bluuebunny/crossref_metadata_2025 huggingface dataset:
Influence of the chromophore ionization potential on speed and magnitude of photorefractive effects in poly(N-vinylcarbazole) based polymer composites
Authors: Van Steenwinckel David , Hendrickx Eric , Persoons André , Van den Broeck Kurt , Samyn Celest
Published: July 2002

We report on the synthesis of three highly polar chromophores and their use as dopants in poly(N-vinylcarbazole) based photorefractive polymer composites sensitized with (2,4,7-trinitro-9-fluorenylidene)malononitrile. Small alterations in the amino donor group substituents were used to tune the dye’s ionization potential (IP) by 0.2 eV. At 780 nm, 5 °C above the glass transition temperature (Tg), and with an applied field of 59 V/μm, we observed complete internal diffraction and a gain coefficient of 167 cm−1. In this temperature range, diffraction efficiency, gain coefficient, and photorefractive phase shift were found to correlate with the chromophore IP. At 20 °C below Tg, the contribution from birefringence to the index modulation is insignificant, and the speed of the photorefractive effect correlates well with the chromophore IP. Analysis of the results suggests that the space–charge field is influenced by the chromophore IP.
Kinetic energy release in electron-induced decay reactions of molecular ions: C3H8+ and C3H7+
Authors: Matt S. , Echt O. , Stamatovic A. , Märk T. D.
Published: July 2002

We have measured the kinetic energy release (KER) distributions for electron-induced dissociation of mass-selected molecular parent and fragment ions of propane. They are compared with distributions determined for spontaneous (metastable) dissociation. The average KER for induced dissociation of C3H8+ into C3H7+ is 13.2±1.2 meV, about 42% larger than for the spontaneous reaction. This large difference is attributed to the dramatically reduced time at which the induced reaction can be sampled. In contrast, the KER for dissociation of C3H7+ into C3H5+, which is characterized by a large reverse activation energy, is hardly affected by the experimental time scale.
Simple model potential and model wave functions for (H–alkali)+ and (alkali–alkali)+ ions
Authors: Patil S. H. , Tang K. T.
Published: July 2002

A simple model potential is proposed to describe the interaction of a valence electron with the alkali core, which incorporates the correct asymptotic behavior in terms of dipolar polarizabilities, and the short-range exchange effects in terms of a hard core adjusted to give the correct energy for the valence electron. Based on this potential, simple wave functions are developed to describe the (H–alkali)+ and (alkali–alkali)+ ions. These wave functions exhibit some important structures of the ions, and provide a universal description of the properties of all (H–alkali)+ and (alkali–alkali)+ ions, in particular, the equilibrium separations of the nuclei and the corresponding dissociation energies. They also allow us to calculate the dipolar polarizabilities of Li2+, Na2+, K2+, