bluuebunny/crossref_metadata_2025 huggingface dataset:
Inhomogeneous rotating universes with closed timelike geodesics of matter
Authors: Soares I.Damião
Published: March 2003

We present a new class of inhomogeneous stationary cosmological solutions of Einstein–Maxwell equations, with rotating dust and electromagnetic fields. For a subclass of these models, the topology of the space–time manifold is S3×R, and the timelike geodesic lines of dust are closed; electromagnetic fields are necessary only to avoid matter singularities, while in the completely homogeneous limit they are essential for consistency of field equations; these electromagnetic fields have the structure of magnetic monopole fields, since the total magnetic flux across the unit 2-sphere is different from zero—that is, magnetic monopoles must be present as a source of the fields.
On the SU2 unit tensor
Authors: Kibler Maurice , Grenet Geneviève
Published: March 2003

This paper deals with the SU2 ⊆ G unit tensor operators tkμα. In the case where the spinor point group G coincides with U1, then tkμα reduces (up to a constant) to the (Wigner–Racah–Schwinger) tensor operator tkqα, an operator which produces an angular momentum state ‖ j+α, m+q〉 when acting upon the state ‖ jm〉. We first investigate those general properties of tkμα which are independent of their realization. We then turn our attention to realizations of tkμα in terms of two pairs of boson creation and annihilation operators. This leads us to look at the Schwinger calculus (found to be connected to the de Sitter algebra so3,2) relative to one angular momentum or two coupled angular momenta. As a by-product, we give a procedure for producing recursion relationships between SU2 ⊆ U1 Wigner coefficients. Expressions for tkqα, which cover the cases k integer and half-an-odd-integer, are derived in terms of boson operators. When k is integer, the latter expressions can be rewritten in the enveloping algebra of so3 or so3,2 according to as α=0 or α≠0. Finally, we study in two appendices some of the properties of (i) the Wigner and Racah operators for an arbitrary compact group and (ii) the SU2 ⊆ G coupling coefficients.
On an infinitesimal approach to semisimple Lie groups and raising and lowering operators of O(n) and U(n)
Authors: Gould M. D.
Published: March 2003

A purely algebraic approach to the evaluation of the fundamental Wigner coefficients and reduced matrix elements of O(n) and U(n) is given. The method employs the explicit use of projection operators which may be constructed using the polynomial identities satisfied by the infinitesimal generators of the group. As an application of this technique, a certain set of raising and lowering operators for O(n) and U(n) are constructed. They are simpler in appearance than those previously constructed since they may be written in a compact product form. They are, moreover, Hermitian conjugates of one another, and therefore are easily normalized.
Field equations in twistors
Authors: Qadir Asghar
Published: March 2003

As part of the twistor program for the ’’quantization of relativity’’ the physical field equations have been translated into twistors.
On the role of space–time topology in quantum phenomena: Superselection of charge and emergence of nontrivial vacua
Authors: Ashtekar Abhay , Sen Amitabha
Published: March 2003

Schwarzschild–Kruskal space–time admits a two-parameter family of everywhere regular, static, source-free Maxwell fields. It is shown that there exists a corresponding two-parameter family of unitarily inequivalent representations of the canonical commutation relations. Elements of the underlying Hilbert space may be interpreted as ’’quantum fluctuations of the Maxwell field off nontrivial classical vacua.’’ The representation corresponding to the ’’trivial’’ sector—i.e., the zero classical solution— is the usual Fock representation. All others are ’’non-Fock.’’ In particular, in all other sectors, the Maxwell field develops a nonzero vacuum expectation value. The parameters labelling the family can be interpreted as electric and magnetic charges. Therefore, unitary inequivalence naturally leads to superselection rules for these charges. These features arise in spite of the linearity of field equations only because the space–time topology is ’’nontrivial.’’ Also, because of linearity, an exact analysis is possible at the quantum level; recourse to perturbation theory is unnecessary.
Finite field equation of Yang–Mills theory
Authors: Brandt Richard A. , Wing-Chiu Ng , Yeung Wai-Bong
Published: March 2003

We consider the finite local field equation −{[1+1/α (1+f4)]gμν⧠−∂μ∂ν}Aνa =−(1+f3) g2N[AcνAaμAνc] +⋅⋅⋅+(1−s)2M2Aaμ, introduced by Lowenstein to rigorously describe SU(2) Yang–Mills theory, which is written in terms of normal products. We also consider the operator product expansion Acν(x+ξ) Aaμ(x) Abλ(x−ξ) ∼ΣMcabνμλc′a′b′ν′μ′λ′ (ξ) N[Aν′c′Aμ′a′Aλ′b′](x ), and using asymptotic freedom, we compute the leading behavior of the Wilson coefficients M......(ξ) with the help of a computer, and express the normal products in the field equation in terms of products of the c-number Wilson coefficients and of operator products like Acν(x+ξ) Aaμ(x) Abλ(x−ξ) at separated points. Our result is −{[1+(1/α)(1+f4)]gμν⧠−∂μ∂ν }Aνa =−(1+f3) g2limξ→0{ (lnξ)−0.28/2b[Acν (x+ξ) Aaμ(x) Aνc(x−ξ) +εabcAμc(x+ξ) ∂νAbν(x)+⋅⋅⋅] +⋅⋅⋅}+(1−s)2M2Aaμ, where β (g) =−bg3, and so (lnξ)−0.28/2b is the leading behavior of the c-number coefficient multiplying the operator products in the field equation.
Superconformal group and curved fermionic twistor space
Authors: Lukierski J.
Published: March 2003

