plane. Both metrics are of Petrov type II and their neutrino fields belong to type [2N-2S](2−1) in the Plebański classification.
An alternative solution of the Bogoliubov’s equation for the two-particle distribution function in the kinetic theory of gases.
Authors: Chen M.
Published: March 2003

In this paper we consider an alternative solution of the Bogoliubov’s equation for the two-particle distribution functions F2 under the assumption that it is a function of the one-particle distribution function F1. In terms of the density expansion F2=Σi=o∞ρiF2(i), we show that F2(n) satisfies a first order linear partial differential equation. The existence of a unique solution for F2(n) can then be proved under some general conditions. Moreover, F2(n) reduces to the result in the classical virial expansions at equilibrium. For the discussion of the kinetic equation, a special solution for F2(O) can be obtained by the method of separation of variables. Following Grad’s method, a kinetic equation can then be derived, which reduces to the ordinary Boltzmann equation for the hard sphere potential. It can be shown that the equilibrium solution of the kinetic equation is just the Maxwell–Boltzmann distribution. Under some restricted conditions the kinetic equation can be proved to satisfy the H theorem.
Existence of Hartree–Fock solutions
Authors: Rosensteel G. , Ihrig Edwin
Published: March 2003

For a finite-dimensional space with only a mild restriction on the Hamiltonian, it is shown that there exist at least as many Hartree–Fock states as the dimension of the many-fermion space. The index of the random phase approximation matrix is determined for these HF states and the relationship between that index and the number of real and complex excitation energies established.
On the singular eigenfunctions for linear transport in an exponential atmosphere
Authors: Larsen Edward W. , Pomraning G. C. , Badham V. C.
Published: March 2003

We prove that under an explicit condition on the parameters in the isotropic-scattering linear transport equation for an exponential atmosphere, the continuum eigensolutions developed by Millikin and Siewert are complete on the half range 0<μ⩽1. We also treat numerically the equation for the outgoing flux, which can be derived using these eigenfunctions, and we show that excellent numerical results are obtained if the above condition is satisfied, while poor results are obtained if the condition is sufficiently violated. Finally, we describe a method for constructing elementary solutions of the anisotropic-scattering transport equation for an exponential atmosphere.
Interaction of isovector scalar mesons with simple sources. II. Isobars and meson scattering
Authors: Bolsterli M.
Published: March 2003

For the case of a static source, appropriate special coherent states are defined so as to give a relatively simple treatment of states of any isospin in the no-meson and one-meson approximations. The analogous localized coherent states for nonstatic sources are described and shown to be suitable for use in translated-localized-state calculations.
Classification of three-particle states according to an orthonormal SU(3)⊇SO(3) basis
Authors: del Aguila F.
Published: March 2003

In this paper we generalize Dragt’s approach to classifying three-particle states. Using his formalism of creation and annihilation operators, we obtain explicitly a complete set of orthonormal functions YλμRLM on S5. This set of functions carries all the irreducible representations of the group SU(3) reduced according to SO(3). The YλμRLM, which are eigenvectors of the togetherness and angular momentum operators, have very simple properties under three-particle permutations. We obtain also explicitly the coefficients ’’3ν’’ which reduce the products of these functions.
Schrödinger spectral problems with energy–dependent potentials as sources of nonlinear Hamiltonian evolution equations
Authors: Martinez Alonso L.
Published: March 2003

We develop a method to derive infinite families of completely integrable nonlinear Hamiltonian evolution equations associated with Schrödinger spectral problems whose potential functions depend on the spectral parameter.
A class of explicitly soluble, local, many-center Hamiltonians for one-particle quantum mechanics in two and three dimensions. I
Authors: Grossmann A. , Hoegh-Krohn R. , Mebkhout M.
Published: March 2003

We derive an explicit formula for the resolvent of a class of one-particle, many-center, local Hamiltonians. This formula gives, in particular, a full description of a model molecule given by point interactions at n arbitrarily placed fixed centers in three dimensions. It also gives a three−dimensional analog of the Kronig–Penney model.
Representations and properties of para-Bose oscillator operators. I. Energy position and momentum eigenstates
Authors: Mukunda N. , Sudarshan E. C. G. , Sharma J. K. , Mehta C. L.
Published: March 2003

