bluuebunny/crossref_metadata_2025 huggingface dataset:
Super Lie groups: global topology and local structure
Authors: Rogers Alice
Published: March 2003

A general mathematical framework for the super Lie groups of supersymmetric theories is presented. The definition of super Lie group is given in terms of supermanifolds, and two theorems (analogous to theorems in classical Lie group theory) are proved. The relationship of the super Lie groups defined here to the formal groups of Berezin and Kac and the graded Lie groups of Kostant is analyzed.
The Lorentz group in the oscillator realization. III. The group SO(3,1)
Authors: Basu Debabrata , Mitra D.
Published: March 2003

Employing the boson operators of Barut and Böhm, we study the oscillator realization of the Lie algebra of the Lorentz group SO(3,1) in the coordinate representation. The construction yields a direct sum of the principal series of representations ( j0,ρ) belonging to the integral or half-integral class. The decomposition of the representation space into the eigenspaces L2j0ρ of irreducible representations leads to a two-variable second order realization of the SO(3,1) algebra acting on fj0 ρ ∈L2j0ρ. The construction is shown to be highly symmetric. While the elements of the SO(2,1) subalgebra are invariant under the pseudorotation group SO(2,2), those of the full SO(3,1) algebra are invariant under the SO(2)×SO(1,1) subgroup of SO(2,2). We use this intrinsic symmetry in the construction to identify the generalized SO(2,1)⊆SO(3,1) eigenbases with the SO(2,2) harmonics in an SO(2)×SO(1,1) basis, and thereby achieve a significant unification among results which would normally appear disconnected.
Bäcklund transformations for the Ernst equation
Authors: Omote M. , Wadati M.
Published: March 2003

Presented is a systematic approach to the transformation theories for the Ernst equation from the viewpoint of the Bäcklund transformation. It is explicitly shown that the method of Clairin gives a simple derivation of various transformations such as transformations found by Ehlers, Neugebauer, and Harrison.
A multidimensional extension of the combinatorics function technique. II. Linear and inhomogeneous partial difference equations
Authors: Phares Alain J.
Published: March 2003

Recently the solution of multidimensional, linear, and homogeneous recurrence relations, or partial difference equations (PDE), was obtained via a multidimensional extension of the combinatorics function technique, developed by Antippa and Phares. Combinatorics functions of the first and second kind are representations of ’’restricted’’ paths connecting two points in an n-dimensional space. These functions are shown to give the solution of the most general linear and inhomogeneous PDE. The consistency of the PDE with the initial value conditions is also discussed. Applications of the method are given elsewhere.
Variable-phase approach to off-shell scattering by nonlocal potentials
Authors: Das U.
Published: March 2003

The basic ideas of the variable-phase approach are used to develop first-order differential equations for the quasiphase parameters which describe the half-off-shell scattering amplitudes for a nonlocal potential. The on-shell equation of Calogero and Sobel’s equation for a local potential are obtained as special cases.
Conformally flat static space–time in Brans–Dicke theory
Authors: Banerjee A. , Santos N. O.
Published: March 2003

For the conformally flat spherically symmetric static space–time we obtain the most general solution for Brans–Dicke field equations for a vacuum. By coupling the electromagnetic field to Brans–Dicke theory and imposing the condition of asymptotical flatness we obtain the most general solution for the space–time. We also present some other solutions of Brans–Dicke field equations with the conformally flat condition but without any particular symmetry. Finally, we give the transformation for generating solutions of Brans–Dicke field equations with or without electromagnetic field for ω = −3/2 from purely vacuum solutions of Einstein’s field equations.
Some spectral properties in algebras of unbounded operators
Authors: Epifanio G. , Trapani C.
Published: March 2003

Some aspects of spectral theory in algebras of unbounded operators are studied. After having pointed out the pathologies of the spectral behavior of these operators we give a sufficient condition in order that a self-adjoint operator admit a spectral decomposition with spectral measure with values in the same algebra. Some examples illustrating the developed ideas are given.
Matrices, differential operators, and polynomials
Authors: Calogero F.
Published: March 2003

It is noted that the matrix Z, of order n, defined in terms of the n arbitrary numbers xj by the formula Zjk = δjk 𝒥′l = 1,η (xj−xl)−1 +(1−δjk)(xj−xk)−1, may be considered (in an appropriate framework) to correspond to the differential operator d/dx. There follow prescriptions to construct explicit matrices of (arbitrary) order n in terms of n (or more) arbitrary numbers or of the n roots of given polynomials, matrices whose eigenvalues (and eigenvectors) are given, fully or in part, by very simple formulas. Novel representations of the classical polynomials (Hermite, Laguerre, Lagrange, Gegenbauer, Jacobi) are also obtained, such as the formula for Hermite polynomials Hn(x) = 2n det[xI−H(φ)], where I is the unit matrix (of order n) and the matrix H(φ), of order n, is defined by Hjk(φ) = (2n)−1/2(δjk(n−1)[exp(2iϑj) + 1/2  exp(−2iϑj)] +(1−δjk) {−exp(2iϑj) +2i sin(ϑj−ϑk)]−1 exp[−i(ϑj+ϑ k)]}), with ϑj = φ+πj/n, φ arbitrary.
Asymptotics of atomic ground states: The relation between the ground state of helium and the ground state of He+
Authors: Combes J. M. , Hoffmann-Ostenhof M. , Hoffmann-Ostenhof T.
Published: March 2003