It is shown that the superconformal transformations describe the isometry group of curved fermionic twistor space, with suitably generalized Fubini–Study Hermitian metric. Further, such a geometry is applied to derive a two-dimensional supersymmetric quark–twistor string model, described by the fermionic nonlinear SU(2,2;1) -invariant σ-model.
Magnetic resonances between massive and massless spin- 1/2 particles with magnetic moments
Authors: Barut A. O.
Published: March 2003

The general effective radial potentials for a spin- 1/2 particle interacting with scalar, electric, and magnetic potentials are given. In the m=0 limit, it is shown that the magnetic potential provides a well deep enough to confine the massless particle. In particular, there are exact zero-energy solutions in which two of the four components of the massless particle are confined; only two can leak out into the asymptotic region. The scattering amplitude is analytic in the entire j plane, hence consists only of Regge poles.
On some representations of the Poincaré group on phase space. II
Authors: Ali S. Twareque
Published: March 2003

Representations of the proper Poincaré group on spaces of functions of the phase space variables q and p have been studied, by starting with the rotation subgroup SO(3), and carrying out an inducing procedure. A complete decomposition theory, for the physically interesting representations, have been developed. Explicit computations of the forms of the generators and certain systems of imprimitivity have been carried out. The role of the Newton–Wigner position and momentum operators, in the setting of phase space representations, has been discussed. The work is a continuation of an earlier paper on phase space representations, inspired ultimately by the possibility of developing a consistent relativistic quantum mechanics for single particles on phase space.
Perturbation of self-adjoint operators by Dirac distributions
Authors: Zorbas J.
Published: March 2003

The existence of a family of self-adjoint Hamiltonians Hϑ, ϑ ∈ [0, 2π), corresponding to the formal expression H0+νδ (x) is shown for a general class of self-adjoint operators H0. Expressions for the Green’s function and wavefunction corresponding to Hϑ are obtained in terms of the Green’s function and wavefunction corresponding to H0. Similar results are shown for the perturbation of H0 by a finite sum of Dirac distributions. A prescription is given for obtaining Hϑ as the strong resolvent limit of a family of momentum cutoff Hamiltonians HN. The relationship between the scattering theories corresponding to HN and Hϑ is examined.
Null infinity and Killing fields
Authors: Ashtekar Abhay , Schmidt B. G.
Published: March 2003

A recent investigation due to Ashtekar and Xanthopoulos of isometries compatible with asymptotic flatness at null infinity is extended by considering space–times which admit ’’only a piece of Jn. This extension makes the interplay between asymptotic conditions and permissible isometries more transparent by bringing out how the various parts of the asymptotic structure individually lead to restrictions on isometries and by separating the consequences of field equations from those of purely geometric asymptotic conditions.
Scale limit and low momentum behavior of Euclidean fields. II
Authors: Haba Z.
Published: March 2003

The problem of the limit behavior of a rescaled random field εαφ (x/ε) as ε→0 is considered as an analog for random fields of the classical limit theorems for sums of random variables. If the random field φ does not depend on the scale ε, the limit is Gaussian in Euclidean field theory with a mass gap. If φ itself is a function of ε (giving a double sequence scheme), any infinitely divisible distribution can appear as the limit. In this formulation the limit of ε−dφ (x/ε) as ε→0 is discussed. It is proved that the limit field (if it exists) is a random field with values independent at every point. A correspondence between this scale limit and low momentum behavior is revealed. It is shown also that the scale limit may be considered as a limit of field theory when m→∞ and the coupling constant g→∞ in superrenormalizable theories and m→∞, g→0 for nonrenormalizable interactions. The scale limit of some ultraviolet regularized Euclidean fields is calculated. As an application some functional integrals are evaluated in the Ginzburg–Landau model in the low momentum limit.
A recursion formula for sp(3,R) matrix elements
Authors: Rosensteel G.
Published: March 2003

A recursion formula is derived for the reduced matrix elements of of the sp(3,R) discrete series with respect to a basis symmetry—adapted to its u(3) subalgebra. These matrix elements are needed in the symplectic nuclear model of collective motion.
Transverse instability of breathers in resonant media
Authors: Kodama Yuji , Ablowitz Mark J.
Published: March 2003

It is shown analytically that the breather (0π pulse) of transparent optical pulse propagation in a resonant medium is unstable with respect to long transverse perturbations.
On the invariant scalar products and the UIR of SO  (n,1)
Authors: Maekawa Takayoshi
Published: March 2003

A quantity, which is invariant under the transformation of h∈SO  (n,1), is found in a form of the series expansion in terms of the D matrix elements of SO  (n) and an invariant scalar product, which is needed for the complementary series of the unitary irreducible representation of SO  (n,1), is introduced in the Hermitian form by using the invariant quantity. The action of the intertwining operator defined through the Hermitian scalar product to the bases of Hc, on which the complementary series of the UIR of SO  (n,1) are realized, is found.
A connection between nonlinear evolution equations and ordinary differential equations of P-type. I
Authors: Ablowitz M. J. , Ramani A. , Segur H.
Published: March 2003

We develop here two aspects of the connection between nonlinear partial differential equations solvable by inverse scattering transforms and nonlinear ordinary differential equations (ODE) of P-type (i.e., no movable critical points). The first is a proof that no solution of an ODE, obtained by solving a linear integral equation of a certain kind, can have any movable critical points. The second is an algorithm to test whether a given ODE satisfies necessary conditions to be of P-type. Often, the algorithm can be used to test whether or not a given nonlinear evolution equation may be completely integrable.
Separating variables in two-way diffusion equations
Authors: Fisch Nathaniel J. , Kruskal Martin D.
Published: March 2003

It is shown that solutions to a class of diffusion equations of the two-way type may be found by a method akin to separation of variables. The difficulty with such equations is that the boundary data must be specified partly as initial and partly as final conditions. In contrast to the one-way diffusion equation, where the solution separates only into decaying eigenfunctions, the two-way equations separate into both decaying and growing eigenfunctions. Criteria are set forth for the existence of linear eigenfunctions, which may not be found directly by separating variables. A speculation with interesting ramifications is that the growing and decaying eigenfunctions are separately complete in an appropriate half of the problem domain. This conjecture is not proved, although it does enjoy some numerical support.
Cotangent bundle approach to noninertial frames
Authors: DeFacio B. , Retzloff D.G.
Published: March 2003

The most general possible noninertial acceleration in special relativity is formulated with differential forms in the cotangent bundle. We show that the Lie derivative plays the same role in the cotangent bundle that the covariant derivative plays in the tangent bundle. We also show that a cotangent bundle analog of Fermi–Walker transport can be based upon the, ’’cotangent-geodesic’’ equation, ℒuω=0. This gives a generalization of the work by Kiehn on classical Hamiltonian mechanics to special relativity.
Diffusion equation derived from the space–time transport equation in anisotropic random media
Authors: Furutsu K.
Published: March 2003

The diffusion equation is derived from the ordinary space–time transport equation with an arbitrary scattering cross section σ (Ω‖Ω′) ≠σ (Ω′‖Ω). After various equations are Fourier transformed with respect to the space–time coordinates, the transport equation is shown to be reduced to an integral equation of the Fredholm type with respect to the angle of scattering, with the variables of Fourier transformation kept constant. The solution is then expanded in the eigenfunction series and, under the diffusion condition, its convergence of series is generally good enough to keep only the first term of the series except for the case where the waves are scattered mostly in forward direction, as in turbulent air. The boundary equations on the surface of medium discontinuity are then obtained, also based on the eigenfunction expansion of the quantities continuous across the boundary surface. A simple application is made to the pulse wave propagation in a space of semi-infinite scattering medium.
The most degenerate irreducible representations of the symplectic group
Authors: Wong M. K. F. , Yeh Hsin-Yang
Published: March 2003

Matrix elements of the generators of the symplectic group Sp(2n) have been obtained for the most degenerate irreducible representations (m2n,?) and (?2n). These are the only two cases for n≳2 where the state labels according to the branching laws of Hegerfeldt give rise to an orthogonal set of basic vectors.
Missing label operators in the reduction Sp(2n) ↓Sp(2n−2)
Authors: Bincer Adam M.
Published: March 2003

I consider the ’’missing label’’ problem for basis vectors of an Sp(2n) representation corresponding to a group reduction chain with links Sp(2ν) ↓Sp(2ν−2) ×U(1), 2⩽ν⩽n. I obtain two different sets of ν−1 missing label operators. These operators, together with the ν Casimir operators of the Sp(2ν) group, the ν−1 Casimir operators of the Sp(2ν−2) subgroup and the one generator of the U(1) subgroup, form a complete set of labeling operators whose eigenfunctions provide a canonical basis in the representation space of Sp(2ν). When the number of missing labels exceeds one the most general solution to the labeling problem is not known. The two particular solutions presented here have certain appealing aspects of symmetry and simplicity.
Models for SU(N) ×SU(N) symmetry breaking with extremum constraints
Authors: Gherman O. , Saliu L.
Published: March 2003

The extremum properties of some functions defined on the compact groups or their representations are investigated. The extremum constraints for the vacuum expectation value of U(N) ×U(N) and SU(N) ×SU(N) ⧠ [Z2(P) ×Z2(C)] symmetry breaking perturbation Hamiltonian are used to determine the models compatible with nonnegative particle mass spectrum in the first perturbation order. Some model-independent properties inferred by extremum constraints of chiral and CP-symmetry breaking are also examined.
Differentiable manifolds and the principle of virtual work in continuum mechanics
Authors: Epstein Marcelo , Segev Reuven
Published: March 2003

A material body is conceived in terms of a global and a local model, the compatibility of which is shown to imply a generalization of the principle of virtual work. The classical notion of stress appears as a particular case of the force associated with the local model when an affine connection is specified in the physical manifold.
The growth and decay of weak waves in relativistic flows of dissociating gases
Authors: Ram Rishi , Singh H. N. , Gaur Madhukar
Published: March 2003