Para-Bose commutation relations are related to the SL(2,R) Lie algebra. The irreducible representation 𝒟α of the para-Bose system is obtained as the direct sum Dβ⊕Dβ+1/2 of the representations of the SL(2,R) Lie algebra. The position and momentum eigenstates are then obtained in this representation 𝒟α, using the matrix mechanical method. The orthogonality, completeness, and the overlap of these eigenstates are derived. The momentum eigenstates are also derived using the wave mechanical method by specifying the domain of the definition of the momentum operator in addition to giving it a formal differential expression. By a careful consideration in this manner we find that the two apparently different solutions obtained by Ohnuki and Kamefuchi in this context are actually unitarily equivalent.
A new proof of absence of positive discrete spectrum of the Schrödinger operator
Authors: Ramm A. G. , Taylor B. A.
Published: March 2003

A new method to prove the absence of positive discrete spectrum of the Schrödinger operator is given.
Tight lower bounds to eigenvalues of the Schrödinger equation
Authors: Hill Robert Nyden
Published: March 2003

A new tight lower bound to eigenvalues of the Schrödinger equation, which tends to be better than the well-known Temple lower bound, is presented. The new bound works (as does the Temple bound) for both ground and excited states. Optimization of both the Temple bound and the new tight bound with respect to a variational trial function is discussed. Numerical results are given for the anharmonic oscillator.
On geometrical properties of spinor structure
Authors: Bugajska Krystyna
Published: March 2003

The Crumeyrolle group ℯ for four-dimensional space-time E is explicitely calculated. It is shown that the complexification of the Lie algebra of the group ℯ is a spinor space. In this manner the condition of the existence of a spinor structure over E, formulated as the reduction of the structure group of the bundle of orthonormal frames to ℯ, enables us to associate the spinor space to each point of space-time in a continuous way.
Stochastic fields from stochastic mechanics
Authors: Moore Steven M.
Published: March 2003

Stochastic field theory for a real scalar field, considering both zero and positive temperatures, is developed from complements to Nelson’s stochastic mechanics. These complements include path integral formulas for the moments of the stochastic process, a functional differential equation for the generating functional, and a virial theorem. Using these and Yasue’s nonstandard analysis formulation of stochastic field theory, a rigorous meaning is given to the path integral formulas for the field moments and to the functional differential equation of the field’s generating functional.
Symmetries of differential equations. II
Authors: González-Gascón F.
Published: March 2003

The importance of the non-pointlike transformations of symmetry is vindicated in relation with the first integrals. A new first integral of a broad class of systems of second order differential equations is obtained out of a symmetry of them without having to impose the restriction that the system be equivalent to a Lagrangian system. The existence of a reciprocal relationship among the local infinitesimal symmetries (l.i.s.) of a Newtonian system of differential equations and the pseudosymmetries of the associated dynamical system is proved. Several applications are developed, and some open problems concerning the dynamical systems of constant divergence are proposed.
A variational principle for resonances
Authors: Ramm A. G.
Published: March 2003

A stationary variational principle for calculation of the complex poles of Green functions is given.
On the proper vectors of real third-order matrices
Authors: Stokes Vijay K.
Published: March 2003

The result that a pseudovector can be associated with a real third order skew-symmetric matrix has been used for establishing some properties of the proper vectors of real third order matrices. It turns out that the pseudovector associated with the skew-symmetric part of such matrices characterizes some interesting properties of proper vectors, such as the question of their orthogonality.
Random walks and quantum currents in networks
Authors: Ringwood G. A.
Published: March 2003

The free electron network model of a metal is reformulated in terms of restricted random walks; this allows direct calculation of the propagator. The reformulation gives more freedom in the choice of boundary conditions and is suitable for the investigation of topologically disordered networks.
Hilbert space approach to the three- and four-nucleon systems
Authors: Kröger H.
Published: March 2003

A Hilbert space formulation is proposed for the three-nucleon scattering problem. Scattering integral equations are given derived from Alt–Grassberger–Sandhas equations. Using the momentum representation, the kernel of the iterated integral equation is shown to be compact in an adjusted Hilbert space. The extension to four nucleons is given.
Degenerate perturbations in nonrelativistic quantum mechanics
Authors: van Haeringen H. , Kok L. P.
Published: March 2003

