bluuebunny/crossref_metadata_2025 huggingface dataset:
Elastic scattering of low-energy electrons by benzene
Authors: Bettega M. H. F. , Winstead C. , McKoy V.
Published: July 2002

We present elastic cross sections obtained from ab initio calculations for low-energy electron scattering by benzene, C6H6. The calculations employed the Schwinger multichannel method as implemented for parallel computers within both the static-exchange and static-exchange-polarization approximations. We compare our results with other theoretical calculations and with available experimental data. In general, agreement is good.
Fragmentation of Na3+ clusters following He impact: Theoretical analysis of fragmentation mechanisms
Authors: Babikov D. , Gislason E. , Sizun M. , Aguillon F. , Sidis V.
Published: July 2002

The process of Na3+ cluster ion fragmentation following excitation by a fast He atom is studied using a theoretical procedure developed earlier. The collision with He leaves Na3+ in any of three electronic states, and each of these can fragment into three product channels (Na2++Na, Na2+Na+ and Na+Na+Na+). Attention is focused on understanding both the dynamics of the Na3+–He interaction and the post-collisional fragmentation of the excited cluster. Four simple fragmentation mechanisms are proposed to describe the major features of the process. Contributions of these mechanisms to different fragmentation pathways are determined and their dependence on the initial internal energy of the cluster is studied. Fragmentation intensity maps are calculated and good agreement with experiment is obtained.
Fourier transform spectroscopy and cross section measurements of the Herzberg III bands of O2 at 295 K
Authors: Yoshino K. , Esmond J. R. , Parkinson W. H. , Thorne A. P. , Learner R. C. M. , Cox G. , Cheung A. S.-C.
Published: July 2002

Fourier transform spectroscopic measurements of the absorption bands of the Herzberg III (A′ 3Δu–X 3Σg−) of O2 at 295 K have been made with a resolution of 0.06 cm−1 in the wavelength region 240 to 275 nm. Rotational line positions are determined with an accuracy of 0.005 cm−1, and rotational term values are presented for the vibrational levels, v′=4–11. Precise band oscillator strengths of the (4,0)–(11,0) bands are obtained for the first time by direct measurement by summing the cross sections of individual rotational lines of the bands. The rotational line strengths and the branching ratios are also presented for the same bands. The continuity relationship for the band oscillator strengths to photodissociation continuum cross sections has been applied to the three-band systems.
Quantum reaction dynamics of O(3P)+HCl on a new ab initio potential energy surface
Authors: Nobusada Katsuyuki , Nakamura Hiroki , Lin Yongjing , Ramachandran B.
Published: July 2002

Quantum reaction dynamics of O(3P)+HCl↔OH+Cl is studied by using a new ab initio potential energy surface calculated by Ramachandran et al. [J. Chem. Phys. 111, 3862 (1999)]. The hyperspherical elliptic coordinate approach is applied with an emphasis on elucidating reaction dynamics for J (total angular momentum quantum number)=0. In terms of the previously established concept that reactive transitions are nothing but vibrationally nonadiabatic transitions at important avoided crossings, clear interpretations are given for the following dynamical features: (i) reactivity depending on potential energy surface topography, (ii) final rotational state distributions for specified initial rovibrational states, and (iii) resonance structures appearing in some reactions. Thermal rate constants are approximately estimated from the present J=0 results by using the J-shift approximation. The present results are compared with our previous ones based on the different potential energy surface calculated by Koizumi–Schatz–Gordon (KSG). The calculated adiabatic potential energy curves of the present new surface have deep wells in the OH+Cl channel in contrast to the KSG potential energy surface. Consequently, the new surface leads to quite different dynamics from those on the KSG surface. Comparisons with the results obtained by quasiclassical trajectory calculations are also made.
Structural and energetic properties of the Br−–C2H2 anion complex from rotationally resolved mid-infrared spectra and ab initio calculations
Authors: Wild D. A. , Milley P. J. , Loh Z. M. , Wolynec P. P. , Weiser P. S. , Bieske E. J.
Published: July 2002

An infrared vibrational predissociation spectrum of the Br−79–C2H2 anion complex has been recorded over the 2800–3400 cm−1 range. Bands are observed that correspond to excitation of bound and free C–H stretches of an acetylene molecule engaged in a linear hydrogen bond with Br−. The band associated with the bound C–H stretch displays rotationally resolved substructure. Lower J transitions are absent from the predissociation spectrum, indicating that the upper levels lie below the dissociation threshold. Analysis leads to constants for lower and upper states: v0=2981.28, B″=0.048 84, ΔB=9.3×10−4 cm−1, and a minimum J′=28 for dissociation. The rotational constants correspond to vibrationally averaged separation between Br− and the C2H2 center of mass of 4.11 Å in the ground state and 4.07 Å in the v3 state. A dissociation energy for Br−–C2H2 of 3020±3 cm−1 is estimated from the energy of the lowest dissociating level. The spectroscopically derived data are corroborated by ab initio calculations conducted at the MP2/aug-cc-pVTZ level.
Experimental and theoretical study of the photofragmentation process: Ar3++hν→Ar2++Ar
Authors: Kirkwood D. A. , Woodward C. A. , Mouhandes A. , Stace A. J. , Bastida A. , Zuniga J. , Requena A. , Gadéa F. X.
Published: July 2002