The propagation of a weak wave in a relativistic flow of a dissociating gas has been studied. The velocity of propagation of a relativistic weak wave has been determined. The fundamental growth equation governing the growth and decay of the wave has been obtained and solved. The relativistic results have been shown in full agreement with earlier results of classical gas dynamics. The problem of breakdown of weak discontinuities has also been solved. The critical time tc is determined when the breakdown of the wave and the consequent formation of a shock wave occur due to nonlinear steepening. It is concluded that there exists a critical amplitude of the wave such that all compressive waves with an initial amplitude greater than the critical one will break down after a finite time tc and a shock-type discontinuity will be formed, while an initial amplitude less than the critical one will result in a decay of the wave. On the other hand, an expansion wave will always decay and will ultimately be damped out. The global behavior of the wave amplitude has also been studied. It is concluded that the dissociative character of the gas is to increase the critical time. The relativistic and dissociative effects on the global behavior of weak discontinuities have also been discussed.
Roots of the modal equation for em wave propagation in a tropospheric duct
Authors: Ott R. H.
Published: March 2003

The solution of the modal equation for electromagnetic wave propagation in a tropospheric duct, having a trilinear refractivity profile, shows the existence of two sets of roots in the complex propagation plane. One of these is of the Whispering Gallery type with very low attenuation and the other is of the creeping wave variety with relatively high attenuation. When the contrast in refractive index is small (the so-called linear atmosphere) the creeping wave modes dominate. A large contrast in refractive index causes the Whispering Gallery modes to dominate (surface or elevated ducts). Several examples of the altitude charts for the modal equation for propagation at 200 MHz through a medium having various constrasts in the refractive index give some physical insight into these two classes of modes. In addition, asymptotic solutions for the Whispering Gallery Modes are derived and used as initial choices in Newton’s method for the solution of the modal equation.
On the irreducible representations of groups containing a subgroup of finite index
Authors: Castrigiano D. P. L. , Mutze U.
Published: March 2003

The objects under consideration are: A group G containing a subgroup S of finite index p, an irreducible representation (= multiplier representation by unitary or by unitary and antiunitary operators on a Hilbert space of arbitrary dimension) U of G, and an irreducible representation W of S. It is shown (1) that the representations U‖S (the restriction of U to S) and W↑G (the representation induced by W) are both orthogonal sums of finitely many irreducible subrepresentations, the number of which does not exceed p; (2) that the multiplicity of W in U‖S equals the multiplicity of U in W↑G if W and U are unitary representations and that these multiplicities are related in a slightly different manner for partially antiunitary representations. For the special case that S is an invariant subgroup, it is shown how the irreducible representations of G can be constructed if the irreducible representations of S and those of certain finite groups are known.
Clebsch–Gordan coefficients for corepresentations. I⊗I
Authors: Dirl R.
Published: March 2003

A general method is given for determining Clebsch–Gordan coefficients for corepresentations in terms of convenient Clebsch–Gordan coefficients for the normal subgroup, at which the considered Kronecker products are composed of corepresentations of type I only.
Clebsch–Gordan coefficients for corepresentations. I⊗III
Authors: Dirl R.
Published: March 2003

A general method is applied to compute Clebsch–Gordan coefficients for corepresentations in terms of such coefficients for the normal subgroup. The considered Kronecker products are composed of corepresentations of type I and III.
Clebsch–Gordan coefficients for corepresentations. II⊗II
Authors: Dirl R.
Published: March 2003

A general procedure is used to determine quite general Clebsch–Gordan coefficients for corepresentations in terms of convenient Clebsch–Gordan coefficients for the normal subgroup. The considered Kronecker products are composed of corepresentations of type II only.
On the local structure of the Euclidean Dirac field
Authors: de Falco Diego , Guerra Francesco
Published: March 2003

A simple Green’s formula for the Euclidean Dirac operator in Schwinger’s real formalism allows us to study some localization properties of the Euclidean Dirac field. A rather complete analysis follows of the connection between the Grassmann structure of the Euclidean field and the Clifford structure of the field at sharp time, analyzed in terms of its independent degrees of freedom.
A variational method in two-group transport theory
Authors: Bl/eński Tomasz
Published: March 2003

The two-group integral transport equation in subcritical homogeneous isotropically scattering medium in arbitrary geometry is considered. A functional is constructed which is stationary for the solution to the integral equation. If the determinant of the transfer matrix is positive, then the solution gives the minimum of the functional. The applications to the cylindrical Milne problem is shown and examples of the numerical results of the extrapolation distances are presented.
A homogeneous Hilbert problem for the Kinnersley–Chitre transformations
Authors: Hauser Isidore , Ernst Frederick J.
Published: March 2003

A homogeneous Hilbert (Riemann) problem (HHP) is introduced for carrying out the Kinnersley–Chitre transformations of the set V of all axially symmetric stationary vacuum spacetimes, and the spacetimes which are like the axially symmetric stationary ones except that both Killing vectors are spacelike. A proof, which is independent of the Kinnersley–Chitre formalism, establishes that the HHP transforms the potential (for certain closed self-dual 2 forms) F0(x, t) of any given member of V into the potential F (x, t) of another member of V. Two illustrative examples involving the Minkowski space F0(x, t) are given. The representation used for the Geroch group K, the singularities and gauge of the potentials, and possible applications of the HHP are discussed.
Symmetric vectors and algebraic classification
Authors: Leibowitz Elhanan
Published: March 2003

