bluuebunny/crossref_metadata_2025 huggingface dataset:
Time-reversal noninvariance of the quantum-mechanical kinetic equation of Kadanoff and Baym
Authors: Nikolić Zlatiborka A.
Published: March 2003

Applying anticausal Green’s function technique, it has been shown that the origin of time-reversal noninvariance of the quantum-mechanical kinetic equation of Kadanoff and Baym lies in the selection of the boundary condition that the system be in thermodynamical equilibrium at time t=−∞.
Effective Lagrangian in spontaneously broken gauge theories
Authors: Incoul R.
Published: March 2003

In gauge theories of weak and electromagnetic interactions, it is generally assumed that the addition of extra groups [simple or U(1)] commuting with the standard Weinberg–Salam SU(2) -U(1) group, generates new degrees of freedom for the model, simply because there are new coupling constants in the game. This assertion is not true in general. When looking at the effective Lagrangian of the physical system (−q2 much smaller than any mass of the massive vector bosons), we see that a coupling constant completely disappears if the generators of its corresponding group do not enter in any surviving unbroken subgroup [U(1) for Weinberg–Salam model]. In those cases, the novelties are provided only by the quantum numbers of the fields and especially by the arbitrariness on the choice of ’’unphysical’’ Higgs fields. This effective Lagrangian is defined and constructed in the case where the initial and final symmetry groups are direct products of simple groups and U(1) groups. Some of its remarkable properties are investigated.
Poincaré is a subgroup of Galilei in one space dimension more
Authors: Elizalde Emili
Published: March 2003

Through an imaginary change of coordinates, the ordinary Poincaré algebra is shown to be a subalgebra of the Galilei one in four space dimensions. Through a subsequent contraction the remaining Lie generators are eliminated in a natural way. An application of these results to connect Galilean and relativistic field equations is discussed.
SU6 × SU3c scalars in E7 irreps
Authors: Wybourne B. G.
Published: March 2003

The branching rules for E7→SU6 × SU3c have been determined for all irreps of E7 of dimension <52 000. Among these irreps only those of dimension 0, 1463, 1539, 7371, and 8645 contain an SU6 × SU3c scalar. The Kronecker square and cube of the 133-dimensional adjoint irrep of E7 are resolved, and the number of symmetric second and third order operators that transform as scalars under SU6 × SU3c determined.
Lower bounds on the total cross section and the slope parameter for some measurable sequences of s→∞
Authors: Uchiyama Tadashi
Published: March 2003

The lower bounds on the total cross section and the slope parameter are obtained on the basis of the analyticity and polynomial upper boundedness of the scattering amplitude and the unitarity of the S matrix: σtot⩽Cs−6 (log s)−2, B⩽Cs−5(log s)−4 for some measurable sequences of s→∞. These bounds hold for any t in 0?t<4m2π. It is unnecessary in order to obtain our bounds that the scattering amplitude has the crossing even property. If we assume this property, we can suppress the logarithmic factors of our bounds. Also we obtain our lower bounds for any sequence of s→∞, if we take the average scattering amplitude.
Explicit results for the quantum-mechanical energy states basic to a finite square-well potential
Authors: Siewert C. E.
Published: March 2003

The theory of complex variables is used to establish explicit expressions for the discrete energy states relevant to a square-well potential.
Symmetry conditions and non-Abelian gauge fields
Authors: Maciejko R.
Published: March 2003

Classical gauge fields are envisaged in the context of fibre bundle theory. General symmetry conditions are found which lead to an Abelian holonomy group. This, in turn, has important consequences on the solutions of the gauge field equations: Symmetric solutions have unphysical properties. Non-Abelian holonomy groups are thus needed.
Splitting and representation groups for Polish groups
Authors: Cattaneo U.
Published: March 2003

It is shown that all continuous unitary/antiunitary projective representations of a Polish group G, with the same subgroup of elements represented into the projective unitary groups, arise from continuous unitary/antiunitary (ordinary) representations of a topological group (called a splitting group) obtained from an extension of G by an Abelian topological group. Moreover, there exists always a splitting group which is ’’minimal’’ in some well-defined sense (a representation group). A sufficient (resp. a necessary and sufficient) condition for the existence of a Polish (resp. of a second countable locally compact) representation group is given.
Inequalities and uncertainty principles
Authors: Faris William G.
Published: March 2003

Sobolev inequalities give lower bounds for quantum mechanical Hamiltonians. These inequalities are derived from commutator inequalities related to the Heisenberg uncertainty principle.
Exact statistical mechanics of some classical 1D systems
Authors: Bountis Tassos , Helleman Robert H. G.
Published: March 2003

The classical partition function QN is calculated in closed form for the following 1D N-body ’’hard-core’’ potentials, V=ΣNi=1 (gxi+b/‖xi−xi−1‖), i.e., a Coulomb nearest neighbor ’’chain’’ in a uniform field, and V= (1/2) ΣNi=0 ΣNj=0 exp (‖xi−xj‖), a ’’fluid’’ with exponential interactions. The QN for both systems is separated into a product of N, similar, tractable integrals each depending on a different value of the index i. All thermodynamic variables are obtained in closed form. In the limit, as N→∞, most of them do not linearly increase with the size of the system, i.e., they are not ’’extensive.’’ This is also discussed in terms of the ’’stability’’ and ’’temperedness’’ properties of the potentials. Nevertheless, both systems do have a heat capacity which is ’’extensive.’’
Solution by iteration of H-equations in multigroup neutron transport
Authors: Kelley C. T. , Mullikin T. W.
Published: March 2003