An experimental study of the photofragmentation of Ar3+ at wavelengths >650 nm has been undertaken in order to investigate the reaction channel Ar3++hν→Ar2++Ar. As a function of photon energy, measurements have been made of the Ar+/Ar2+ branching ratio and the relative kinetic energy of the photofragments. A steady decline observed for the latter as a function of decreasing photon energy, suggests that the dimer ions emerges from the photodissociation processes with a very high level of internal excitation. Supporting semiclassical calculations of the decay dynamics confirm the trend seen for the Ar+/Ar2+ branching ratio, but do not reproduce the quantitative details. The calculations do, however, provide strong support for an experimental analysis of the energetics of fragmentation, and show that Ar2+ can appear either in the electronic ground state, but with a very high degree of vibrational excitation, or in the weakly bound Πg2 electronic excited state.
Compact expression for Löwdin’s alpha function
Authors: Antone A. A.
Published: July 2002

A simple analytical expression for Löwdin’s alpha function is derived. This expression is expected to be more convenient with the expansion of a general function about a displaced center than any other available in the literature.
Numerical integration in many dimensions. I
Authors: Schwartz Charles
Published: July 2002

If a d-dimensional integral involves an integrand of the functional form F( f1(x1)+f2(x2)+⋅⋅⋅), then one can introduce an integral transform (Fourier or Laplace or variants on those) which allows all the integrals over the coordinates xi to factor. Thus a d-dimensional integral is reduced to a one-dimensional integral over the transform variable. This is shown to be a very powerful and practical numerical approach to a number of problems of interest. Among the examples studied is the computation of the volume of phase space for an arbitrary collection of relativistic particles. One important aspect of the approach involves numerical integration along various contours in the complex plane.
Stochastic difference equations for a spin system
Authors: Falk H.
Published: July 2002

An N-spin model is given with a discrete-time evolution specified by a system of stochastic difference equations. A Markov chain associated with the evolution is decomposed into two, nonhomogeneous, absorbing Markov chains. Analysis of each chain yields the probability, given a specific initial state, of ultimate absorption into a specific state. As time t→∞ the spin model will, with probability equal to 1, have all spins up, all spins down, or will oscillate between two antiferromagnetic (Néel) states. The time-dependent correlation functions 〈si(t)sj(t)〉 are also obtained.
Conservation laws in the Dirac theory
Authors: Boudet Roger
Published: July 2002

It is well known that the Dirac equations determine three conservation laws, for current, for energy momentum, and for angular momentum. Dividing the Dirac equations in two parts, one, DI, which does not contain the density ρ, the other, DII, which contains ρ, it is shown that DI together with the three conservation equations, determine DII. From this result, a model of formulation of the Dirac theory is proposed, following a scheme similar to that of classical mechanics, in which principles regarding the motion of one particle are associated with conservation theorems concerning statistical ensembles of particles.
The infinite coupling limit of perturbative expansions from a variational extrapolation method
Authors: Bonnier B. , Hontebeyrie M. , Ticembal E. H.
Published: July 2002

A method for extrapolating perturbative power series to infinity is described. It is a Borel partial resummation stabilized by a variational parameter. Two kinds of series relative to the anharmonic oscillators ‖x‖k, k>0, are extrapolated in order to illustrate the effectiveness of the method: the Rayleigh–Schrödinger series, on the one hand, which, after extrapolation, provides the strong coupling expansion of the energy levels, and their lattice expansion, on the other hand, from which is extracted the continuum limit.
Some exact inhomogeneous solutions of Einstein’s equations with symmetries on the hypersurfaces t=const
Authors: Argüeso F. , Sanz J. L.
Published: July 2002

The solution of Einstein’s field equations is studied for a metric written in the form (δ≠γ)ds2=−α2(t,r,θ,φ)dt2 +e2β(t,r) dr2+e2γ(t,r) dθ2 +e2δ(t,r)M2(θ)dφ2. A perfect fluid, which flows orthogonally to the hypersurfaces t=const is considered as matter content. These hypersurfaces admit a translational Killing vector, which will not be, in general, a Killing vector of the whole space-time. All the possible solutions are obtained when α depends on the variable φ. These solutions represent either a perfect fluid without expansion or vacuum with a cosmological constant Λ0. Some particular inhomogeneous solutions are obtained for α independently of φ. These solutions are physical, the fluid obeys an equation of state p=ρ (stiff matter), and the space-time admits, apparently, only a group G2 of isometries. A vacuum family is also obtained in this case.
Quantum angular momentum fluctuations
Authors: Nachtergaele Bruno
Published: July 2002

An exact derivation of the angular momentum fluctuations for quantum mechanical systems with two-body interactions is given under suitable cluster conditions. The deviation from the classical result in the presence of a phase transition is discussed.
Quantum statistical derivation of the hydrodynamics of a plasma model
Authors: Sewell Geoffrey L.
Published: July 2002

We derive macroscopic electrohydrodynamical equations of Euler and Maxwell from the many-particle Schrödinger equation of the Jellium model, subject to viable initial conditions, together with certain simple assumptions of macroscopic regularity. The dynamics of the model becomes tractable, on a suitable macroscopic scale and in the limit where its size becomes infinite, because of simple scaling properties and the long range of the Coulomb forces. Our derivation of its phenomenological dynamics is obtained via that of the classical Vlasov equation.
On the phase retrieval problem in two dimensions
Authors: Stefanescu I. Sabba
Published: July 2002