The concept of symmetric vector field in Riemannian manifolds, which arises in the study of relativistic cosmological models, is analyzed. Symmetric vectors are tied up with the algebraic properties of the manifold curvature. A procedure for generating a congruence of symmetric fields out of a given pair is outlined. The case of a three-dimensional manifold of constant curvature (’’isotropic universe’’) is studied in detail, with all its symmetric vector fields being explicitly constructed.
Coordinate free relativity
Authors: Carlson Paul
Published: March 2003

A technique is presented using orthonormal tetrads which enables efficient algebraic manipulation of Einstein’s equations by computer and ease of physical interpretation. The results are applied to the spherically symmetric case and Birkhoff’s theorem is proved in the formalism. Several exact solutions such as Tolman’s and Schwarzschild’s are derived, and isotropic expansion of Pefect fluids considered.
Conformal coupling of gravitational wave field to curvature
Authors: Grishchuk L. P. , Yudin V.M.
Published: March 2003

Conformal properties of the equations for weak gravitational waves in a curved space–time are investigated. The basic equations are derived in the linear approximation from Einstein’s equations. They represent, in fact, the equations for the second-rank tensor field hαβ, restricted by the auxiliary conditions hαβ;α =0, h≡γαβhαβ=0, and embedded into the background space–time with the metric tensor γαβ. It is shown that the equations for hαβ are not conformally invariant under the transformations γ̂αβ =e2σγαβ and ĥαβ =eσhαβ, except for those metric rescalings which transform the Ricci scalar R̂ of the original background space–time into e−2σR, where R is the Ricci scalar of the conformally related background space–time. The general form of the equations for hαβ which are conformally invariant have been deduced. It is shown that these equations cannot be derived in the linear approximation from any tensor equations which generalize the Einstein equations.
Two approaches to nonstationary relativistic thermodynamics
Authors: Bampi F. , Morro A.
Published: March 2003

A nonstationary thermodynamic theory in general relativity is set up through a hidden variable approach. Such a theory, which is especially suited to the description of the behavior of heat conducting viscous fluids, considers evolution equations involving the gradient of the hidden variables too. The expression adopted for the second law differs from the usual Clausius–Duhem inequality because of the presence of an entropy extra-flux. Besides other results it is shown that, via a suitable choice of the free energy function, the theory so obtained reduces just to Müller–Israel’s one.
Localized solutions of a charged nonlinear spinor field in a Coulomb-like potential
Authors: Rañada Antonio F. , Usón Juan M.
Published: March 2003

We study some global properties of a self-interacting Dirac field which has been used to construct a classical stable model of the hydrogen atom. It is shown that the normalization condition produces the correct values of both charge and spin and also the correct Landé factors for the states with  j=1/2. The linear limit is given by the branching points of the continuum of solutions.
A connection between nonlinear evolution equations and ordinary differential equations of P-type. II
Authors: Ablowitz M. J. , Ramani A. , Segur H.
Published: March 2003

It is known through the inverse scattering transform that certain nonlinear differential equations can be solved via linear integral equations. Here it is demonstrated ’’directly,’’ i.e., without the Jost-function formalism that the solution of the linear integral equation actually solves the nonlinear differential equation. In particular, this extends the scope of inverse scattering methods to ordinary differential equations which are found to be of Painlevé type. Some global properties of these nonlinear ODE’s are obtained rather easily by this approach.
A commutator representation of Painlevé equations
Authors: Flaschka H.
Published: March 2003

This paper further develops the connection between partial differential equations solvable by inverse scattering methods and ordinary differential equations of Painlevé type. The main result given here is that Painlevé equations have a concise algebraic formulation [L,B]=L when written in the Lax representation.
Towards a factorization of M4
Authors: Nash Patrick L.
Published: March 2003

It may be desirable to eliminate M4 as the underlying manifold in which some physical theories are cast, and recast these theories in the space ’’√M4.’’ We investigate some of the properties of one such space, which we denote by S8. S8 can be coordinatized by real eight-component spinors. The spinor algebra on this space is developed in this paper. It is shown that a (nondegenerate) spinor in S8 determines an orthogonal tetrad on M4 (the set of these spinors determines the space of orthogonal frames over M4), and that this spinor corresponds to a ’’particle.’’ A simple geometrical interpretation of the Dirac equation arises in arriving at this correspondence.
On the application of the Sommerfeld–Maluzhinetz transformation to some one-dimensional three-particle problems
Authors: Lipszyc K.
Published: March 2003

The reformulation of the one-dimensional three-body problems with boundary condition and delta function interactions, based on the Sommerfeld–Maluzhinetz transformation, is presented. The argumentation is carried out as exemplified by two models–the exactly soluble model of two identical particles interacting through delta potential and each of which interacts with a third one through boundary condition interactions, and a model of two identical particles and a fixed wall, all interactions being of the delta function type. The problems are reduced to those of solving coupled systems of functional equations for the Sommerfeld transforms of the wavefunction. The functional properties of the transforms are then used to derive expressions relating them to the half off-shell extensions of the elastic and exchange probability amplitudes as defined in the Faddeev–Lovelace approach.
Extended Numerov method for the numerical solution of the Hartree–Fock equations
Authors: Burke Edward A.
Published: March 2003