We investigate the effects on the discrete spectrum of an arbitrary quantum mechanical Schrödinger operator H, which are caused by the addition of a real rank N separable potential to H. For such a potential the bound state energies En(λ) as function of the real potential strength λ are in general confined to certain bounded intervals. This remarkable phenomenon can be seen as a particular case of the general situation of complex potential strengths.
Aharonov–Bohm scattering and the velocity operator
Authors: Henneberger Walter C.
Published: March 2003

It is shown that the existence of Aharonov–Bohm scattering depends upon the criteria used for establishing the stationary states. If one applies Pauli’s criterion, there is no scattering. It is shown further that applying the usual criteria that the wave functions be continuous and single valued, as was done by Aharonov and Bohm, leads to stationary state wave functions which, with two exceptions, are eigenstates of the acceleration operator corresponding to eigenvalue zero. The acceleration operator is undefined for the remaining two states. Thus, only the eigenfunctions satisfying the Pauli criterion lead to well-defined, sensible physics.
Some models of anisotropic spheres in general relativity
Authors: Cosenza M. , Herrera L. , Esculpi M. , Witten L.
Published: March 2003

A heuristic procedure is developed to obtain interior solutions of Einstein’s equations for anisotropic matter from known solutions for isotropic matter. Five known solutions are generalized to give solutions with anisotropic sources.
On the Hoenselaers–Kinnersley–Xanthopoulos spinning mass fields
Authors: Yamazaki Masatoshi
Published: March 2003

The metrics of the Hoenselaers–Kinnersley–Xanthopoulos family of spinning mass solutions with arbitrary positive number distortion parameter δ and with twin rotation-reflection parameters besides mass parameter are studied. When values of two parameters are unequal or equal, the metrics are asymmetric or symmetric with respect to the reflection at the equatorial plane, respectively. The metrics for any distortion parameter δ contain no event horizon.
On stationary axially symmetric Einstein–Maxwell scalar and Brans–Dicke–Maxwell fields
Authors: Singh T. , Rai L.N.
Published: March 2003

A particular type of exact solutions of Einstein–Maxwell massless scalar field equations corresponding to stationary axially symmetric fields is presented here. The solutions are linear combinations of static fields with constant coefficients. Further, by a proper choice of conformal transformation the solutions have been transformed to the Brans–Dicke fields coupled with source-free electromagnetic fields. Finally these solutions have been transformed to a general form through unit transformations.
The quantum equivalence principle and finite particle creation in expanding universes
Authors: Castagnino Mario , Weder Ricardo
Published: March 2003

A formulation of the equivalence principle in quantum field theory is introduced. The quantum equivalence principle yields implementable Bogolyubov transformations. In this way we find a theory for a scalar field in curved space–time where particle creation is finite for every value of the coupling constant. In the particular case of conformal coupling the initial conditions of positive and negative frequency wave functions coincide with the ones of a first order WKB approximation. The coefficients of the Bogolyubov transformations are exactly computed and the created energy density is also finite.
Percolation theory on pairs of matching lattices
Authors: van den Berg J.
Published: March 2003

An important magnitude in percolation theory is the critical probability, which is defined as the supremum of those values of the occupation-probability p, for which only finite clusters occur. In 1964 Sykes and Essam obtained the relation P(s)c(L) +P(s)c(L*) =1, where L and L* are a pair of matching lattices and P(s)c denotes the critical probability (site-case). The proof was not complete, but based on certain assumptions about the mean number of clusters. Though Sykes and Essam suggested that the above relation holds for all mosaics (i.e., multiply-connected planar graphs) and decorated mosaics, we have constructed a counterexample. Subsequently, for a more restricted class of graphs, an alternative derivation of the Sykes–Essam relation is given, this time based on the usual assumption that below the critical probability the mean cluster size is finite. The latter assumption is also used to prove for some nontrivial subgraphs of the simple quadratic lattice S, that their critical probability is equal to P(s)c(S). Finally, for a certain class of lattices, sequences of numbers are constructed, which converge to the critical probability. In the case of the site process on S, the number with highest index we found, is 0.5925±0.0002, which seems to be a reasonable estimate of P(s)c(S).
On one method of solving the Helmholtz equation. I
Authors: Verbitskii I. L.
Published: March 2003