The Chandrasekhar H-equations for matrix-valued functions are solved by an iterative method. Complex variables and positivity techniques are used to obtain convergence. This approach may be applied to subcritical neutron transport in a slab with isotropic scattering.
Phase-space approach to relativistic quantum mechanics. II. Geometrical aspects
Authors: Kaiser Gerald R.
Published: March 2003

The formalism introduced in Paper I [J. Math. Phys. 18, 952 (1977)] is made manifestly covariant by including as an admissible phase space any 2n-dimensional submanifold of the forward tube 𝒯={x−iy∈Cn+1‖ y0≳‖y‖} which is of the ’’product’’ form σ=S−iΩλ, where Ωλ ={y∈Rn+1‖ y0= (λ2+y2)1/2}, λ≳0, and S is any space-or-lightlike submanifold of space–time Rn+1. The σ’s have natural symplectic structures covariant with respect to the Poincaré group, and a norm ∥¨∥σ on the space 𝒦 of solutions is defined by integrating with respect to the Liouville measure on σ. This automatically gives ∥f∥2σ as the total flux of a conserved space–time vector field, implying that ∥f∥σ is independent of σ. Some inconsistencies encountered in the space–time theory of Klein–Gordon particles appear to be resolved in the phase-space framework.
A kinetic formulation of the three-dimensional quantum mechanical harmonic oscillator under a random perturbation
Authors: Besieris Ioannis M. , Stasiak Wojciech B. , Tappert Frederick D.
Published: March 2003

The behavior of a three-dimensional, nonrelativistic, quantum mechanical harmonic oscillator is investigated under the influence of three distinct types of randomly fluctuating potential fields. Specifically, kinetic (or transport) equations are derived for the corresponding stochastic Wigner equation (the exact equation of evolution of the phase-space Wigner distribution density function) and the stochastic Liouville equation (correspondence limit approximation) using two closely related statistical techniques, the first-order smoothing and the long-time Markovian approximations. Several physically important averaged observables are calculated in special cases. In the absence of a deterministic inhomogeneous potential field (randomly perturbed, freely propagating particle), the results reduce to those reported previously by Besieris and Tappert.
Lorentz transformations as space–time reflections. II. Timelike reflections
Authors: Krause Jorge
Published: March 2003

Continuing previous work, some features of the covariant factorization of Lorentz transformations, into complementary space–time reflections, are further discussed in terms of timelike reflections. Several properties of timelike reflections are shown, which bear interesting relations with the Lorentz tensor performing active isometric transformations between two inertial observers, while their geometric meaning is also briefly examined. Some product rules for timelike reflections appear, as a background enabling the discussion of the group multiplication laws for Lorentz isometry tensors. This brings into the fore the realization of the restricted Lorentz group attained in the present formalism. The instances of two multiplication laws of the Lorentz tensors are examined. Next, the same problem (i.e., factorization of an ordinary rotation into two complementary reflections) is readily solved for the Euclidean 3-space. Both formalisms (Euclidean and Minkowskian) are essentially the same. Indeed, factorization of an isometric transformation into two complementary reflections is a general property of flat Riemannian geometry. A few concluding remarks are presented.
Interaction and stability of localized solutions in a classical nonlinear scalar field theory
Authors: Vázquez Luis
Published: March 2003

The interaction between the localized solutions of a nonlinear scalar field theory are studied. We also study the stability of the above solutions under certain time-dependent perturbations.
The SU(4) ⊃ SU(2) ⊗ SU(2) chain
Authors: Partensky A. , Maguin C.
Published: March 2003

We consider the physical SU(4) ⊃ SU(2) ⊗ SU(2) chain. With the help of the three vectors (Sα, Ti, Qαi), (VαS, VtT, VαiQ), (WSα, WiT, WαiQ) we can easily write the three fundamental invariants I2, I3, I4; the two operators Ω and Φ (eigenvalues ω and φ) of Moshinsky and Nagel [Phys. Lett. 5, 173 (1963)] and we are able to construct a new pair of operators playing the same last role. We write them s =Σμ(−)μVSμVs−μ and t =Σi(−)iViTVT−i (eigenvalues σ and τ). In any (pp′p″) irreducible representation (IR) we define semireduced matrix elements 〈ϑ′S′T′∥Q∥ϑST〉 (and the same for VQ and WQ), where ϑ is any of the two pairs (ωφ) or (στ). For the unknown Σϑϑ′〈ϑ′S′T′∥T1Q ∥ϑST〉 〈ϑ′S′T′∥T2Q∥ϑST〉 (TQ any one among Q, VQ or WQ) we give a set of equations which allows the complete solution of the calculation of these quantities. Besides we give the explicit values of these unknown for TQ1=T2Q=Q for any (pp′p″) IR and, S=p and any T, or T=p and any S. In the particular case of the (320) IR [with ϑ= (ωφ)] where the multiplicity reaches 3 for S=1, T=2 and S=2, T=1, we have completely solved the problem; i.e., we have calculated the square of the semireduced matrix elements of Q for any value of the label (ωφST), together with all the eigenvalues ω and φ.
Self-gravitating irrotational barotropic fluid in a conformally flat space
Authors: Ray Dipankar
Published: March 2003