The paper contains a discussion of the phase retrieval problem in two dimensions and proposes criteria to select those resolutions of the discrete ambiguity of the zero trajectories which are compatible with the analyticity in two variables of the scattered field.
On the Wigner coefficients of the generalized Lorentz groups in the parabolic basis
Authors: Kerimov G. A.
Published: July 2002

Wigner coefficients for the class 1 representations of the generalized Lorentz groups SO(n+1,1) in the parabolic basis corresponding to the group reduction SO(n+1,1)⊃E(n)⊃T(n) are calculated. They are in general expressible in terms of Appell’s F4 hypergeometric functions of two variables. However, in the case of n=1,2 they can also be expressed in terms of ordinary hypergeometric functions 2F1.
The symmetric and antisymmetric structure constants for SU(6)
Authors: Sarid Uri
Published: July 2002

The 124 completely antisymmetric fijk and 221 completely symmetric dijk (nonzero) structure constants for a simple representation of SU(6) are tabulated. The basis matrices λi used to generate the structure constants are also given.
Quantum-mechanical representations of the group of diffeomorphisms and local current algebra describing tightly bound composite particles
Authors: Goldin Gerald A. , Menikoff Ralph
Published: July 2002

A semidirect product of Schwartz’ space functions on R3 and the group of diffeomorphisms of R3 can describe quantum-mechanical systems. We interpret a class of continuous unitary representations of this group, characterized by multipole moments, as describing tightly bound composite particles.
Closed, analytic, boson realizations for Sp(4)
Authors: Klein Abraham , Zhang Qing-Ying
Published: July 2002

The problem of determing a boson realization for an arbitrary irrep of the unitary simplectic algebra Sp(2d) [or of the corresponding discrete unitary irreps of the unbounded algebra Sp(2d,R)] has been solved completely in recent papers by Deenen and Quesne [J. Deenen and C. Quesne, J. Math. Phys. 23, 878, 2004 (1982); 25, 1638 (1984); 26, 2705 (1985)] and by Moshinsky and co-workers [O. Castaños, E. Chacón, M. Moshinsky, and C. Quesne, J. Math. Phys. 26, 2107 (1985); M. Moshinsky, ‘‘Boson realization of symplectic algebras,’’ to be published]. This solution is not known in closed analytic form except for d=1 and for special classes of irreps for d>1. A different method of obtaining a boson realization that solves the full problem for Sp(4) is described. The method utilizes the chain Sp(2d)⊇SU(2)×SU(2) ×⋅⋅⋅×SU(2) (d times), which, for d≥4, does not provide a complete set of quantum numbers. Though a simple solution of the missing label problem can be given, this solution does not help in the construction of a mapping algorithm for general d.
The initial value problem for colliding gravitational and hydrodynamic waves
Authors: Xanthopoulos Basilis C.
Published: July 2002

The collision of two plane gravitational and hydrodynamic waves with parallel polarizations is studied. In the interaction region, to the future of the collision, the space-time admits two hypersurface orthogonal Killing fields, and the problem reduces to solving two (decoupled!) linear partial differential equations. The characteristic initial value problem for these equations is explicitly solved by means of Riemann’s method. In the appendices the relevant field equations are written in two different coordinate systems that have been proved useful in the studies of colliding waves, relationships among the solutions of the gravitational and the hydrodynamic equations are obtained, separable solutions involving Bessel functions are constructed, and integral identities among the Legendre functions are obtained.
On the summation of the Birkhoff–Gustavson normal form of an anharmonic oscillator
Authors: Ali M. K. , Wood W. Robert , Devitt J. S.
Published: July 2002

The classical Birkhoff–Gustavson normal form (BGNF) has played an important role in finding approximate constants of motion, and semiclassical energies. In this paper, this role is examined in detail for the well-known anharmonic oscillator H=1/2(p2+x2+gx4). It is shown that, with appropriate restrictions, this is the only perturbation series that preserves the period of this system. This series has a nonzero radius of convergence in contrast to the zero radius of convergence of its quantum analog, the Rayleigh–Schrödinger perturbation series. In addition, the BGNF is generated to high order, and a technique is given based on Padé approximants for summing this series. The summation of this series makes possible an accurate comparison of torus quantization energies with the known quantum energies over the entire range of quantum numbers. This example also demonstrates that divergence of the BGNF series of a Hamiltonian is not sufficient to refute its global integrability.
PCT theorem for fields with arbitrary high-energy behavior
Authors: Lücke W.
Published: July 2002

A neutral scalar field A(x) is considered that has to be smeared by Fourier transforms of C∞ functions with compact support but otherwise fulfills all the Wightman axioms, except strict local commutativity. It is shown to fulfill the PCT symmetry condition (where Ω denotes the vacuum state vector) 〈Ω‖A(x1) ⋅⋅⋅  A(xn)Ω〉 =〈Ω‖A(−xn) ⋅⋅⋅  A(−x1)Ω〉 if and only if 〈Ω‖A(x1) ⋅⋅⋅  A(xn)Ω〉 −〈Ω‖A(xn) ⋅⋅⋅  A(x1)Ω〉 can be represented, in a sense, as an infinite sum of derivatives of measures with supports containing no Jost points.
Layer-stripping solutions of multidimensional inverse scattering problems
Authors: Yagle Andrew E. , Levy Bernard C.
Published: July 2002