A method is suggested to solve the Helmholtz equation in an arbitrary domain with general form boundary conditions. The method permits reducing this equation to that of Poisson and an infinite set of simultaneous linear algebraic equations. Convergence of the method is proved for any wave number. Thus, it becomes possible to solve the Helmholtz equation by using any known method developed to solve the Poisson equation. As an illustration, an effective algorithm is constructed to solve the two dimensional diffraction problem on the arbitrary periodic boundary for any wavelength by using the conformal mapping techniques. If the boundary contains irregular points, then the field in all approximations has in all these points singularities of the needed type.
Representation and properties of para-Bose oscillator operators. II. Coherent states and the minimum uncertainty states
Authors: Sharma J. K. , Mehta C. L. , Mukunda N. , Sudarshan E. C. G.
Published: March 2003

The energy, position, and momentum eigenstates of a para-Bose oscillator system were considered in paper I. Here we consider the Bargmann or the analytic function description of the para-Bose system. This brings in, in a natural way, the coherent states ‖z;α〉 defined as the eigenstates of the annihilation operator ?. The transformation functions relating this description to the energy, position, and momentum eigenstates are explicitly obtained. Possible resolution of the identity operator using coherent states is examined. A particular resolution contains two integrals, one containing the diagonal basis ‖z;α〉〈z;α‖ and the other containing the pseudodiagonal basis ‖z;α〉〈−z;α‖. We briefly consider the normal and antinormal ordering of the operators and their diagonal and discrete diagonal coherent state approximations. The problem of constructing states with a minimum value of the product of the position and momentum uncertainties and the possible α dependence of this minimum value is considered.
Ermakov systems, velocity dependent potentials, and nonlinear superposition
Authors: Ray John R. , Reid James L.
Published: March 2003

We derive new Ermakov systems with velocity-dependent potentials. The extended Ermakov system presented contains all known one-dimensional cases and many new systems. These Ermakov systems lead to a nonlinear superposition law for the solutions.
The linear integral equations associated with any antiexact solution of the Yang–Mills free field equations
Authors: Edelen Dominic G. B.
Published: March 2003

Any system of r antiexact 1-forms, Aα, that solves the Yang–Mills free field equations associated with a semisimple r-parameter gauge group is shown to satisfy a system of linear inhomogeneous integral equations. These equations take the form Aα = Aαi dxi, Aαi = Rαi +Yαjiρ( Aρj), where Rαi dxi are r antiexact 1-forms, each of which solves Maxwell’s free field equations, and Yαjiρ are linear Riemann–Graves integral operators that are also linear in the structure constants of the gauge group. The standard iteration procedure for solving such systems may be looked upon as generating a sequence of corrections to the Rαi fields that account for the nonabelian character of the gauge group.
On invariant group integrals in lattice QCD
Authors: Eriksson K. E. , Svartholm N. , Skagerstam B. S.
Published: March 2003

A closed expression of the SU(3) [and U(3)] one-link invariant group integral in lattice gauge theories is derived. The U(3) result is compared to the expression recently derived by Brower, Rossi, and Tan. Applications of our results are briefly touched upon.
Minkowski space Yang–Mills fields from solutions of equations in the three-dimensional Euclidean space
Authors: Kyriakopoulos E.
Published: March 2003

Equations in the three-dimensional Euclidean space are derived by combining the Yang–Mills field equations with the conditions which are imposed on a Yang–Mills field in Bernreuther’s method of constructing Yang–Mills fields in Minkowski space from Yang–Mills fields in Euclidean space. By a proper ansatz for the Yang–Mills fields these equations are reduced to a single differential equation. The differential equation is identical with merons’ equation in Euclidean space if we consider solutions of the latter equation which are functions of the ratio t/ρ, where t is the Euclidean time and ρ is the three-dimensional radius. One such solution is the single meron solution in Euclidean space. Starting from this and applying the method we get the de Alfaro–Fubini–Furlan solution in Minkowski space. Then, a more general ansatz is considered, which leads to a system of three nonlinear differential equations.
Symplectic formulation of relativistic quantum mechanics
Authors: Kim Y. S. , Noz Marilyn E.
Published: March 2003