Solutions to Einstein’s equation for a conformally flat metric eψ(dx12+dx22+dx32 −dx42) are sought for a self-gravitating irrotational barotropic fluid. It is found that velocity potential φ can be expressed in one of the two forms x12+x22+x32−x42 or x4, and ψ, p, and ρ are functions of φ.
Elementary construction of graded Lie groups
Authors: Rittenberg V. , Scheunert M.
Published: March 2003

We show how the definitions of the classical Lie groups have to be modified in the case where Grassmann variables are present. In particular we construct the general linear, the special linear and the orthosymplectic graded Lie groups. Special attention is paid to the question of how to formulate an adequate ’’unitarity condition.’’
A geometric theory of charge and mass
Authors: Shurtleff Richard
Published: March 2003

A geometric model of a charge is constructed by defining several geometries on the same spacetime manifold. A Riemannian geometry describes the vacuum. On the same spacetime, two Weyl geometries are constructed for the charge description. The geometries are constrained by a variational principle. Energy conservation requires the equality of active and passive mass. Chargeless particles have essentially no mass. The treatment of radiation relies on the approximate nature of the wave equation. Variable mass terms in the wave equation cause the 2S–2P levels in hydrogen to separate by 30 000 Mhz. This unobserved transition together with the lack of spin sets a limit to the correspondence of the model to real electrons.
Large time behavior of the superfluorescent decay
Authors: Benza V. , Montaldi E.
Published: March 2003

The large time behavior of the superfluorescent decay is investigated by the inverse scattering technique.
Homogeneous and isotropic world models in the Yang–Mills dynamics of gravity. The structure of the adiabats
Authors: Camenzind M.
Published: March 2003

The time evolution of homogeneous and isotropic matter distributions is analyzed for the restricted Yang–Mills curvature dynamics of gravity. This theory of gravity is a tidal dynamics for which relativistic matter in detailed balancing cannot produce tidal forces. It defines a dynamical system on the curvature plane spanned by the two components of the Riemann curvature of Robertson–Walker space–times; the essential features of the cosmological solutions are presented by means of their phase portraits in the curvature plane. In the asymptotic limit (S→∞) the phase portrait, which in general depends on the equation of state and on the change of the entropy per particle, is structurally stable under the transition from Einstein’s dynamics to the Yang–Mills dynamics for any realistic equation of state. The phase portraits are explicitly constructed for the equation of state p=nρ, 0≦n≦1, and constant entropy per particle. A criterion for the existence of regular trajectories is given for the full Yang–Mills dynamics including entropy production. Finally, we discuss the relations between the observational parameters.
Quantization of spinor fields
Authors: Garbaczewski Piotr
Published: March 2003

Influenced by Klauder’s investigations on the same subject, we study the question of correspondence principle for Dirac fields, looking for its formulation without use of Grassman algebras. We prove that with each Fermi operator (the series with respect to asymptotic free fields): Ω (ψ,ψ̄): one can associate the functional ΩC(ψC, ψ̄C) with respect to classical spinor fields. Here the projector 1F and the Hilbert (Fock) space ℱF=1FℱB are given such that the identity 1F: ΩC(ψB, ψ̄B): 1FℱF = :Ω (ψ, ψ̄):ℱF defines the mediating boson level, where coherent state expectation values of operator expressions are in order: 〈:ΩC(ψB, ψ̄B):〉=ΩC(ψC, ψ̄C). For proofs we employ functional differentiation (resp. integration) methods, especially in connection with the use of functional representations of the CCR and CAR algebras.
On the stationary Einstein–Maxwell equations
Authors: Hoenselaers C.
Published: March 2003

The ansatz Φ=Φ (ℰ, ε̄) for a solution of the stationary Einstein–Maxwell equations is analyzed. The possible forms of this function are listed and it is shown that one obtains from every solution of the vacuum Ernst equations an at most two-parameter solution of the Einstein–Maxwell equations.
Evaluation of simple Feynman graphs
Authors: Nickel Bernie G.
Published: March 2003

A number of one-loop graphs with arbitrary external momenta and internal masses contributing to the perturbation expansion of a Euclidean φ4 theory are evaluated exactly in three and two dimensions. The final expressions are simple closed forms involving elementary functions only. A method for handling the multidimensional angular integrations that arise in calculations of massless QED or φ4 in four dimensions is also discussed.
The geometry of the gravitational field at spacelike infinity
Authors: Sommers Paul
Published: March 2003

The asymptotic structure of gravitational fields at large spacelike separation from sources is studied. Limits of spacetime fields are discussed in terms of a three-dimensional boundary manifold representing spacelike infinity. The boundary is endowed with the metric of a timelike unit hyperboloid. With sufficiently stringent conditions on the asymptotic spacetime geometry, the total energy–momentum and angular momentum emerge as integrals over any cross section of the hyperboloid at infinity. It is possible to identify physically relevant weaker conditions under which the energy–momentum, but not the angular momentum, is well defined. Under still weaker conditions, the energy–momentum also loses its meaning even though the spacetime admits a Minkowskian asymptote.
Global thermodynamical stability and correlation inequalities
Authors: Fannes M. , Verbeure A.
Published: March 2003