The asymptotic behavior of ground states of two-electron atoms is investigated. Suppose ψ(x1,x2) is the ground state of helium, ρ(x1) = ℱψ2(x1,x2) dx2 the corresponding electron density, and Φ(x2) the ground state of He+. We show that in the L2(dx2)-sense, lim‖x1‖→∞ ψ(x1,x2)[ρ(x1)]−1/2 = Φ(x2), and that ψ[ρ(x1)]−1/2 solves for large ‖x1‖ the Schrödinger equation for He+ in the quadratic form sense. The rate of convergence of these limits is also discussed.
Exact solution of the Dicke model for the interaction of one atom with the electromagnetic field
Authors: Ramirez Ricardo , Orszag Miguel
Published: March 2003

A formal solution is found for the probability amplitude of emission of a photon by an atom coupled with the electromagnetic radiation, without the assumption of the rotating wave approximation.
The expansion of cylindrical fiber modes in a spherical coordinate
Authors: Morita Nagayoshi , Kumagai Nobuaki
Published: March 2003

Rigorous expansions of cylindrical fiber modes in a spherical coordinate are obtained. The expansions are possible not only for the case in which the origin of the spherical coordinates is located just on the center axis of the fiber but also for the case in which the origin is in an arbitrary position in the transverse cross-sectional plane including the exterior cladding region where the fields are of the evanescent type.
On the mass operators for multiquark systems
Authors: Szczyrba Igor
Published: March 2003

The vector space of tensor operators transforming according to the adjoint representation of the unitary group is investigated for arbitrary (even infinite) dimension of the group. In particular, a natural basis consisting of generalized number operators is constructed and some properties are studied. The results are applied to the construction of mass operators for arbitrary multiquark systems with arbitrary dimsension of the one-quark flavor space. It is shown, also, how the proved properties of the spectrum simplify the obtaining of certain mass formulas.
The elastic pendulum: A nonlinear paradigm
Authors: Breitenberger Ernst , Mueller Robert D.
Published: March 2003

A pendulum with an elastic instead of an inextensible suspension is the simplest realization of an autonomous, conservative, oscillatory system of several degrees of freedom with nonlinear coupling; it can also have an internal 1:2 resonance. A fairly complete study of this system at and near resonance is here undertaken by means of the ’’slow-fluctuation’’ approximation which consists in developing the x2y-type interaction into a trigonometric polynomial and keeping only the term with the slowest frequency. Extensive computations showed that up to moderately large amplitudes the approximate solutions were virtually as accurate as numerical integrations of the exact equations of motion. The slow-fluctuation equations of motion can be completely integrated by quadratures. Explicit solutions for amplitudes and phases are given in terms of elliptic functions, and can be linked to initial conditions. There exist two branches of purely periodic, harmonic, constant-amplitude motions which are orbitally stable but Liapunov unstable. The pure suspension motion is Liapunov unstable and remains orbitally stable only up to and including a critical amplitude; the standard ’’method of variational equations’’ leads to a slightly different stability criterion but is shown to be unreliable. In the dynamical neighborhood of the unstable pure suspension mode are motions which convert to it after infinite time. When a motion has an amplitude modulation minimum at or near zero, a phase reversal of the suspension takes place which is shown to be an artefact inherent in the description in terms of amplitudes and phases. In addition there is in the pendulum (but not in the exactly soluble system having the slow–fluctuation Hamiltonian) a fast phase transient which vitiates the slow-fluctuation technique for a few periods around the suspension amplitude minimum; this is the only restriction on the method. An appendix outlines formal isomorphisms between the elastic pendulum and the process of second-harmonic generation in nonlinear optics.
Exact propagators for multidimensional quadratic Hamiltonians—Initial-value approach
Authors: Tikochinsky Yoel
Published: March 2003

A practical method suitable for both analytic and numerical computation of propagators for multidimensional quadratic Hamiltonians in presented. The traditional two-end-point problem is replaced by a manageable initial-value problem. As a by-product, the classical path and action are also obtained as a solution to an initial-value problem. The method is illustrated analytically as well as numerically by solving for the motion of a particle in a constant magnetic field.
On the irreducibility of projective corepresentations—Application to double Shubnikov point groups
Authors: Dirl R.
Published: March 2003

An irreducibility criterion for projective corepresentations is stated and specified to projective corepresentations of double Shubnikov point groups, where the choice of the considered factor systems is influenced by the representation theory of double Shubnikov space groups.
Objects for the symmetric group
Authors: Soto M. F. , Mirman R.
Published: March 2003

The permutations, group multiplication tables, decomposition of permutations into neighboring transpositions, representation matrix elements, basis states, and basis state operators have been constructed for the symmetric groups S(n), n = 1,...,5. Part of the results have been relegated to PAPS. The algorithm for generating the permutations of the symmetric groups is discussed.
Dimension and character formulas for Lie supergroups
Authors: Balantekin A. Baha , Bars Itzhak
Published: March 2003

A character formula is derived for Lie supergroups. The basic technique is that of symmetrization and antisymmetrization associated with Young tableaux generalized to supergroups. We rewrite the characters of the ordinary Lie groups U(N), O(N), and Sp(2N) in terms of traces in the fundamental representation. It is then shown that by simply replacing traces with supertraces the characters of certain representations for U(N/M) and OSP(N/2M) are obtained. Dimension formulas are derived by calculating the characters of a special diagonal supergroup element with (+1) and (−1) eigenvalues. Formulas for the eigenvalues of the quadratic Casimir operators are given. As applications, the decomposition of a representation into representations of subgroups is discussed. Examples are given for the Lie supergroup SU(6/4) which has physical applications as a dynamical supersymmetry in nuclei.
Infeld–Hull factorization, Galois–Picard–Vessiot theory for differential operators
Authors: Hermann Robert
Published: March 2003

The Infeld–Hull theory of factorization of second order differential operators is related, on the one hand, to the classical Picard–Vessiot theory and, on the other hand, to work by the author, Gel’fand, and Kirillov on Lie algebras contained in the field of fractions or algebraic extensions of the enveloping associative algebra of a Lie algebra.
Isomonodromy as a curvature-zero condition
Authors: Hermann Robert
Published: March 2003

The ’’isomonodromy deformation’’ condition is expressed as a curvature-zero condition, thus bringing to the foreground the relations to other approaches in the theory of nonlinear waves.
The lump solutions and the Bäcklund transformation for the three-dimensional three-wave resonant interaction
Authors: Kaup D. J.
Published: March 2003

A Bäcklund transformation is found for the three-dimensional three-wave resonant interaction, and from it, N-lump exact solutions may be constructed. The one-lump solution is analyzed in detail, and it is shown that it describes such effects as pulse decay, upconversion, and explosive instabilities, all in three dimensions.
Two-sided Padé approximations for the plasma dispersion function
Authors: Németh G. , Ág Á. , Páris Gy.
Published: March 2003

Two-sided Padé approximations are determined for the plasma dispersion function. An exact closed form solution is given. The convergence problem is considered with regard to the real axis. Some applications from the theory of charged particle beams are also given
Matrix elements of operators in symmetrical U(6)⊇U(3)⊇U(2)⊇U(1) and U(6)⊇SU(3)⊇SO(3)⊇SO(2) basis
Authors: Quesne C.
Published: March 2003

In this paper we consider a basis for N boson states classified by the chain of groups U(6)⊇U(3)⊇U(2)⊇U(1). We determine analytical expressions for the matrix elements of the boson creation and annihilation operators, as well as for the U(6) generators, with respect to that basis. For such purpose, we use the Wigner–Eckart theorem with respect to U(3) and calculate the reduced matrix elements of the appropriate irreducible tensors from their matrix elements between highest weight states. Then we apply the transformation brackets from the chain U(6)⊇U(3)⊇U(2)⊇U(1) to the physical chain U(6)⊇SU(3)⊇SO(3)⊇SO(2) to obtain the matrix elements of the above-mentioned operators in a basis corresponding to the latter. The matrix elements so determined can be used either in the nuclear interacting boson model of Arima and Iachello or in the microscopic nuclear collective model of Vanagas et al.
Numerical evaluation of integrals containing a spherical Bessel function by product integration
Authors: Lehman D. R. , Parke William C. , Maximon L. C.
Published: March 2003

A method is developed for numerical evaluation of integrals with k-integration range from 0 to ∞ that contain a spherical Bessel function jl(kr) explicitly. The required quadrature weights are easily calculated and the rate of convergence is rapid—only a relatively small number of quadrature points is needed—for an accurate evaluation even when r is large. The quadrature rule is obtained by the method of product integration. With the abscissas chosen to be those of Clenshaw–Curtis and the Chebyshev polynomials as the interpolating polynomials, quadrature weights are obtained that depend on the spherical Bessel function. An inhomogenous recurrence relation is derived from which the weights can be calculated without accumulation of roundoff error. The procedure is summarized as an easily implementable algorithm. Questions of convergence are discussed and the rate of convergence demonstrated for several test integrals. Alternative procedures are given for generating the integration weights and an error analysis of the method is presented.
Decomposition of vector fields and mixed dynamics
Authors: Mendes R. Vilela , Duarte J. Taborda
Published: March 2003

Some theorems are proved concerning the decomposition of vector fields into gradient and Hamiltonian components. A constructive method to carry out one of the decompositions is applied to some three- and four- dimensional dynamical models.
An alternative derivation of transition amplitudes for time-dependent harmonic oscillators
Authors: De Meyer H. E. , Vanden Berghe G.
Published: March 2003

It is shown that the relations which link the x and p operators of a time-dependent harmonic oscillator to the x and p operators of the corresponding time-independent oscillator can be cast into a generalized Bogoliubov transformation on the standard harmonic oscillator boson creation and annihilation operators. Once this fact has been recognized, various techniques can be invoked to derive in a short way transition amplitudes.
Bound state perturbation theory for the one-space and one-time dimension Klein–Gordon equation
Authors: Au C. K. , Aharonov Y.
Published: March 2003

We present a perturbation theory for an arbitrary bound state in the one-space and one-time dimension Klein–Gordon equation in the presence of a scalar potential and a vector (fourth component only) potential by reducing it to a Ricatti equation with the method of logarithmic perturbation expansions. All corrections to the energies and wavefunctions, including corrections to the positions of the nodes in excited states, are expressed in quadratures in a hierarchical scheme, without the use of either the Green’s function or the sum over intermediate states.
On the structure of phase space
Authors: Moshinsky M. , Seligman T. H.
Published: March 2003