To match the intrinsic accuracy of an expanded basis set solution of atomic orbitals by numerical orbitals requires integration formulas of comparable intrinsic accuracy. Integration of the coupled, integro-differential, Hartree–Fock equations is most easily done using Numerov’s formula. without increasing the number of mesh points, one must extend the basic formula to include more points. Herein is presented the derivation of the general (2N+1)-point Numerov formula, including the error term, as well as suggestions for numerical determination with specific formulas of 3-, 5-, 7-, and 9- point fits.
An application of Ray–Reid invariants
Authors: Lutzky M.
Published: March 2003

The formalism of Ray–Reid invariants is applied to a certain nonlinear system, first treated by Reid using a different approach. In addition, a generalization of the Ray–Reid invariant is given.
The hydrogen atom: Quantum mechanics on the quotient of a conformally flat manifold
Authors: Ringwood G. A. , Devreese J. T.
Published: March 2003

The regularization of the Kepler problem proposed by Kustaanheimo and Stiefel provides an example of quantum mechanics on the quotient of a conformally flat manifold.
Decaying systems with degenerate Livsic matrix
Authors: Katznelson E.
Published: March 2003

The spectral analysis given by Wong for the resolvent of a non-self-adjoint operator with arbitrary multiplicity is utilized for the description of the time evolution of an unstable system. After studying the case for which the operator is independent of the resolvent variable z, the Wong analysis is extended to the physically interesting case for which the operator depends on z. The case of infinite multiplicity is treated, and it is found that the flow of probability through the generalized eigenstates is analogous to the approach to equilibrium in statistical mechanics.
Phase-integral calculation of physically important quantities for nonrelativistic bound s states of the linear central potential
Authors: Thidé Bo
Published: March 2003

Energy levels, normalization factors, quantal expectation values, and probability densities at the origin for nonrelativistic bound s states of the linear central potential are calculated by means of phase-integral formulas, given by N. Fröman in two recent papers. The accuracy of the phase-integral method is exhibited by a numerical comparison with exact results. During the last few years the potential in question has been widely used as a model potential describing quark confinement in heavy mesons.
Space–times with distribution valued curvature tensors
Authors: Taub A. H.
Published: March 2003

A space–time in which in an admissible coordinate system the metric tensor is continuous but has a finite jump in its first and second derivatives across a submanifold will have a curvature tensor containing a Dirac delta function. The support of this distribution may be of three, two, or one dimension or may even consist of a single event. Lichnerowicz’s formalism for dealing with such tensors is modified so as to obtain a formalism in which the Bianchi identities are satisfied in the sense of distributions. The resulting formalism is then applied to the discussion of the Einstein field equations for problems in which the source of the gravitational field is given by a distribution valued stress-energy tensor. Gravitational shocks are also discussed and their theory is compared with that of high-frequency gravitational waves given by Y. Choquet-Bruhat. By considering a class of line sources as obtainable from cylindrical shells by a limiting process, as was proposed by Israel, one may use the distribution formalism developed for hypersurfaces to treat line sources. The line source model proposed by Israel to represent the Kerr metric in the neighborhood of its singular disk is shown to lead to a gravitational mass and angular momentum inconsistent with those of the latter metric. It is proposed to remove this difficulty by changing the assumptions made by Israel concerning the nature of the space–time inside the cylindrical shell which is the support of the distribution in the curvature tensor. The details of the effect of this change are not given in this paper.
Gravitation as an internal gauge theory of the Poincaré group
Authors: Luehr C. P. , Rosenbaum P. M.
Published: March 2003

We describe a gauge theory of gravitation based on the poincaré group treated as an internal symmetry group acting on five-dimensional fiber spaces. One special feature of the theory is that the metric structure of the manifold which serves as the base space appears as a natural consequence of the formalism and is not imposed a priori. The theory encompasses general relativity and the Einstein–Cartan theory as particular cases, as well as other gravitation theories with torsium which have been recent proposed.
Gauss–Bonnet and Bianchi identities in Riemann–Cartan type gravitational theories
Authors: Nieh H. T.
Published: March 2003

We present elementary derivations of the Gauss–Bonnet type and Bianchi type identities for Riemann–Cartan geometry. The identities are derived directly in terms of the vierbein field eaμ and the spin-connection field 𝒱abμ, in the spirit of gauge theory, and are suitable for discussing Riemann–Cartan type gravitational theories.
Some properties of static general relativistic stellar models
Authors: Lindblom Lee
Published: March 2003

A number of properties of static general relativistic stellar models are presented which appear to be relevant to the ongoing search for a proof that all such models must have spherical symmetry. It is shown that any such model, having conformally flat spatial sections, must have spherical symmetry. A general procedure is described which allows one to construct the type of ’’divergence equals positive quantity’’ identities for static stellar models, which were used to prove that static black holes must have spherical symmetry. This procedure is used to produce a large new class of identities for the exterior vacuum regions of static stellar models and identities are constructed for the interior regions of uniform density models. These identities are used to prove that static uniform density stellar models must have spherical symmetry.
The unitary multiplicity-free representations of SL4(R)
Authors: Friedman John L. , Sorkin Rafael D.
Published: March 2003

Those unitary representations of S̄L̄4$̄(̄R̄)́bar)= are classified which contain each irreducible S̄Ō(̄4̄)́bar)= representation at most once.
Minimal and centered graded spin-extensions of the SL(3,R) algebra
Authors: Ne’eman Y. , Sijacki Dj.
Published: March 2003

We construct the minimal-size infinite-dimensional ’’supergauge’’ algebras containing sl(3,R) and spinorial generators, with the possibility of having a central term as in the Heisenberg algebra. The results describe the spin-excitations of a membrane and may provide [when extended to sl(4,R)] the framework for an infinitely supersymmetric (renormalizable?) gravity.
A symmetry approach to exactly solvable evolution equations
Authors: Fokas A. S.
Published: March 2003

A method is developed for establishing the exact solvability of nonlinear evolution equations in one space dimension which are linear with constant coefficient in the highest-order derivative. The method, based on the symmetry structure of the equations, is applied to second-order equations and then to third-order equations which do not contain a second-order derivative. In those cases the most general exactly solvable nonlinear equations turn out to be the Burgers equation and a new third-order evolution equation which contains the Korteweg-de Vries (KdV) equation and the modified KdV equation as particular cases.
Evolution of a stable profile for a class of nonlinear diffusion equations. III. Slow diffusion on the line
Authors: Berryman James G.
Published: March 2003

We show that the nonlinear diffusion equation ∂n/∂t =∂2(n1+δ/∂x2 with compact initial data on −∞<x<∞ can be transformed into another nonlinear diffusion equation α(∂ϑ∂t)=ϑ1+α ×∂2ϑ/∂?2 on a fixed finite interval of the ? axis. Thus, the original moving boundary problem is transformed into a fixed boundary problem. The new form of the equation has advantages both analytically and computationally as the examples illustrate. Linear stability analysis for the transformed equation is straightforward whereas the moving boundaries of the original problem complicate the analysis for that case. The advantages of the resulting computational algorithm for solving the moving boundary problem are also discussed. A nonlinear Rayleigh–Ritz quotient and a Lyapunov functional are shown to be bounded, monotonically decreasing functions of time. Both functionals give added insight into the mathematical character of the diffusion process.
A Hilbert–Padé method for multipole approximations. Application to the Gaussian function
Authors: Martín Pablo , Zamudio-Cristi Jorge , Donoso Guillermo
Published: March 2003

A method is developed where a Hilbert transform is combined with an asymptotic Padé method in order to obtain good multipole approximations for functions whose power series have a large radius of convergence. This method has been used to find two- to eight-pole approximations for the Gaussian function.
Existence and completeness of the Möller wave operators for radial potentials satisfying ∫01 r‖v(r)‖d
r+∫1∞‖v(r)‖d
r< ∞
Authors: Dollard J. D. , Friedman C. N.
Published: March 2003

We give an elementary proof of the existence of the (three-dimensional) Möller wave operators and the unitarity of the S operator (weak asymptotic completeness) for radial Kato potentials v(r) satisfying ℱ01 r‖v(r)‖dr+ℱ1∞‖v(r)‖dr< ∞.
Construction of two-dimensional quantum electrodynamics
Authors: Ito Keiichi R.
Published: March 2003

We investigate quantum electrodynamics in two dimensions, (QED)2, in the constructive method. We construct a cutoff Hamiltonian defined on the Fock space with an indefinite metric, and discuss its properties and renormalization counterterms. When the fermion is massless, this model is exactly solvable (known as the Schwinger model). We study the massless model through the Bogolyubov transformation (canonical linear transformation) extended to this Fock space, through which the properties of the Hamiltonian and the physical vacuum are clarified. When the mass of the fermion M≠0, we discuss the transformation of the renormalized Hamiltonian into the one of the so-called sine-Gordon model. The properties of the operator which implements this transformation are clarified; it is an unbounded operator which is isometric with respect to the indefinite metric.
Relativistic wave equations coupled to external fields: An algebraic study of the problem of constraints
Authors: Mathews P. M. , Govindarajan T. R. , Seetharaman M. , Prabhakar J.
Published: March 2003

A general matrix algebraic study is made of higher spin wave equations with minimal electromagnetic interaction, in relation to one of the basic problems, namely the problem of possible change in the number of constraints implied in the equation on introducing the interaction. Considering equations of the general form (βπ−m)ψ=0, wherein the matrix β0 is required to have a minimal equation β0n = β0n−2 to ensure uniqueness of mass, we show that when n = 4 extra constraints may be generated at critical external fields, while for n = 5 there may also be loss of constraints on introduction of external fields. We obtain general algebraic criteria which determine whether or not such pathologies would arise in any particular case, and verify the validity of these criteria by considering a variety of known equations.
Extended phase space. II. Unified meson fields
Authors: Das A.
Published: March 2003

The classical scalar equation in the extended phase space V8 is studied. It is the generalization of the usual Klein–Gordon equation and is covariant under the extended Poincaré group P8. In this equation there is obvious symmetry of the variables q and p and thus the principle of reciprocity is automatically incorporated. The scalar field is expressed as a Fourier integral φ(q,p)∼dk dx α(k,x)ei(kq+px) to compute the integral constants like the total energy, total momentum, etc. Then the integral constants turn out to be meaningful quantities by interpreting f(k,x)∼‖α‖2 as the statistical distribution function for the scalar field particles. Next the scalar field is expressed as the Fourier–Bessel integral φ( ρ,ϑ)∼ ∑t=−∞∞ ∫0∞ dk kα( k, t)Jt(kρ)eitϑ=∑t=−∞∞φ (t)   q2+p2, ϑ=arctan( p/q). The integral constants are computed from a single (t)-mode φ(t). These are accessible to physical interpretations. Especially, the total charge can be linked up with the Gell-Man–Nishijima’s formula, provided one of the quantum numbers (t), say t3, is identified with the isotopic quantum number and 2t4 is identified with strangeness. With each of the (t)-mode φ(t) a meson field is associated so that the φ-field itself is the unified meson field.
Narrow resonances as an eigenvalue problem and applications to high energy magnetic resonances: An exactly soluble model
Authors: Barut A. O. , Berrondo M. , García-Calderón G.
Published: March 2003

We formulate the problem of finding the narrow positive energy resonances in a deep potential well as an eigenvalue problem (thereby extending the scope of the discrete spectrum problem). We determine the number of resonances in an exactly soluble case. The method is then applied to a nonperturbative treatment of the magnetic resonances occurring in charge-dipole interactions, and the existence of the previously conjectured high mass narrow resonances in this model is proved.
Orbital angular momentum of ‘‘lumps’’
Authors: Ahmed S. , Schiff H.
Published: March 2003

We formulate the external orbital angular momentum of a ’’lump’’ so that L=r×p on any space-like hyperplane. The systems considered are scalar, spinor and vector fields with eiωt time dependence, each interacting with its own electromagnetic field. Particular attention is given to cases involving nonzero dipole moments.
Classical supersymmetric particles
Authors: Galvao Carlos A. P. , Teitelboim Claudio
Published: March 2003

The dynamics of classical spinning particles is studied from the point of view of gauge supersymmetry. The central idea is that the natural way of introducing intrinsic spin degrees of freedom into a physical system is to take the square root of the Hamiltonian generators of the system without spin, which is equivalent to rendering the system gauge supersymmetric. This is accomplished by describing the spin degrees of freedom by means of ’’anticommuting c-numbers’’ (odd Grassman algebra elements) and relying on Dirac’s theory of constrained Hamiltonian systems. The requirement of gauge supersymmetry fixes completely the action principle and leaves neither room nor need for ad hoc subsidiary conditions on the relative direction of the spin and the velocity as in the more traditional treatments. Both massive and massless particles free and in interaction with electromagnetic and gravitational fields are discussed. It is found that there exists a supergauge in which the spin tensor of a massive particle in a gravitational field is transported in parallel but the particle does not follow a geodesic. Massless particles on the other hand have the property of possessing a supergauge where their helicity is conserved and in which at the same time the worldline is a geodesic. Special attention is paid to the meaning and properties of the supergauge transformations. The main aspects of that discussion are applicable to more complicated systems such as supergravity. In particular phenomena such as necessity of invoking the equations of motion to close the gauge are analyzed.
Partition permuting array approach to few-body Hamiltonian models of nuclear reactions
Authors: Goldflam R. , Kowalski K. L. , Tobocman W.
Published: March 2003

The approximate Hamiltonian formulation of many-body scattering recently proposed by Polyzou and Redish is used to derive approximate Baer–Kouri–Levin–Tobocman (BKLT) integral equations. It is shown that these equations have connected kernels after a finite number of iterations and the approximation defined by them is unitary. Integral equations imbedding the approximation in the exact theory are also given. Some lemmas which relate to the connectivity of operator products are established and are employed to prove the connected-kernel properties of both the BKLT as well as the imbedding integral equations
A multigroup criticality condition for a space-independent multiplying assembly via the Chapman–Kolmogorov equation
Authors: Aviram I. , Goshen S.
Published: March 2003

We consider the multigroup time-dependent probability distribution of neutrons in a space-independent, source-free multiplying assembly. The first-order partial differential equation for the probability generating function can be derived from the forward Chapman–Kolmogorov equations of the stochastic process, and solved—in the principle—by the method of characteristics. It is well known that the asymptotic extinction probability is related to the singular point of the system of characteristic equations. An analysis of the location of this point in the hyperspace of dummy variables associated with neutrons of various velocity groups leads to a multigroup criticality condition for the assembly.
Quantum Heisenberg ferromagnets and stochastic exclusion processes
Authors: Thomas Lawrence E.
Published: March 2003

Let H be the isotropic spin-s quantum ferromagnetic Heisenberg Hamiltonian associated with a finite volume in Zd. In an appropriate representation, the restriction of −H to the N-spin wave sector −HN can be regarded as the generator of a Markov semigroup exp(−tHN). For s= 1/2 the corresponding process XN(t) is identified as a simple N-particle exclusion process; for higher spin it is a more complicated exclusion process involving different species of particles. A Feynman–Kac, Cameron–Martin perturbation formula for exp(−tHN) is developed in the s= 1/2 case, and the formula is used to obtain some thermodynamic correlation inequalities.