Using spatially homogeneous dissipative perturbations, we derive a correlation inequality for states satisfying the variational principle for infinitely extended quantum lattice systems.
Matrix element expansion of a spin wavefunction
Authors: Smith George B.
Published: March 2003

An expansion of the wavefunction for a free, massive particle with spin is obtained in terms of the matrix elements for the unitary, irreducible representations of SL(2,c) by a method based on the theory of induced representations. It is further shown that this expansion is equivalent to the Shapiro integral transformation for the wavefunction.
Multidimensional wave radiation from a source with Gaussian time variation and Gaussian-approximated distribution about a spherical sheet
Authors: Chee-Seng Lim
Published: March 2003

This paper concerns the wave field of a source with the title-indicated space–time function which, additionally, possesses an arbitrary directional variation. The multivariate solution obtained comprises an estimated error plus peak-induced spherical harmonics that are hyperconically confined, i.e., bounded by diverging and converging spherical fronts. Such fronts are not necessarily singular. Compliance with the radiation principle ensues, through contour integration, from Cauchy initial conditions. For an odd number of spatial dimensions, an inner zone created after a focusing phenomenon exhibits an analogy with a Petrowsky’s lacuna. Naturally, the wave field varies with direction, but only because its source does so. Spherically as well as axially symmetric cases constitute major corollaries. Asymptotic developments, evolving ultimately into steady limits, are also deducible. An indirect application is illustrated for magnetoacoustic flow parallel to a magnetic field; on induction by a cylindrical Gaussian-approximated current distribution, weak effects appear everywhere during the steady state and are superposed upon strong stationary wave effects bounded by cone sheets which project either (i) downstream for a supersonic–super-Alfvénic flow, or (ii) upstream for a restricted subsonic–sub-Alfvénic flow. Finally, the main results are directly applied to elastic wave propagation from a two-component Gaussian body force concentrated about a spherical base; a spherically symmetric radial component generates a strong irrotational wave field normally involving an instantaneous point singularity; an axisymmetric azimuthal component generates a strong solenoidal wave field.
The local von Neumann algebras for the massless scalar free field and the free electromagnetic field
Authors: Benfatto G. , Nicolò F.
Published: March 2003

The properties of the von Neumann algebras of local observables for the free scalar field of zero mass are studied. The local algebras possess a lattice structure, and the duality condition is satisfied. The problem of duality for the free electromagnetic field is discussed.
Type N gravitational field with twist. II
Authors: Hauser I.
Published: March 2003

A full derivation is given of that one parameter family of type N twisting gravitational fields which was previously reported by the author. Explicit forms of this solution are obtained, and the coordinate ranges are specified for all possible cases. The general problem of the search for other type N twisting gravitational fields is also discussed; the differential equations required for that search are derived, and the extension of these equations to type (3,1) is given without derivation.
Birkhoff’s theorem and magnetic monopole solutions for a system of generalized Einstein–Maxwell field equations
Authors: Horndeski Gregory Walter
Published: March 2003

In this note I establish a ’’Birkhoff’s type theorem’’ for the most general second-order vector–tensor theory of gravitation and electromagnetism, which is such that its field equations are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, (iii) compatible with Maxwell’s equations in a flat space, and (iv) in agreement with Einstein’s equations in the absence of electromagnetic fields. I also present solutions to these field equations which can be regarded as representing the gravitational and electromagnetic field outside of a magnetic monopole. It turns out that these magnetic monopole solutions admit event horizons when the mass of the source is sufficiently large.
New variational bounds on generalized polarizabilities
Authors: Robinson Peter D.
Published: March 2003

New variational bounds are derived on the generalized polarizabilities of a quantum-mechanical system, for arbitrary complex frequencies ζ=ν+iω and two different perturbations u and v. No power of the Hamiltonian h higher than h2 is involved in the bounding functionals. For a certain range of ν-values, upper and lower bounding functionals are obtained which contain merely a single trial vector but also introduce an inverse operator like h−1. This impractical feature can be avoided with a subsidiary variational principle, leading to bivariational upper and lower bounds. Explicit bivariational bounds are also derived which are valid for all values of ζ. Both theoretical and practical aspects of the bounds are discussed.
Charge conservation in metric–torsion gravitational theories
Authors: Aldersley S. J.
Published: March 2003

The concepts of charge conservation and dimensional consistency are employed to derive conditions which uniquely characterize the field equations of electromagnetism and gravitation in a vector–metric–torsion field theory which contains no cosmological constant. Using these results, it is shown that the Einstein–Maxwell field equations are unique among all possible field equations of gravitation and electromagnetism involving a vector field in a metric gravitational theory.
Exact propagators for quadratic Hamiltonians
Authors: Tikochinsky Yoel
Published: March 2003

The problem of finding the exact propagator for a given quadratic Hamiltonian is presented as an initial-value problem — a form suitable for both analytic and numerical computation. We illustrate the method by finding the propagator for (a) the Hamiltonian with constant coefficients and (b) and (c) Hamiltonians associated with damped harmonic motion.
Multiple density correlation functions for inhomogeneous systems
Authors: Rajan V. T. , Woo Chia-Wei , Wu F. Y.
Published: March 2003