We consider phase space as the carrier space of canonical transformations and see that this implies, for nonbijective ones, a much subtler structure than the one commonly assumed. Discussing only problems of one degree of freedom, i.e., a phase plane, we are able to clarify this structure by analogy with the better-known situation of conformal mapping in the complex plane. Apart from the usual Riemann sheet concept, an alternate method is developed that involves the irreducible representations of the ambiguity group, i.e., the group of transformations that connects all points that are mapped on a single point by the conformal or canonical transformation. The algebra of variables then becomes a matrix algebra for which bijectiveness is retrieved.
Quantization on the sphere
Authors: Bayen F. , Fronsdal C.
Published: March 2003

When phase-space is a sphere, then conventional quantization is not available and the Heisenberg algebra is most naturally replaced by so(3). Quantization may be carried out in terms of invariant star-products. This leads to the study of an interesting family of polynomials that are defined in a natural and intrinsic way on the enveloping algebra of sl(2). These polynomials are related to Legendre polynomials by a reordering rule that resembles the relation between Hermite polynomials and normal ordered monomials; they are identified as Pasternack polynomials and related to Jacobi polynomials. New orthogonality properties are found and interpreted in terms of unitary representations of SL(2,R) and SO(3).
New nonlinear evolution equations from surface theory
Authors: Gürses Metin , Nutku Yavuz
Published: March 2003

We point out that the connection between surfaces in three-dimensional flat space and the inverse scattering problem provides a systematic way for constructing new nonlinear evolution equations. In particular we study the imbedding for Guichard surfaces which gives rise to the Calapso–Guichard equations generalizing the sine-Gordon (SG) equation. Further, we investigate the geometry of surfaces and their imbedding which results in the Korteweg–deVries (KdV) equation. Then by constructing a family of applicable surfaces we obtain a generalization of the KdV equation to a compressible fluid.
A discussion of the relation ‘‘closer than’’ within simple regions of curved space-time
Authors: Williams Gareth
Published: March 2003

A relation ’’closer than’’ is introduced for simple regions of curved space-time. This is a total relation on events within a light cone and a partial relation for events on a cone. The group of bijective automorphisms of the relation is the group of bijective homothetic mappings.
On the analysis of the gravitational field by reduction of the Weyl tensor to canonical form: Algebraically general case
Authors: Agacy R. L. , Clendenning L. M.
Published: March 2003

From the Weyl tensor, which can be split up into an ’’electric’’ and ’’magnetic’’ part of the gravitational field, one can construct a ’’flux of superenergy.’’ This is analogous to the electromagnetic case where the flux of energy is described by the Poynting vector. In the electromagnetic case, a suitable boost can be made to make the energy flux vanish in a certain frame. By analogy, in this paper we exhibit a variety of methods by which we find a frame in which the flux of superenergy vanishes. These methods are linked together involving spin, Lorentz and complex rotation matrices which are inherently related to a study of the quartic. The algebraically general case only is considered.
Vacuum counterexamples to the cosmic censorship hypothesis
Authors: Miller Bonnie D.
Published: March 2003

In cylindrically symmetric vacuum spacetimes it is possible to specify nonsingular initial conditions such that timelike singularities will (necessarily) evolve from these conditions. Examples are given; the spacetimes are somewhat analogous to one of the spherically symmetric counterexamples to the cosmic censorship hypothesis.
Solutions to wave equations on black hole geometries
Authors: Couch W. E.
Published: March 2003

Classes of explicit special solutions to the scalar wave equation on black hole spacetime geometries are given. Some analogous solutions also exist for fields of spin one or two. The spin-zero radial equation on the Reissner-Nordström geometry with m = e and on the Kerr geometry with m = a is shown to be related to the Whittaker-Hill equation.
Linear transport in nonhomogeneous media. I.
Authors: Larsen Edward W.
Published: March 2003

A set of elementary solutions of the linear transport equation is constructed for a class of scattering ratios which vary continuously in space. These solutions are shown to be complete on the half-range 0<μ⩽1 for a restricted class of scattering ratios.
Yang–Mills classical solutions with a remaining U(1) invariance
Authors: Brihaye Yves
Published: March 2003

Recently, sufficient conditions have been established, characterizing Yang-Mills fields invariant under a space–time-dependent U(1) subgroup of the full gauge symmetry group SU(2). In this paper we make precise the meaning of the equations and extend the known solutions for larger classes of sources.
Chain of the Bäcklund transformation for the KdV equation
Authors: Nakamura Akira
Published: March 2003

We study the chain of the Bäcklund transformation (≡BT) by the example of the KdV equation. The previously obtained chain of the BT, KdV→modified KdV (≡mKdV)→second mKdV, has been extended one step further to the third mKdV case. From this lowest order example, the structure of ’’infinity’’ of the chain process has been foreseen.
A limit on the variation of bounded positive operators
Authors: Fleming Gordon N.
Published: March 2003

An upper limit is obtained for the rate at which the expectation value, of a bounded positive operator in an arbitrary state, can change with the parameters of a unitary transformation of the state.
The criticality problem for an exponential atmosphere
Authors: Pomraning G. C.
Published: March 2003

The criticality problem for a half-space with an exponential single scatter albedo is analyzed. Analytic results are presented in the limits of very weak and very strong exponential behavior, and numerical results are given for general exponential behavior.
Some properties of the operator algebra generated by Hodge’s star and the exterior derivative
Authors: Sharma C. S. , Egele U.
Published: March 2003

Some properties of the operator algebra generated by Hodge’s star and the exterior derivative are established and in particular it is shown that viewed as an algebra over its center, this algebra is four-dimensional.
Finite subgroups of SU(3)
Authors: Bovier A. , Lüling M. , Wyler D.
Published: March 2003

We present a new class of finite subgroups of SU(3) of the form Zm s Zn (semidirect product). We also apply the methods used to investigate semidirect products to the known SU(3) subgroups Δ(3n2) and Δ(6n2) and give analytic formulae for representations (characters) and Clebsch–Gordan coefficients.
Tensor products of positive energy representations of S̃O(3,2) and S̃O(4,2)
Authors: Heidenreich W.
Published: March 2003

The Clebsch–Gordan series of the tensor product of a wide class of unitary irreducible positive energy representations of the universal covering groups of SO(3,2) and SO(4,2) are calculated by comparing weight diagrams.
Conservation laws and discrete symmetries in classical mechanics
Authors: Lutzky M.
Published: March 2003

A method is given for deriving conserved quantities from discrete symmetries in classical mechanics.
A generalized Weyl correspondence: Applications
Authors: Gadella M. , Santos E.
Published: March 2003

A so-called generalized Weyl correspondence is defined among random variables on one side and linear operators in a separable Hilbert space ℋ on the other. Besides such a correspondence, there is a relation among states on ℋ (considered as positive nuclear operators on ℋ) and the distribution functions of the random variables. By adding some new assumptions, several relations are shown. Later, we study two particularly interesting cases. In the first we connect dichotomic random variables with number operators in a Grassmann algebra ℋ, and nuclear operators on ℋ with probability measures in the set of all sequences made up of zero and one. In the second case we relate states between stochastic and quantum electrodynamics.
Representations of a local current algebra in nonsimply connected space and the Aharonov–Bohm effect
Authors: Goldin G. A. , Menikoff R. , Sharp D. H.
Published: March 2003

A recent paper established technical conditions for the construction of a class of induced representations of the nonrelativistic current group 𝒮Λ𝒦, where 𝒮 is Schwartz’s space of rapidly decreasing C∞ functions, and 𝒦 is a group of C∞ diffeomorphisms of Rs. Bose and Fermi N-particle systems were recovered as unitarily inequivalent induced representations of the group by lifting the action of 𝒦 on an orbit Δ⊆𝒮′ to its universal covering space δ̃. For s⩾3, δ̃ is the coordinate space for N particles, which is simply connected. In two-dimensional space, however, the coordinate space is multiply connected, implying induced representations other than those describing the usual Bose or Fermi statistics; these are explored in the present paper. Likewise the Aharonov–Bohm effect is described by means of induced representations of the local observables, defined in a nonsimply connected region of Rs. The vector potential plays no role in this description of the Aharonov–Bohm effect.
The mathematical structure of arrangement channel quantum mechanics
Authors: Evans J. W.
Published: March 2003

A non-Hermitian matrix Hamiltonian H appears in the wavefunction form of a variety of many-body scattering theories. This operator acts on an arrangement channel Banach or Hilbert space 𝒞 = ⊕αℋ where ℋ is the N-particle Hilbert space and α are certain arrangement channels. Various aspects of the spectral and semigroup theory for H are considered. The normalizable and weak (wavelike) eigenvectors of H are naturally characterized as either physical or spurious. Typically H is scalar spectral and ’’equivalent’’ to H on an H-invariant subspace of physical solutions. If the eigenvectors form a basis, by constructing a suitable biorthogonal system, we show that H is scalar spectral on 𝒞. Other concepts including the channel space observables, trace class and trace, density matrix and Möller operators are developed. The sense in which the theory provides a ’’representation’’ of N-particle quantum mechanics and its equivalence to the usual Hilbert space theory is clarified.
Orthogonal transitivity, invertibility, and null geodesic separability in type D electrovac solutions of Einstein’s field equations with cosmological constant
Authors: Debever R. , McLenaghan R. G.
Published: March 2003

It is shown without explicit integration that all Petrov type D electrovac solutions with cosmological constant for an aligned, nonsingular electromagnetic field which satisfy the generalized Goldberg–Sachs theorem, admit at least a two-parameter, abelian, orthogonally transitive group of local isometries. In the case when the group orbits are non-null the group is invertible, and a symmetric null tetrad is shown to exist in which the principle null congruences defined by the type D Weyl tensor are indistinguishable. An explicit example is given of a solution with null group orbits which contains as a subcase a Kinnersley vacuum solution (with the same property). It is also demonstrated that the Hamilton–Jacobi equation for the null geodesics is always solvable by separation of variables in these solutions, a fact which explains the existence of a conformal Killing tensor therein, and which gives rise to a coordinate system in which the field equations may be integrated in terms of polynomial functions.
An exact stationary solution of the combined Einstein–Maxwell–Klein–Gordon equations
Authors: Gegenberg J. D. , Das A.
Published: March 2003