A layer-stripping procedure for solving three-dimensional Schrödinger equation inverse scattering problems is developed. This method operates by recursively reconstructing the potential from the jump in the scattered field at the wave front, and then using the reconstructed potential to propagate the wave front and the scattered field further into the inhomogeneous region. It is thus a generalization of algorithms that have been developed for one-dimensional inverse scattering problems. Although the procedure has not yet been numerically tested, the corresponding one-dimensional algorithms have performed well on synthetic data. The procedure is applied to a two-dimensional inverse seismic problem. Connections between simplifications of this method and Born approximation inverse scattering methods are also noted.
On the DLR equation for the two-dimensional sine–Gordon model
Authors: Gielerak R.
Published: July 2002

The Dobrushin–Lanford–Ruelle equation is studied in a certain space of measures in the case of two-dimensional trigonometric interactions. The uniqueness theorem extending the results of Albeverio and Hoegh-Krohn [S. Albeverio and R. Hoegh-Krohn, Commun. Math. Phys. 68, 95 (1979)] is proved. The extension is obtained by the application of some correlation inequalities of the Ginibre-type, which reduce the proof of the uniqueness of the translationally invariant, regular, tempered Gibbs states to the question on the independence of the infinite-volume free energy of the boundary conditions. The required independence is proved in this paper.
Nahm’s equations, singular point analysis, and integrability
Authors: Steeb W.-H. , Louw J. A.
Published: July 2002

A singular point analysis (Painlevé test) for certain special cases of Nahm’s equations is performed. It is shown that there are cases in which the equations do not pass the test. The Laurent expansion does not contain the right number of arbitrary expansion coefficients. Nevertheless the systems under consideration are completely integrable.
Traveling-wave solutions and the coupled Korteweg–de Vries equation
Authors: Guha-Roy C. , Bagchi B. , Sinha D. K.
Published: July 2002

Some coupled nonlinear equations are considered for studying traveling-wave solutions. By introducing a stream function Ψ it is shown that if one of the solutions is of the form v≡v(x−ct), the other also must be of the form u≡u(x−ct). In addition, the possibility of including cubic nonlinear terms has been considered and such a system, assuming that the solutions are of the traveling-wave type, has been solved.
The action of a general gauge field theory: Minimum or stationary. II
Authors: Bishop N. T.
Published: July 2002

In a previous paper the author has shown that for a gauge field theory with positive definite Cartan–Killing metric Cαβ and space metric gij the action functional is locally strictly minimum provided that the critical point and the variation both satisfy the gauge condition Aαi,i=0. This result is now extended so that no assumption is needed about gauge conditions.
Two-fluid cosmological models
Authors: Coley A. A. , Tupper B. O. J.
Published: July 2002

Homogeneous and isotropic, relativistic two-fluid cosmological models are investigated. In these models two separate fluids act as the source of the gravitational field, as represented by the FRW line element. The general theory of two-fluid FRW models in which neither fluid need be comoving or perfect is developed. However, attention is focused on the physically interesting special class of flat FRW models in which one fluid is a comoving radiative perfect fluid and the second a noncomoving imperfect fluid. The first fluid is taken to model the cosmic microwave background and the second to model the observed material content of the universe. One of the motivations of the present work is to model the observed velocity of our galaxy relative to the cosmic microwave background that was recently discovered by G. F. Smoot, M. V. Gorenstein, and R. A. Muller [Phys. Rev. Lett. 39, 898 (1977)]. Several models within this special class are found and analyzed. The models obtained are theoretically satisfactory in that they are represented by solutions of Einstein’s field equations and the laws of thermodynamics in which all the physical quantities occurring in the solutions are suitably well behaved. In addition, the models are in agreement with current observations. Consequently it is believed that the models obtained are physically acceptable models of the universe.
On the electromagnetic field and the Teukolsky–Press relations in arbitrary space-times
Authors: Coll Bartolomé , Fayos Francesc , Ferrando Joan Josep
Published: July 2002

The relations on the electromagnetic field obtained by Teukolsky and Press for type D vacuum space-times are considered; these are four second-order equations in two complex components of the field with respect to a principal null tetrad. A rigorous geometric interpretation of these relations is given, showing the essential role played by the Maxwellian character of the basic null tetrad. It appears that, generically, the Teukolsky–Press relations are incomplete. Once completed, their generalizations to the general Maxwell equations (with source term) with respect to non-necessarily Maxwellian tetrads on arbitrary space-times are given.
Quadratures for self-dual GL(2,C) Yang–Mills fields
Authors: Chakravarty S. , Newman E. T.
Published: July 2002

It is the purpose of this paper to show that the GL(2,C) Yang–Mills equations can be solved in terms of integrals over the characteristic initial data. The method is based on showing that enough gauge freedom exists in the choice of characteristic initial data so that the data can always be put into either upper or lower triangular form. With triangular form data the Sparling equation (a linear first-order equation equivalent to the self-dual Yang–Mills equations) can be solved by explicit quadratures.
On the symmetric representations of SU(5). Matrix elements of the generators in the subgroup bases SU(2)×SU(2)×U(1) and SU(2)×SU(2)
Authors: Vanthournout J. , De Meyer H. , Vanden Berghe G.
Published: July 2002