In applying the method of correlated basis functions to inhomogeneous systems such as electrons in a solid, in systems bounded by surfaces, and in systems with impurities, matrix elements of multiple density fluctuation operators are needed. These are the multiple density correlation functions. We evaluate these functions in the convolution approximation and express them in usable forms.
Asymptotic eigenfrequency distribution for even-parity perturbations of hot perfect-fluid relativistic neutron stars
Authors: Cazzola P. , Lucaroni L. , Semenzato R.
Published: March 2003

Making two assumptions regarding the analytical continuation of the external solution to the region Imω<0, we give the asymptotic distribution for ω→∞ of the eigenfrequencies of a hot perfect fluid relativistic neutron star. It results that the real parts of the complex eigenfrequencies grow as the integers, while their imaginary parts grow as ln‖ωn‖ with coefficients depending inversely on the ’’optical path’’ of the uncoupled gravitational waves through the star.
Diffraction by two parallel slits in a plane
Authors: Otsuki Takuro
Published: March 2003

The diffraction of scalar waves by two parallel slits in a plane screen is examined by a method which uses orthogonal functions and Fourier transformations. A solution is obtained in the case of a perfectly soft screen. Numerical results of the plane wave transmission coefficients for normal incidence are given for k=0.2∼4.0 and D=3∼10, where k is the wavenumber and D is the distance between slits.
Generating functions for polynomial irreducible tensors
Authors: Gaskell R. , Peccia A. , Sharp R. T.
Published: March 2003

A general method for constructing a generating function for all irreducible polynomial tensors, with respect to a given compact semisimple group, out of a given set of tensors is derived. The method is applied to the construction of polynomial bases for the IR’s of a group reduced according to a subgroup and to the finding of subgroup scalars in the enveloping algebra of a group. A number of examples are worked out.
Gel’fand lattice polynomials and irreducible representations of U(n)
Authors: Gazeau J.-P. , Dumont-Lepage M.-Cl. , Ronveaux A.
Published: March 2003

A finite difference equation defines the exponential of a square tableau, extension of the usual Gel’fand pattern. These exponentials or ’’K powers’’ are homogeneous polynomials useful in the theory of group representations. The theory of these polynomials is developed, and some important addition and multiplication theorems are deduced. The application to the group U(n) gives explicitly the Gel’fand states for n=4, and it is conjectured that the given relation is true in general for any dimension. The matrix elements with respect to this basis are calculated for n=3 and the Clebsch–Gordan decomposition of the n product of U(2) is also given.
A conformal invariant model of localized spinning test particles
Authors: Duval C. , Fliche H. H.
Published: March 2003

A purely classical model of massless test particle with spin s is introduced as the dynamical system defined by the ten-dimensional O(4,2) co-adjoint orbit with Casimir numbers (s2,0,0). The Mathisson, Papapetrou et al. equations of motion in a gravitational field are recovered, and the particle appears to travel on null geodesics. Several implications are discussed.
The moments of the multiple distribution functions
Authors: Hoffmann Patrick
Published: March 2003

The equations of moments equivalent to BBGKY and to the master equations are established with the introduction of an appropriate formalism. We end with the deduction of equations generalizing hydrodynamics. This article is limited to the monoparticle populations.
No-interaction theorem of Currie, Jordan, and Sudarshan. Expansions in c−1
Authors: Martin J. , Sanz J. L.
Published: March 2003

By means of an expansion in c−1 (c being the velocity of light) it is shown that the no-interaction theorem of Currie, Jordan, and Sudarshan is valid only when terms of order of at least c−6 are included. To confirm this result, we derive the most general family of approximate Lagrangians up to order c−4, whose limit is Newtonian.
A method for calculation of Regge poles in atomic collisions
Authors: Bosanac S.
Published: March 2003

A method for solving the Schrödinger equation is given. It is specially developed for applications in atomic (short wavelength) collisions. The method is also useful for calculating Regge poles, without having to define the potential for complex coordinate. The stability of the method is discussed.
Electromagnetic radiation near black holes and neutron stars
Authors: Arenstorf Richard F. , Cohen Jeffrey M. , Kegeles Lawrence S.
Published: March 2003

Analytic solutions to Maxwell’s equations in the Schwarzschild geometry are given. These are obtained by differentiating a single superpotential, which is valid (and bounded) at and everywhere outside the gravitational radius. The results have application to black-hole and neutron-star electrodynamics.
Lorentz-type internal symmetry
Authors: Davidson A. , Dar A.
Published: March 2003

An internal symmetry, which is based on a generalization of SU(3) in analogy to the external Poincaré group, is proposed for elementary particles. The so-called exact symmetry limit is assumed to be valid in some intrinsic ’’rest frame,’’ while the symmetry breaking is geometrically obtained by leaving this frame by some defined SU(3) boosts. The baryon number, which SU(3) does not fix for a given representation, can be defined here in analogy to the ordinary helicity. Thus it can be used to characterize some restricted SU(3) representations which provide the basis for a generalized quark model. Two kinds of quarks exist in the theory: the conventional ones and pseudoquarks possessing unexpected leptonic-like properties. For the quarks of the first kind strong currents are constructed and a strong interaction model, built as local couplings of those currents, is also presented. The model is consistent with dual quark diagrams and contains a mathematical mechanism by which n quarks and N̄ antiquarks enter an interaction vertex only if n−N̄≡0 (mod 3). Finally the mass operator is discussed in the light of the proposed symmetry.
Local supersymmetry in (2+1) dimensions. I. Supergravity and differential forms
Authors: Howe P. S. , Tucker R. W.
Published: March 2003

The theory of supergravity in (2+1) dimensions, both with and without a cosmological term, is presented. In the latter case, we discover a manifold that has torsion but no curvature. We make extensive use of differential forms and the dimensionality of our space–time allows us to use SL(2,R) spinors. Our results enable us to discuss in an accompanying paper an action describing the theory of a spinning membrane.
Complex line bundles in relativity
Authors: Curtis W. D. , Lerner D. E.
Published: March 2003

We exhibit the complexified spin and conformally weighted functions as sections of holomorphic line bundles over P1(C) ×P1(C). As an example of a nontrivial bundle, we discuss the complex null cone in some detail.
Geometry of motion of a single elastic body point
Authors: Atanackovic T. M.
Published: March 2003

A four-dimensional space LX̂, in which body point X̂ of a simple elastic body describes a geodesic line during the process of deformation, is constructed. It is shown that LX̂is a torsion-free non-Riemannian space. The structure of LX̂ is examined for universal dynamical solutions for incompressible elastic bodies.
On the relaxation to quantum-statistical equilibrium of the Wigner–Weisskopf atom in a one-dimensional radiation field. VIII. Emission in an infinite system in the presence of an extra photon
Authors: Davidson Russell , Kozak John J.
Published: March 2003

In this paper we study the emission of a two-level atom in a radiation field in the case where one mode of the field is assumed to be excited initially, and where the system is assumed to be of infinite extent. (The restriction to a one-dimensional field, which has been made throughout this series, is not essential: It is made chiefly for ease of presentation of the mathematical methods.) An exact expression is obtained for the probability ρ (t) that the two-level quantum system is in the excited state at time t. This problem, previously unsolved in radiation theory, is tackled by reformulating the expression found in VII [J. Math. Phys. 16, 1013 (1975)] of this series for the time evolution of ρ (t) in a finite system in the presence of an extra photon, and then constructing the infinite-system limit. A quantitative assessment of the role of the extra photon and of the coupling constant in influencing the dynamics is obtained by studying numerically the expression derived for ρ (t) for a particular choice of initial condition. The study presented here casts light on the problem of time-reversal invariance and clarifies the sense in which exponential decay is universal; in particular, we find that: (1) It is the infinite-system limit which converts the time-reversible solutions of VII into the irreversible solution obtained here, and (2) it is the weak-coupling limit that imposes exponential form on the time dependence of the evolution of the system. The anticipated generalization of our methods to more complicated radiation-matter problems is discussed, and finally, several problems in radiation chemistry and physics, already accessible to exact analysis given the approach introduced here, are cited.
Natural connections on Stiefel bundles are sourceless gauge fields
Authors: Nowakowski Jerzy , Trautman Andrzej
Published: March 2003

It is shown that the natural connections defined on real and complex Stiefel bundles over Grassmannian manifolds are sourceless gauge fields corresponding to the gauge groups G=SO(k), k=2,3,⋅⋅⋅ and U(k), k=1,2,⋅⋅⋅, respectively. Stiefel bundles and their connections are important in view of their universality: Any gauge field, with group G, defined on a compact manifold may be obtained by embedding the manifold in a Grassmannian of sufficiently high dimension.
The group structure of pseudo-Riemannian curvature spaces
Authors: Tilgner Hans
Published: March 2003

The linear conformal group G (pseudo-orthogonal automorphisms and dilatations) on a pseudo-orthogonal vector space induces an action in the space of pseudo-orthogonal curvature structures, which leaves Singer and Thorpe’s direct decomposition in trivial, non-Einsteinian and Weyl curvature structures invariant. It is shown that the condition of a curvature to be homogeneous, reductive, or symmetric is G-invariant. A condition for a non-Weyl curvature to be symmetric is formulated explicitly. Nomizu’s injection of the Jordan algebra of Lorentz-self-adjoint matrices is used to describe some G-orbits of non-Einsteinian curvatures. The Duffin–Kemmer–Petiau meson triple allows the construction of a cosmological model with trivial curvature.
Nonlinear tunnelling
Authors: Newell Alan C.
Published: March 2003

The propagation of a soliton pulse towards a finite potential barrier is examined, and it is found that in certain circumstances, depending on the ratio of soliton amplitude to barrier height, the soliton can tunnel through the barrier in a lossless manner. It is suggested that the phenomenon of barrier penetration by nonlinear pulses may have widespread application.
Analytic connection between configuration–interaction and coupled-cluster solutions
Authors: Živković Tomislav P. , Monkhorst Hendrik J.
Published: March 2003