The Einstein–Maxwell–Klein–Gordon equations are simplified by imposing stationarity, isometric motion, the Weyl–Majumdar–Papapetrou condition, and axial symmetry. An exact (nonstatic) stationary solution is found such that the electric field vanishes, the magnetic field is constant and parallel to the polar axis, and the wavefunction of the matter field is of the form of a ’’pure phase.’’ The energy–momentum tensor satisfies the strong energy condition of Hawking and Ellis. The metric tensor resembles that of the Gödel solution and has similar causal properties.
Radiation gauge covariance
Authors: Krause Jorge
Published: March 2003

A manifestly covariant relation is discussed between electromagnetic gauge transformations and Lorentz transformations, while analyzing the contributions to the free field 4-potential coming exclusively from lightlike momenta. Transverse 4-potentials are thus introduced relative to each inertial frame which belong in the Lorentz gauge, behave as completely invariant objects under general guage transformations, and give rise to one and the same frame-free electromagnetic field tensor. The (proper orthochronous) Lorentz covariant transformation law of the guage-invariant transverse 4-potential is established, from the standpoint of the active transformation from one inertial observer to another.
A new integral equation for summing Feynman graph series (φ3 ladder graph case)
Authors: Gilain C. , Levy D.
Published: March 2003

The Schwinger parameter formalism is used to derive a new integral equation verified by the sum of the ’’open amplitudes’’ of the ladder graph series with a φ3 interaction. We prove the existence of a solution to this equation and of the corresponding Green’s function. This solution, for any finite value of the coupling constant, is a finite sum of solutions to Fredholm integral equations plus the sum of a convergent series. Its set of singularities is a set of poles from which the spectrum of Regge poles is obtained.
Convex covariant entropy density, symmetric conservative form, and shock waves in relativistic magnetohydrodynamics
Authors: Ruggeri Tommaso , Strumia Alberto
Published: March 2003

The system of conservation laws governing the relativistic magnetohydrodynamics (MHD) is shown to possess a covariant entropy density which is a convex function of suitable field variables. Therefore, the results of a general theory developed in a previous paper hold and in particular: (a) there exists a main field such that the system exhibits a conservative symmetric hyperbolic form, in the sense of Friedrichs, and therefore the local Cauchy problem is well posed in a Sobolev space Hs (s⩾4); (b) the entropy increases across a shock wave front; (c) the shock propagation velocities do not exceed the speed of light; (d) the jump of thermodynamic entropy determines the jumps of each field variable.
On black holes in magnetic universes
Authors: Hiscock William A.
Published: March 2003

The magnetized black hole solutions discovered by Ernst are studied. It is shown that no static magnetic-universe Kerr–Newman black holes exist if either a, the Kerr angular momentum parameter, or e, the electric charge parameter, is nonzero. Robinson’s identity is used to prove that the Schwarzschild–Melvin black hole solution is the unique static, axisymmetric black hole solution of the sourceless Einstein–Maxwell equations which asymptotically resembles Melvin’s magnetic universe. This may be viewed as a generalization of Israel’s theorem, in which one extra assumption (axisymmetry) is required, but the boundary conditions at infinity are somewhat relaxed.
Path integral quantization of the supersymmetric model of the Dirac particle
Authors: Ogielski A. T. , Sobczyk J.
Published: March 2003

We investigate in detail the representation of the Dirac propagator as a path integral over virtual trajectories in the phase space with anticommuting variables. Using the reparametrization and supergauge invariant action integral proposed by Berezin and Marinov [Ann. Phys. 104, 336 (1977)], we analyze the relation of causality to reparametrization invariance, and we construct the Faddeev–Popov measure for the symbol of the evolution operator. We present a precise definition of the path integral as a limit of finite-dimensional integrals, and we explicitly perform the integration obtaining the familiar result. We also analyze another approach, where reparametrization and supergauge invariance of the action is preserved with the help of independent einbein variables. This method, as opposed to Faddeev–Popov technique, dispenses with the gauge fixing problem and allows us to construct the correct functional measure by explicit factorization of the volume of reparametrization group and supergauge group; the former is infinite, the latter identically vanishes. A sequence of finite-dimensional approximations to the functional measure is given also in this case together with explicit calculations.
Spectral estimates, stability conditions, and the rotating screw-pinch
Authors: Hameiri Eliezer
Published: March 2003

This article presents two sufficient conditions for the linear stability of rotating ideal plasmas, the first based on conservation of circulation and the second based on circle theorems applicable to linear Hamiltonian systems. The circle theorems also provide bounds on eigenmodes in the complex plane. All results are applied to the rotating screw-pinch which can be described by a single second-order ordinary differential equation.
Path integration for time-dependent metrics
Authors: Nelson Bruce , Sheeks Benny
Published: March 2003

We define path integrals for systems with time-dependent metrics in terms of prodistributions and discuss the relation of the path integral quantization to the Schrödinger one. We work an example that displays the elegance and utility of the prodistribution definition. We also discuss how our definition is particularly suited for changing integration variables.
Dynamical symmetries of the Schrödinger equation
Authors: Mitchell Thomas P.
Published: March 2003

The conditions are derived under which a symmetry operator quadratic in the momenta exists for a spin-zero structureless point charge interacting with an externally applied uniform magnetic field in the presence of a potential field. The conditions apply to the possible forms of the potential. The explicit form of the symmetry operator in general is constructed and some particular examples are examined.
Eigenvalues of an anharmonic oscillator
Authors: Kesarwani R. N. , Varshni Y. P.
Published: March 2003

The five-term WKBJ approximation is applied to calculate the eigenvalues for the potential V(x) = 1/2 kx2+ax4, k≳0 and a≳0. Numerical results are compared with those of Hioe and Montroll. It is found that the accuracy of the calculated eigenvalues improves rapidly with increase in the quantum number n. At n = 4, a seven significant figure accuracy is achieved and at n = 6, a nine significant figure accuracy.
A nonmanifold theory of space–time
Authors: Mashford J. S.
Published: March 2003

A Zeeman topology is defined in the general framework of any set W of events which has been equipped with an acyclic signal relation ∼ →. The Wssumption that the ∼ → structure of W is locally that of Minkowski space and that the ’’piecing together’’ maps are smooth in an appropriate sense, allows a tangent bundle p:E→W to be defined. This bundle has, as structure group, the group G of linear causal automorphisms of Minkowski space.
Weyl tensors for asymmetric complex curvatures
Authors: Oliveira Colber G.
Published: March 2003

Considering a second-rank Hermitian field tensor and a general Hermitian connection we construct the associated complex curvature tensor. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory.
On the analyticity of stationary gravitational fields at spatial infinity
Authors: Kundu P.
Published: March 2003

It is proved that all stationary, vacuum solutions of Einstein’s equations which satisfy certain weak differentiability conditions characterizing asymptotic flatness, possess an analytic structure near spatial infinity. This analyticity theorem implies the existence of a multipole expansion whose coefficients can be expressed in terms of the Geroch–Hansen multipole moments defined at the point at infinity on the conformal manifold. This proves a longstanding conjecture that these moments uniquely determine the local structure of a stationary, asymptotically flat, vacuum metric.
Thermal fluctuations in quantum gravity: A semiclassical description
Authors: Magnon-Ashtekar Anne
Published: March 2003

By Wick rotating the Levi-Civita metric in an appropriate coordinate range, a positive definite, asymptotically Euclidean metric is obtained on R4. This metric has the following properties: (a) it is smooth everywhere except on a 3-sphere Σ, where it suffers (finite) discontinuities; (b) it is Ricci-flat everywhere except on Σ; and (c) it is periodic in ’’imaginary time’’ both inside and outside Σ but with two distinct periods (reflecting the fact that the corresponding Lorentzian section covers the region bounded by two distinct horizons). In the Euclidean approach to quantum gravity, each region with a fixed period may be regarded as being at a fixed temperature. Therefore, in the semiclassical approximation, the metric represents an interesting extension of the familiar states of thermal equilibrium of the gravitational field.
Validity of the Bethe–Yang hypothesis in the delta-function interaction problem
Authors: Fung M. K.
Published: March 2003

We give an explicit verification of the Bethe–Yang hypothesis in the one-dimensional delta-function interaction problem.
On the stability of periodic orbits of two-dimensional mappings
Authors: Bountis Tassos , Helleman Robert H. G.
Published: March 2003

We present a closed form stability criterion for the periodic orbits of two-dimensional conservative as well as ’’dissipative’’ mappings which are analogous to the Poincaré maps of dynamical systems. Our stability criterion has a particularly simple form involving a finite, symmetric, nearly tridiagonal determinant. Its derivation is based on an extension of the stability analysis of Hill’s differential equation to difference equations. We apply our criterion and derive a sufficient stability condition for a large class of periodic orbits of the widely studied ’’standard mapping’’ describing a periodically ’’kicked’’ free rotator. As another example we also obtain explicitly and in closed form the intervals of bounded (and unbounded) solutions of a discrete ’’Schrödinger equation’’ for the Kronig and Penney crystal model.
Geodesic first integrals with explicit path-parameter dependence in Riemannian space–times
Authors: Katzin Gerald H. , Levine Jack
Published: March 2003

In a Riemannian space Vn general formulas are obtained for geodesic first integrals which are mth order polynomials in the tangent vector and which are assumed to depend explicitly on the path parameter s. It is found that such first integrals must also be polynomials in s. Necessary and sufficient conditions are found for the existence of these first integrals. The existence of many well-known symmetries such as homothetic motions (scale change), affine collineations, conformal motions, projective collineations, conformal collineations, or special curvature collineations are shown to be sufficient for the existence of such first integrals with explicit path-parameter dependence. To illustrate the theory, geodesic first integrals of this type have been calculated for four Riemannian space–times of general relativity.
On the inverse problem of the calculus of variations
Authors: Hojman Sergio , Urrutia Luis F.
Published: March 2003

We consider the inverse problem of the calculus of variations for any system by writing its differential equations of motion in first-order form. We provide a way of constructing infinitely many Lagrangians for such a system in terms of its constants of motion using a covariant geometrical approach. We present examples of first-order Lagrangians for systems for which no second-order Lagrangians exist. The Hamiltonian theory for first-order (degenerate) Lagrangians is constructed using Dirac’s method for singular Lagrangians.
Dispersion relations for linear wave propagation in homogeneous and inhomogeneous media
Authors: Weaver Richard L. , Pao Yih-Hsing
Published: March 2003