It is shown that the covariant harmonic oscillator formalism in the light-cone coordinate system discussed in previous papers is a realization of the symplectic group. It is shown in particular that the Lorentz transformation of the wave function along a given direction corresponds to a one-parameter subgroup of Sp(4). The diagonal form in the light-cone coordinate system is discussed in detail. The oscillator formalism is known to represent the Poincaré group for relativistic extended hadrons, while serving as a simple calculational device for basic high-energy hadronic phenomena. Likewise, the symplectic formulation given in the present paper may serve as the basic spacetime/momentum-energy symmetry for a relativistic quantum mechanics of bound-state quarks.
Analytical solutions of geometric optics with an approximation of diffraction
Authors: Hillion P. , Quinnez S.
Published: March 2003

In the first part of this paper, starting with geometric optics equations, we give some simple formulas for the intensity of collimated and focused beams when the refractive index has the special form n(r) = 1+εμ(r), where ε is a very small number. In the second part, we deal with diffraction as a perturbation of the refractive index and give corresponding formulas for essentially transversally bounded beams, i.e., beams with smooth boundary and most of the intensity near the propagation axis.
Generalized Bessel series and multiplicity problem in complex semisimple Lie algebra theory
Authors: Bretin C. , Gazeau J. P.
Published: March 2003

The connection between Bessel series and SU(2) is reviewed from the standpoint of the outer multiplicity problem for this group. Its extension to any complex semisimple Lie algebras allows one to introduce new objects called ’’generalized Bessel series.’’ Some applications concerning the special function theory (addition theorems) are given.
Canonical realizations of Lie superalgebras: Ladder representations of the Lie superalgebra A(m,n)
Authors: Palev Tchavdar D.
Published: March 2003

A simple formula for realizations of Lie superalgebras in terms of Bose and Fermi creation and annihilation operators is given. The essential new feature is that Bose and Fermi operators mutually anticommute. The Fock representation of these operators is used in order to construct a class of irreducible finite-dimensional representations of the simple Lie superalgebra A(m,n). The matrix elements of the generators are written down. For m≳0 all representations turn out to be nontypical.
Inverse scattering. III. Three dimensions, continued
Authors: Newton Roger G.
Published: March 2003

This paper presents further progress in the solution of the three-dimensional inverse scattering problem for the Schrödinger equation. We prove that if the potential is in a specified class and produces no bound states, then the kernel of the generalized Marchenko equation defines a compact operator and the equation has a unique solution unless the operator has the eigenvalue 1. A partial characterization of scattering amplitudes associated with underlying local potentials without bound states is given and the potential is constructed without assuming its existence. An improved generalization of the Marchenko equation is presented for the case with bound states. The generalized Gel’fand–Levitan equation is critically reviewed.
A perturbative look at the dynamics of extended systems in quantum field theory
Authors: Semenoff G. , Matsumoto H. , Umezawa H.
Published: March 2003

The structure of a quantum field theory with an extended object is explored perturbatively. The perturbative expansion consists of coupled differential equations which are derived from the Heisenberg field equation. These equations are used to reduce the zero mode problem to a choice of boundary conditions. They are then integrated and the constraint of the equal time commutation relations is used to set the boundary conditions and derive commutation relations for the physical fields and the quantum coordinate. Using this information the quantal Hilbert space is constructed.
Electric charge is vectorlike
Authors: Barr S. , Zee A.
Published: March 2003

Electric charge is vectorlike in the real world. We formulate this fact in terms of an infinite hierarchy of trace conditions. Contemporary physics offers an understanding of only the first two conditions. We discuss the requirement of a vectorlike charge in the context of grand unification. We give an argument against elementary Higgs fields. A number of group theoretic assertions bearing on the issue of vectorlike electric charge are proven. We argue that the observation of color nontriplet quarks would signal a rich fermionic spectrum. Several unsolved mathematical problems are stated.
Some applications of Postnikov systems in gauge theories
Authors: Bonora L. , de Pantz A. , Pasti P.
Published: March 2003