Matrix elements of the group generators for the totally symmetric irreducible representations of SU(5) are obtained in closed form employing the decomposition chain SU(5)⊇SU(4)×U(1)⊇SO(4)×U(1). The SU(4)≈SU(2)×SU(2) subgroup herein also occurs at the tail of the inclusion chain SU(5)⊇SO(5)⊇SO(4). Therefore, closed form expressions for the matrix elements of the SU(5) generators in the latter basis are established, too.
Spectral transform and solitons for generalized coupled Bloch systems
Authors: Leon Jérôme J.-P.
Published: July 2002

The spectral transform and Bäcklund transformation for a generalization of the coupled Bloch system arising in nonlinear optics are studied. The equation is related to a singular dispersion relation and is treated as a representative example of a general method for studying such equations. The spectral transform is developed through the ∂̄ formalism. The Bäcklund transformation is derived in a very general way and solved to obtain the one-soliton and breatherlike solutions. The nonlinear superposition formula is also constructed.
Curvature of generic space-times in general relativity
Authors: Rendall A. D.
Published: July 2002

Transversality theory is used to study the curvature of generic space-times in general relativity and some applications to unique determination of the metric by the curvature are given.
Solutions of Euclidean σ models on noncompact Grassmann manifolds
Authors: Antoine J.-P. , Piette B.
Published: July 2002

A method for constructing explicit solutions of classical, two-dimensional, Euclidean σ models on Grassmann manifolds of noncompact type, and their supersymmetric extensions, is presented. It generalizes the ‘‘holomorphic’’ method developed by Din, Zakrzewski, and Sasaki in the compact case, by taking properly into account the geometry of indefinite metric spaces. The solutions obtained are local, in the sense that they may become singular on certain curves in the plane, and the signature of the solution may change across such a curve.
Exact analytic solutions for the quantum mechanical sextic anharmonic oscillator
Authors: Dutta A. K. , Willey R. S.
Published: July 2002

Exact analytic solutions for low-lying states of the O(N) invariant sextic anharmonic oscillator are presented. The exact results are compared with Gaussian approximations and general 1/N expansions.
Lie algebraic solutions of linear Fokker–Planck equations
Authors: Wolf Fritz
Published: July 2002

Nonstationary solutions of linear Fokker–Planck equations with arbitrary drift and diffusion coefficients are derived. Using Lie algebraic techniques the time-evolution operator is given as a product of exponentials of the differential operators appearing in the equations.
Dirac bracket revisited
Authors: Ruggeri G. J.
Published: July 2002

Among all possible singular (Lie) brackets in classical dynamics of discrete systems, the matrix of Dirac brackets between phase-space coordinates is uniquely characterized by having the symplectic (Lagrange) matrix as a generalized inverse. This result is used to prove an explicit representation of the Dirac bracket in terms of its singular functions.
The dynamics of a class of quantum mean-field theories
Authors: Bóna Pavel
Published: July 2002

An infinite quantum system with correctly defined dynamics τQ as an automorphism group of a C*-algebra 𝒞 of observables is determined by any continuous unitary representation U(G) of a connected Lie group G, as well as by an arbitrary differentiable real function Q on the dual space 𝔤* to the Lie algebra 𝔤 of G with the canonically defined Poisson flow φQ on 𝔤*. For specific choices of Q and G, the system can be obtained as the thermodynamic limit of a net of finite lattice systems with the mean-field type interaction of Hepp and Lieb [Helv. Phys. Acta 46, 573 (1973)]. A simple nontrivial model of this type is the quasispin BCS model of superconductivity in the strong coupling limit, or a corresponding model of the Josephson junction. A peculiar feature of the considered models is τQ noninvariance of the usually considered C*-algebra 𝒜 of quasilocal observables, as well as an important role of classical dynamics of a set of macroscopic (intensive) observables Qφ in the description of τQ. The work is restricted here to norm-continuous representations U(G), in which case 𝒞 is isomorphic to the tensor product 𝒜⊗𝒩, where 𝒩 is the commutative algebra of classical (intensive) observables of the considered infinite quantum system.
A supersymmetric generalization of von Neumann’s theorem
Authors: Grosse H. , Pittner L.
Published: July 2002

A formulation of supersymmetric quantum mechanics is given and superunitary and generalized canonical transformations are defined acting in a module. Next it is assumed that there are operators that give an irreducible representation of the canonical commutation and anticommutation relations, respectively, and it is proved that two such representations are connected by a uniquely determined superunitary transformation, under suitable domain assumptions. This extends the well-known uniqueness theorem of von Neumann to canonical (anti−) commutation relations using anticommuting parameters.
Dirac equation in external vector fields: Separation of variables
Authors: Shishkin German V. , Villalba Víctor M.
Published: July 2002

The method of separation of variables in the Dirac equation in the external vector fields is developed through the search for exact solutions. The essence of the method consists of the separation of the first-order matricial differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with the operator of the equations or between them is not assumed. This approach, which is perfectly justified in the presence of gravitational fields, permits one to prove rigorous theorems about necessary and sufficient conditions on the field functions that allow one to separate variables in the Dirac equation. In analogous investigations by other authors [Bagrov et al., Exact solutions of Relativistic Wave Equations (Nauka, Novosibirst, 1982)] for electromagnetic fields an essential demand related to the operators that define the dependence of the bispinor on the separated variables is the demand for the commutation of a complete set of operators between them or with the operators of the Dirac equation. For this reason a series of possibilities that do not satisfy this demand escape the attention of these other authors. The present work liquidates this gap, solving the problem for external vector fields in general.
The Birkhoff–Gustavson normal form of one-dimensional double-well Hamiltonians
Authors: Ali M. K. , Wood W. Robert
Published: July 2002

The Birkhoff–Gustavson normal form (BGNF) is employed to study general double-well anharmonic oscillators with polynomial potentials of degree 4. Via an analytic continuation of the BGNF series, expressions are presented that provide classical and semiclassical results for all energies. A surprising observation of the classical period and an interesting feature of the semiclassical quantum numbers are reported. It is shown that except for a small region near the top of the potential barrier, the BGNF approach yields accurate quantum energies.
The Φ4 equations of motion. III. The sweeping factors
Authors: Manolessou Marietta
Published: July 2002

This is the third in a series of three papers concerning the study of the infinite system of Φ4 equations of motion for the Schwinger functions by a fixed-point method. In Paper II [J. Math. Phys. 30, 175 (1989)] the solution of the zero- (one-) and two-dimensional systems was constructed inside particular subsets of the corresponding Banach spaces characterized by the ‘‘signs’’ and ‘‘splitting’’ properties of the Green’s functions at zero external momenta. In the present article the recursive formulas and the absolute bounds of the sweeping factors, presented without proof in II, are proved. These sequences of sweeping factors for the global terms of the equations have been the most important combinatorial tools throughout the arguments, and their properties have been used in the proofs of the basic theorems in II. In Appendix A a first confirmation of the method, provided by the numerical identification of the author’s zero-dimensional solution, with the one obtained directly by the standard functional integral formalism, is presented.
Coupled nonlinear Schrödinger equations arising in the study of monomode step-index optical fibers
Authors: Newboult G. K. , Parker D. F. , Faulkner T. R.
Published: July 2002

In this paper it is shown that nonlinear propagation in a step-index, ‘‘monomode’’ optical fiber is not generally governed by the nonlinear Schrödinger equation, even when the fiber is axially symmetric. It is governed by a coupled pair of nonlinear partial differential equations that includes the nonlinear Schrödinger equations only as a special case. Three simple types of solution to the coupled system are analyzed and the corresponding field patterns are interpreted. One case shows that, for uniform wavetrains, nonlinearity not only alters the phase speed but also causes the field pattern in an ‘‘elliptically polarized’’ mode to rotate gradually about the fiber axis. The other two cases each allow the system to be reduced to a single nonlinear Schrödinger equation, so showing two distinct situations in which solutions have soliton properties.
On the compatibility of relativistic wave equations in Riemann–Cartan spaces
Authors: Buchdahl H. A.
Published: July 2002

The so-called compatibility problem for relativistic wave equations in Riemann spaces V4 has its counterpart in Riemann–Cartan spaces U4. What is to be understood by incompatibility is elucidated. It is shown that in a U4, the minimally coupled massive spin-S Dirac equations imply constraints for all values of S> 1/2 . In a U4 (though not in a V4), one has a constraint already when S=1. It is shown that the equations can be compatible (when S≥1) only if torsion is absent, i.e., if the U4 is in fact a V4. If one contemplates the equations on the level of first quantization, the minimal coupling prescription is inappropriate, and minimal Hermitian coupling is prescribed in its place. However, the previous conclusion, that for S≥1 the equations are always incompatible in the presence of torsion, remains valid.
Spatially homogeneous cosmological models of Bianchi type III
Authors: Ram Shri
Published: July 2002

Some analytic solutions to Einstein’s equations with perfect fluids are presented that are of Bianchi type III. The geometrical and physical properties of the solutions are studied.
On the dynamics of singular, continuous systems
Authors: Güler Y.
Published: July 2002

The Hamilton–Jacobi theory of a special type of singular continuous systems is investigated by the equivalent Lagrangians method. The Hamiltonian is constructed in such a way that the constraint equations are involved in the canonical equations implicitly. The Hamilton–Jacobi partial differential equation is set up in a similar manner to the regular case.
Fractals and ultrasmooth microeffects
Authors: Herrmann Robert A.
Published: July 2002

In this paper, a portion of the nonstandard methods first introduced by Nottale and Schneider [J. Math. Phys. 25, 1296 (1984)] for the investigation of fractal behavior are replaced by methods employing polysaturated enlargements. This process yields internal functions that are ultrasmooth and have a standard part equal to the original fractal. These ultrasmooth nonstandard functions also possess a well-behaved * integral length concept. Additionally, a method is presented that shows that if certain behavior is modeled after a simple finitely discontinuous step function, then this function is also the standard part of an internal hypersmooth nonstandard approximation.
A note on super Fock space
Authors: Bergvelt M. J.
Published: July 2002

An explicit realization is given in terms of even and odd differential operators of certain highest weight representations for the affine Lie superalgebra gl1/1.
Observation versus evolution: A short time theorem for positive definite functions, unitary groups, and quantum processes
Authors: Kanter Marek
Published: July 2002

The change of state of a quantum process is studied in the limit when the time t between observations tends to 0. General quantum processes are treated, as represented by a strongly continuous group G of unitary operators on a Hilbert space. Observation is defined as the effect of a self-adjoint operator A on the state vector. When A has countable spectrum and nondegenerate eigenvalues, the limiting change of state (given there is a change) is completely characterized. The most interesting special case occurs when the initial state is an eigenvector of A not in the domain of the Hamiltonian generating G: the whereabouts of the next observed state become infinitely diffuse as t→0. The results involve some analytic and geometric facts about complex valued positive definite functions.
Lorentzian structures of open, spin manifolds
Authors: Bugajska Krystyna
Published: July 2002

The possible set of inequivalent Lorentz structures on an open, connected, spin four-manifold M is investigated. Using the Steenrod correspondence between Lorentz metrics and tangent line bundles, the family of all homotopy classes of possible Lorentz structures on M is obtained. This approach allows one to distinguish explicitly between time-orientable and time-nonorientable Lorentzian metrics. Moreover, it is shown that any two inequivalent, time-orientable Lorentzian structures that correspond to generators of the torsionless part of H1(M, Z) can be related to each other by using a Morse function with one nondegenerate critical point of index 1 which describes a surgery of type (1, 3) in some decomposition of M=∪i=1∞ Ui.
o(4,2)×o(4,2) group theoretical expression of the interelectronic Coulomb potential
Authors: de Prunelé E.
Published: July 2002

The interelectronic Coulomb interaction between two electrons is expressed in terms of the o(4,2) generators of each electron. The formulation allows an expansion in terms of scaled hydrogenic (also called Sturmian) states of each electron with respect to a common center if the total orbital angular momentum is different from zero. The formulation is exact in the limit where a dimensionless parameter goes to infinity. Numerical evaluation of matrix elements of the interelectronic potential between hydrogenic configurations illustrates the convergence with respect to this parameter.
Hamiltonian methods for nonlinear sigma models
Authors: Pak N. K. , Percacci R.
Published: July 2002

Nonlinear sigma models are studied in n space dimensions with values in a coset space G/H as infinite dimensional Hamiltonian systems. An ‘‘intrinsic’’ formulation is discussed in terms of coordinates on G/H, an ‘‘embedded’’ formulation in terms of fields satisfying a constraint and a ‘‘lifted’’ formulation in terms of fields having values in G/H̄, where H̄ is a normal subgroup of H. The coupling of the sigma model to Yang–Mills fields with structure group G is then considered, and it is shown that this system is equivalent to a massive Yang–Mills theory.
Equilibrium states of a class of quantum mean-field theories
Authors: Bóna Pavel
Published: July 2002

The general structure and existence of equilibrium and ground states of infinite spin systems with the mean-field type interaction of Hepp and Lieb [Helv. Phys. Acta 46, 573 (1973)] is investigated. The form and the role of the ‘‘Bogoliubov–Haag’’ Hamiltonians is cleared. The analysis is based on a recent mathematically correct definition of the corresponding time automorphism group τQ (specified by a classical Hamiltonian Q) of an appropriately defined ‘‘physical’’ C*-algebra of observables 𝒞 containing an abelian subalgebra 𝒩 of classical macroscopic quantities as well as the conventional ‘‘bare’’ quasilocal (sub-) algebra 𝒜, 𝒞=𝒜⊗𝒩 [P. Bóna, J. Math. Phys. 29, 2223 (1988)]. A Lie group G of ‘‘hidden symmetries’’ acting nontrivially (also) on 𝒩 plays an essential role in the presented theory. The applications to the quasispin strong-coupling version of the BCS model of superconductivity, and to the corresponding model of the Josephson junction illustrate possibilities of the developed formalism as well as an easy manipulation with it. A simple mathematical description of ‘‘symmetry breaking’’ is sketched for the considered class of mathematical models of large quantal systems.
Vectorlike coherent states with noncompact stability group
Authors: Papaloucas L. C. , Rembieliński J. , Tybor W.
Published: July 2002

An investigation is made of coherent states that differ from the usual ones in two ways: (a) they are connected with the coset space G/H, where the stability subgroup H may be noncompact; and (b) the notion of an H-invariant ray is replaced by the more general notion of an H-invariant subspace. A general framework is given for vectorlike coherent states with the help of the nonlinear realization technique as well as with the rigged Hilbert space theory. The vectorlike coherent states are found for the Poincaré group and the hyperbolic coherent states are found for the SU(1,1) group.
Asymptotic transition probabilities
Authors: Arredondo R. J. H.
Published: July 2002

The impact parameter model for the scattering of two heavy particles and a light one is studied. The asymptotic behavior of the transition probability is studied when the relative velocity of the heavy particles goes to zero. In particular, rigorous proof is given from first principles, within the context of the model, of the validity of Massey’s criterion.
Symmetry preserving deformations of generalized Taub–NUT space-times to all orders in perturbation theory
Authors: Moncrief Vincent
Published: July 2002