The coupled-cluster (CC) equations in the work of Coester, Kümmel, Čižek, Paldus, and others are inhomogeneous, nonlinear and algebraic in the cluster operators to be determined. If taken to all orders, they are equivalent to complete configuration–interaction (CI) equations, except for states orthogonal to the reference state Φ. However, if taken only to nth order, they are not equivalent to the nth order CI equations, and due to their nonlinear form, the existence and the number of the solutions is not guaranteed. Also, the reality of the associated energy values is not certain since these values do not arise as eigenvalues of a Hermitian operator. We show that the equations can be cast in the form of perturbed CI equations, with the ’’perturbations’’ being non-Hermitian and nonlinear in the CI-like coefficients to be calculated. In the case of a finite number of single-particle states, we construct the solutions to the CC equations by analytic continuation from the CI solutions. Singularities peculiar to the method are identified and studied, and conditions for reality and the maximum multiplicity of solutions are given. In general, the energy will be real, and the number of solutions equals that of the associated CI problem. Singularities or instabilities in the coupled-cluster equations can be traced to unphysical assumptions in the basis set Hamiltonian, or a poor description to highly excited states.
Quantization of the Liouville mechanics for systems with singular Lagrangians
Authors: Boisseau B. , Barrabes C.
Published: March 2003

Quantum mechanics, in phase space formulation, is directly deduced from the Liouville mechanics by a correspondence principle. The latter is applied to systems with singular Lagrangians.
The zero-energy Coulomb problem
Authors: Chen Augustine C.
Published: March 2003

A new operator denoted as a zero-energy Runge–Lenz vector is used to derive a differential equation for the zero-energy Schrödinger wavefunction in the u representation. An integral equation is also derived in terms of a generalized Fock 4-vector which, in the zero-energy limit, yields the correct integral equation for the zero-energy Green’s function. The zero-energy aspect of the problem is further exemplified by extracting the zero-energy results directly from those for negative energies through the taking of the zero-energy limit, which is construed as making a group contraction from O(4) to E(3).
Four Euclidean conformal group in atomic calculations: Exact analytical expressions for the bound–bound two-photon transition matrix elements in the H atom
Authors: Gazeau J. P.
Published: March 2003

By combining Sturmian–Coulomb techniques with a local representation of the four Euclidean conformal group SU* (4) ≃Spin(1,5), a compact analytical form, suitable for any analytic continuation on the energy variable, is obtained for the following bound–bound two-photon transition matrix element in the H atom: INN′(E) =〈N‖p⋅ε1 exp(ik1⋅r) G (E)p ⋅ε2exp(ik2⋅r) ‖N′〉, where G (E) is the Coulomb Green’s function.
Invariance and conservation laws for Lagrangian systems with one degree of freedom
Authors: Sarlet Willy
Published: March 2003

For a general class of linear transformations of both the dependent and the independent variable in Lagrangian systems with one degree of freedom, we investigate the relationship between invariances for the Lagrangian, the equation of motion, and a constant of the motion. Unlike Denman’s work on this subject, we try to show that for every invariance in the equation of motion a Lagrangian can be found with the related invariance. Furthermore, a constant of the motion is considered as being implied by the invariance of the equation of motion if it has the same invariance as the Lagrangian.
On the normalization of one-dimensional lattice statistics
Authors: McQuistan R. B.
Published: March 2003

It is shown that the normalization of the statistics associated with the distribution of λ-bell particles [λ=1 for simple particles; λ=2 for dumbbell particles, etc.] on a one-dimensional lattice space, is given by a simple, two-term recursion relation. This normalization, for a lattice consisting of N sites, is shown to be (1/x+)N, where x+ is the real positive root of the equation xλ +x−1=0. A general recursion expression is also developed that describes the higher order moments of the statistics.
Cluster expansion for lattice gauge theories with fermions
Authors: Challifour J. L. , Weingarten D.
Published: March 2003

A cluster expansion is constructed for Euclidean lattice gauge theories including fermions. For sufficiently small values of the bare qauge coupling constant g−2 and the fermion propagation constant k, we prove the existence of gauge invariant infinite volume vacuum expectation values, convergence of Wilson’s strong coupling expansion, and an inequality related to quark confinement.
On the positivity of energy in general relativity
Authors: Jang Pong Soo
Published: March 2003

We show that the positive energy argument of Geroch for time-symmetric initial data sets can be generalized to general initial data sets.
A simple model of the integrable Hamiltonian equation
Authors: Magri Franco
Published: March 2003

A method of analysis of the infinite-dimensional Hamiltonian equations which avoids the introduction of the Bäcklund transformation or the use of the Lax equation is suggested. This analysis is based on the possibility of connecting in several ways the conservation laws of special Hamiltonian equations with their symmetries by using symplectic operators. It leads to a simple and sufficiently general model of integrable Hamiltonian equation, of which the Korteweg–de Vries equation, the modified Korteweg–de Vries equation, the nonlinear Schrödinger equation and the so-called Harry Dym equation turn out to be particular examples.
Tensor harmonics on the 3-sphere
Authors: Jantzen Robert T.
Published: March 2003

The scalar, vector, and tensor harmonics on the 3-sphere are developed by its identification with SU(2), enabling familiar angular momentum techniques to be employed. The application to spatially homogeneous cosmology is discussed. In this context the classic work of Lifshitz and the recent approach of Hu are bridged. Finally spinor harmonics are introduced.
II. Exact solutions of disordered Ising spin chains in a magnetic field
Authors: Haley Stephen B.
Published: March 2003