For the dispersion of waves in a homogeneous medium there exist the Kramers–Kronig relations for the wave number K(ω) = ω/c(ω). The usual mathematical proof of such relations depends on assumptions for the asymptotic behavior of c(ω) at high frequency, which for electromagnetic waves in dielectrics can be evaluated from the microphysical properties of the medium. In this paper such assumptions are removed and the necessary asymptotic behavior is shown to follow the representation of K(ω) as a Herglotz function. From the linear, causal, and passive properties of the media we thus establish the Kramers–Kronig relations for all linear wave disturbances including acoustic, elastic, and electromagnetic waves in inhomogeneous as well as homogeneous media without any reference to the microphysical structure of the medium.
Construction of (J
J*)−1 in the Chandler–Gibson reaction theory
Authors: Polyzou Wayne
Published: March 2003

We exhibit a technique to construct formally the operators (JJ*)−1 and (JΠJ*)−1 in the Chandler–Gibson theory. Our construction is based on integral equations whose kernels can be made contractive with an appropriate choice of parameters. We discuss uniqueness and give representations of the solutions as uniformly convergent series.
Quantum-mechanical scattering by impenetrable periodic surfaces
Authors: Sáenz A. W.
Published: March 2003

In this paper, we investigate the existence and completeness of the wave operators W± = s-limt→±∞  exp (itH) P exp (−itH0) corresponding to the quantum-mechanical scattering of nonrelativistic particles by certain classes of impenetrable noncompact surfaces bounding domains Ω ⊆Rν (ν ⩾2) which contain a half-space and are contained in another half-space. Here, H0 is the usual negative (distributional) Laplacian−Δ in H0 = L2(Rν ), H is the negative Dirichlet Laplacian in H = L2(Ω), and P is an appropriate identification operator. Under these conditions, we prove by elementary methods that W± exist as partially isometric operators whose initial sets have a transparent physical meaning. Suppose now that the domain Ω ⊆Rν also has the periodicity property (x̃,xν)∈Ω→(x̃+l,xν)∈Ω when l ranges over a Bravais lattice in Rν−1 , where we write x∈Rν as (x̃,xν), with x̃∈Rν−1 and xν ∈R. Then (a) RanW± = Hscatt (H) and (b) W± are asymptotically complete, in the sense that H = Hscatt(H)⊕Hsurf(H). Here, Hscatt (H) and Hsurf (H) are suitably defined subspaces of scattering and surface states of H, respectively. Results (a) and (b) are proved by reducing the original scattering problem to a family of ’’scattering’’ problems in a periodicity cell of Ω, using direct-integral methods, and by then using methods analogous to those of Lyford. The present work constitutes a rigorous foundation for the theory of scattering of low-energy atomic beams by crystal surfaces, considered as impenetrable periodic barriers. Our methods should also be applicable to rigorous investigations of classical scattering by periodic surfaces with Dirichlet or Neumann boundary conditions.
On a completely symmetric choice of space–time coordinates
Authors: Derrick G. H.
Published: March 2003

It is shown that for a wide class of space–times the four coordinates may be chosen in a completely symmetric way. Such symmetric coordinates have the same causal nature in that they are all measured by the same type of prescription involving clocks and/or measuring rods. In these coordinate systems the metric tensor is invariant with respect to any permutation of the coordinate labels 0, 1, 2, 3.
The KMS condition and regularity for the ideal Bose gas
Authors: de Smedt Ph. , Stragier G.
Published: March 2003

We prove that the KMS condition for the infinite ideal Bose gas at any temperature 1/β and chemical potential μ⩽0 implies regularity under certain conditions on the test function space. Also, explicitly irregular solutions are constructed indicating the difference between the KMS condition and Gibbs states.
The kinetic analog of Boltzmann’s principle
Authors: Lavenda B. H. , Santamato E.
Published: March 2003

A general expression for the transition density of nonequilibrium diffusion processes is derived that is valid for non-Gaussian fluctuations. Using the thermodynamic principle, that relates the relative probability density of paths for absolutely continuous diffusion processes to the thermodynamic force, the kinetic analog of Boltzmann’s principle is derived. The transition density can be expressed in terms of the difference in entropies of the endpoints of the transition and the joint entropy. The gradient of the joint entropy is a measure of the strength of statistical correlations between nonequilibrium states and its difference (sum) between the thermodynamic forces determines the rates of growth (decay) of fluctuations. These rates are mirror images in time of one another and display a symmetry in past and future. The macroscopic laws of irreversible thermodynamics emerge in the exact balance of these two phenomena.
The global symmetries of spin systems defined on abelian groups. I
Authors: Marcu M. , Regev A. , Rittenberg V.
Published: March 2003

We consider the classification problem of the global symmetry groups of spin systems defined on abelian groups. Its implications on the generating functional, the transfer matrix, the Hamiltonian formalism, and factorization properties of spin systems are discussed. The duality properties of spin systems defined on semidirect products of abelian groups are revisited. In the first of this series of three papers we list the groups for systems defined on Zp (p prime), Z2⊗Z2, and Z2⊗Z2⊗Z2 manifolds. They are direct or wreath products of M-metacyclic groups and symmetric groups.
The global symmetries of spin systems defined on abelian groups. II
Authors: Marcu M. , Rittenberg V.
Published: March 2003

We present the classification of the global symmetry groups of spin systems defined on Zp⊗Zq,Zp2, and Zp⊗Zp abelian groups ( p and q are prime numbers).