Generalized Taub–NUT (Newman–Unti–Tamburino) space-times have compact Cauchy horizons and (generically) admit one (spacelike) Killing field in their globally hyperbolic regions. A large family of such vacuum space-times can be defined on circle bundles over K×R, where K is a compact two-manifold, with the circular fibers of the bundle being defined by the orbits of the Killing field. For the simplest case of product circle bundles the symmetry preserving vacuum perturbations of such backgrounds to arbitrarily high order in perturbation theory are considered. The analytic form of the general solution of the nth-order perturbation equations for all n is derived under the restriction that the perturbations considered preserve the (one Killing field) symmetry of the background. The evolution equations are treated first and then the constraint equations are imposed, recovering along the way the well-known result that linearization instabilities arise only if one attempts to perturb from one (Killing) symmetry class to another. Gauge transformations, decompositions, and the natural symplectic structure associated with the perturbation formalism are also discussed. The possibility of extending these results to the case of symmetry breaking perturbations and of using the results to derive the asymptotic behavior of solutions near their singular boundaries is briefly discussed.
Killing tensor conservation laws and their generators
Authors: Rosquist Kjell
Published: July 2002

The generators of Killing vector and tensor geodesic conservation laws are derived. It is shown that the generator of a Killing vector conservation law coincides with the Killing field itself. For Killing tensors the generators are not space-time vector fields but rather depend on the geodesic tangent vector and therefore lie in a jet space of the geodesic equations. By regarding the metric as a field on the one-jet space of the geodesic equations, the action of the Killing tensor generators on the metric can be defined in a natural way. It is found that the metric is not invariant under Killing tensor symmetries. This happens because the Killing tensor symmetries, unlike the Killing vector symmetries, are divergence symmetries.
Dirac equation in external vector fields: New exact solutions
Authors: Shishkin German V. , Villalba Victor M.
Published: July 2002

New exact solutions are searched for on the basis of the method of separation of variables proposed in earlier work by the present authors [J. Math. Phys. 30, 2132 (1989)]. The essence of this method consists of constructing first-order matrix differential operators that define the dependence of the Dirac bispinor on the related variables, but commutation of such operators with the operator of the equation or between them is not assumed.The classical problems are considered as possibilities, namely, electrons in the field of plane monochromatic electromagnetic waves (Volkov’s problem) and electrons in the Coulomb field (hydrogen atom). Then ‘‘plane’’ external electromagnetic fields are considered for which some new exact solutions are obtained in terms of special functions. Four new exact solutions of the Dirac equation in the fields with axial cylindrical symmetry are also shown, and lastly one ‘‘free’’ solution with exotic geometry is demonstrated, namely, ‘‘free’’ parabolic cylindrical spinor waves.
Free energy density for continuous systems with and without superstability assumptions
Authors: Gielerak Roman
Published: July 2002

The thermodynamic limit of the free energy density for a large class of continuous, charged systems with stable and sufficiently regular many-body forces is studied. The main effort is placed on demonstrating rigorously that thermodynamic functions do not depend on the typical boundary conditions. Among the results the most important and new ones are the following. (1) For any superstable or superstable in an extended sense and sufficiently regular many-body interactions, the thermodynamic limit of the conditioned free energy density exists and is equal to that corresponding to the free boundary condition case. (2) A new criterion for the nondependence of the limiting free energy density on the typical boundary condition is formulated and proved. This criterion does not require any superstability type of assumptions. Among several applications of the results we list only two: (a) to the case of two-dimensional, neutral Yukawa gas in the monopole phase, which is not even stable according to the standard notion of stability, and (b) the uniqueness of a limiting Gibbs grand canonical state (modulo some technical conjecture) is proved for a class of continuous systems with two-body potentials of positive type.
Time-dependent inverse scattering from gradient-type interfaces using an exact solution
Authors: Kreider K. L.
Published: July 2002

In the context of one-dimensional linear wave propagation, a gradient-type interface is a point at which the velocity profile of a scattering medium suffers a jump in first derivative. In this paper, a time domain approach to scattering from such an interface leads to an integrodifferential equation involving the kernel of the reflection operator (impulse response), which can be solved exactly if the velocity profile is piecewise parabolic. This special case provides the basis for an approximate numerical scheme to solve the inverse scattering problem (recover the velocity profile from reflection data) for a general velocity profile. The algorithm is fast and affords good results if the velocity profile is nearly parabolic or the interest is in short time only. A detailed error estimate for the approximation is provided.
Conformal transformations and the effective action in the presence of boundaries
Authors: Dowker J. S. , Schofield J. P.
Published: July 2002

The conformal properties of the heat kernel expansion are used to determine the local form of the coefficients in a manifold with boundary. The conformal transformation of the effective action is obtained. A novel derivation of the boundary term in the Gauss–Bonnet–Chern theorem is detailed.
Complete integrability of two-dimensional gravity with dynamical torsion
Authors: Katanaev M. O.
Published: July 2002

The most general Lagrangian for two-dimensional gravity with dynamical torsion is considered. A general solution of the system of nonlinear equations of motion is found. Also found is a global solution of the Cauchy problem.
Shear-free perfect fluids in general relativity II. Aligned, Petrov type III space-times
Authors: Carminati J.
Published: July 2002

Petrov type III, shear-free, perfect fluid solutions of the Einstein field equations, with a barotropic equation of state p=p(w) satisfying w+p≢0, are investigated. It is shown that if the acceleration of the fluid is orthogonal to the two-spaces spanned by the repeated principal null direction of the Weyl tensor and the fluid four-velocity, or if the fluid four-velocity lies in the two-spaces spanned by the principal null directions of the Weyl tensor, then the fluid’s volume expansion is zero.