We use Postnikov systems for spaces relevant to gauge theories in order to derive results on characteristic classes and to prove Singer-like theorems about the impossibility of a continuous gauge choice on compactified space–time manifolds.
Solution of Poisson’s equation: Beyond Ewald-type methods
Authors: Weinert M.
Published: March 2003

A general method for solving Poisson’s equation without shape approximation for an arbitrary periodic charge distribution is presented. The method is based on the concept of multipole potentials and the boundary value problem for a sphere. In contrast to the usual Ewald-type methods, this method has only absolutely and uniformly convergent reciprocal space sums, and treats all components of the charge density equivalently. Applications to band structure calculations and lattice summations are also discussed.
Similarity solutions for the Ernst equations with electromagnetic fields
Authors: Kaliappan P. , Lakshmanan M.
Published: March 2003

A class of exact similarity solutions is shown to exist for the Ernst equations with electromagnetic fields. We reduce the underlying coupled nonlinear partial differential equations for the potentials into a system of coupled ordinary nonlinear differential equations for the similarity variables. The reduced system is exactly solvable in terms of elementary functions. These solutions are bounded everywhere.
Interpolation theory and refinement of nested Hilbert spaces
Authors: Antoine J.-P. , Karwowski W.
Published: March 2003

Using the method of quadratic interpolation between Hilbert spaces, we show that a nested Hilbert space with countable index set admits arbitrarily many proper refinements by nested Hilbert spaces.
Equivalent potentials in classical mechanics
Authors: Collas Peter
Published: March 2003

We show, within the framework of classical conservative system mechanics, that there exist local diffeomorphisms which connect Hamiltonians of different potentials. Thus, solutions for a given potential may be transformed into solutions for a different potential. Most of these results can be extended to quantum mechanics.
A note on stochastic dynamics in the state space of a commutative C* algebra
Authors: Alberti Peter M. , Uhlmann Armin
Published: March 2003

In this paper a functional characterization of stochastic evolutions within the state spaces of commutative C* algebras with identity is derived. Consequences concerning the structure of those linear evolution equations (master equations) that give occassion to stochastic evolutions are discussed. In part, these results generalize facts which are well known from the finite-dimensional classical case. Examples are given and some important particularities of the W* case are developed.
On the triangle anomaly number of SU(n) representations
Authors: Patera J. , Sharp R. T.
Published: March 2003

A simple geometrical interpretation of the triangle anomaly number of SU(n) representations is demonstrated. The number is equal to the sum of cubes of projections of weights on the U(1) direction; U(1) is the group in the reduction SU(n)⊇U(1)×SU(n−1). Properties of the anomaly number are then consequences of properties of weight systems. Explicit formulas are derived for the anomaly numbers for reducible representations corresponding to general plethysms based on an arbitrary representation of SU(n). Generalizations to ’’anomaly numbers’’ corresponding to degrees other than three are discussed.
Nonscalar extension of shift operator techniques for SU (3) in an O(3) basis. I. Theory
Authors: De Meyer H. E. , Vanden Berghe G. , Hughes J. W. B.
Published: March 2003

A set of relations is set up which connect quadratic products of the shift operators Okl (k = 0,1,2), which are nonscalar with respect to the O(3) subgroup of SU (3). The usefulness of these relations is illustrated by the calculation of the eigenvalues of the scalar shift operator O0l for various irreducible representations ( p,q) of SU (3).
Lorentz and SU(2)⊗U(N) analysis of the Lie algebra sp(4N;r) [gl(4N;r)] for any integer N≥1
Authors: Adams Mitchell D.
Published: March 2003

The generators of the fundamental representation of the Lie group GL(4N;r), integral N?1, are constructed from Kronecker products of smaller matrices in such a way that their tensor character under the action of the (unique) full null-plane Lorentz subgroup is apparent. Commutation relations of these tensors are given in terms of symmetric and antisymmetric structure constants for the fundamental representation of U(N) used in their construction. Generators of the Sp(4N;r) subgroup are classified according to transformation character under a U(N) subgroup. Commutation relations of sp(4N;r) are given in terms of SU(2)spin ⊗U(N) multiplets.