The one-dimensional Ising model with arbitrary nearest neighbor interactions and a magnetic field is formulated in terms of the spin correlation function relations derived in the preceding article I. The local magnetization and the two-spin correlation functions are shown to satisfy a set of coupled algebraic summation equations. The solution of this set is given in terms of a power series in hyberbolic tangents of the magnetic field strength, for chains of arbitrary length. For cases in which the interaction constants are random variables, explicit expressions are derived for the configurational averaged magnetization and the two-spin correlation functions to the lowest order in the magnetic field.
Eigenstates of complex linear combinations of J1,J2,J3 for any representation of SU(2)
Authors: Bacry H.
Published: March 2003

The states which minimalize the uncertainty relation ΔJ1 ΔJ2? (1/2) ‖〈J3〉‖ are eigenstates of complex linear combinations of J1 and J2 [S. Rushin and Y. Ben-Aryeh, Phys. Lett. A 58, 207 (1976)]. This kind of state is shown to have a very simple geometrical interpretation in the constellation formalism. A detailed description is given in the present paper.
On the covariant equations of the relativistic electrodynamics of continua. III. Elastic solids
Authors: Maugin G. A.
Published: March 2003

Based on the thermodynamical equations of a previous work, which synthesized the axiomatic approach to relativistic continuum physics with the acceptance of the relativistically invariant ponderomotive force and couple and electromagnetic power derived by de Groot and Suttorp from a microscopical treatment, this paper develops a constitutive theory for general relativistic deformable solids. After a review of the essentials of deformation theory of general relativistic continua, particular attention is paid to nonlinear elastic electromagnetic solids in normal conditions of pressure and temperature, then to the linear piezoelectric scheme which can be used for the theoretical analysis of gravitational-wave detectors that use a piezoelectric device, and, finally, to magnetoelasticity under high pressure which describes the magnetomechanical behavior of matter in certain astrophysical objects (neutron stars).
Entropy production for quantum dynamical semigroups
Authors: Spohn Herbert
Published: March 2003

In analogy to the phenomenological theory of irreversible thermodynamics we define the entropy production for an arbitrary quantum dynamical semigroup with a stationary state. We prove that the entropy production is convex and positive and that the entropy production is a measure of dissipativity of the semigroup. The entropy production is used to prove the approach to equilibrium and to classify the stationary states of semigroups arising in the weak coupling limit.
High-energy behavior of renormalized Feynman amplitudes
Authors: Manoukian Edward B.
Published: March 2003

The high-energy polynomial and logarithmic behavior of renormalized Feynman amplitudes, involving subtractions, is derived with total generality when some or all of the external momentum components of the graphs in question become large in Euclidean space nonexceptionally. This is achieved by explicitly carrying out the subtractions of renormalization as dictated, for example, by the improved Dyson–Salam renormalization scheme directly in momentum-space.
Spectral theory for the acoustic wave equations with generalized Neumann boundary conditions in exterior domain
Authors: Chen K. -H. , Yang C. C.
Published: March 2003

In this paper we studied the spectral theory of the operator (either in the exterior domain or in the whole space) that is induced from problems in the n-dimensional Euclidean space for the hyperbolic linear partial differential equations with the generalized Neumann boundary condition. The resulting theory provides a foundation for studying the wave operator and scattering operator involved in scattering theory and possibly also for studying the respective inverse problem.
The use of the symmetric group in the construction of multispinor Lagrangians
Authors: Larsen M. L. , Repko W. W.
Published: March 2003

The construction of Lagrange functions for nth rank multispinor (Bargmann–Wigner) fields is developed using the symmetric group Sn. Restrictions on the number of fields present in the Lagrangian and their couplings to one another are obtained by constructing differential operators which transform irreducibly under Sn. The technique is illustrated by a brief discussion of the second and third rank cases and a more detailed fourth rank example. The Lagrangians thus obtained are precisely those specified by Lorentz invariance, but the method used greatly facilitates their construction.
Definition of polarization of a spin 1/2 particle in an external electromagnetic field
Authors: Sidhu S. S. , Good R. H.
Published: March 2003

The 3-vector polarization of a Dirac particle with Pauli anomalous moment, in external electric and magnetic fields, is shown to be given by a certain ratio of components of the wavefunction. The result is valid in the same approximation as leads to the Bargmann–Michel–Telegdi classical equations for the polarization.
The asymptotic reduction of products of representations of the universal covering group of SU(1,1)
Authors: Rühl W. , Yunn B. C.
Published: March 2003

Irreducible representations are realized on nuclear spaces. Products of certain elements of two such spaces can be expanded into an almost everywhere convergent series that possesses rudimentary covariance properties. This unique expansion is therefore called ’’asymptotic reduction.’’ Products of elements of three such spaces possess a simultaneous expansion only in an asymptotic sense. We define recoupling coefficients for this reduction and give them explicitly.
Local supersymmetry in (2+1) dimensions. II. An action for a spinning membrane
Authors: Howe P. S. , Tucker R. W.
Published: March 2003

We present a locally supersymmetric action for a spinning membrane. This is obtained by supersymmetrizing the induced volume element action which is reformulated in terms of a three-dimensional field theory. We also discuss more complex actions which are possible due to the nontriviality of (super) gravity in three dimensions.
Some constraints on finite energy solutions in non-Abelian gauge theories
Authors: Magg M.
Published: March 2003

We exploit dilatational invariance and some inequalities for the stress tensor to derive constraints for finite energy solutions in sourceless non-Abelian gauge theories. The results extend known no-go theorems considerably and provide some hints on what nondissipative finite energy solutions could look like.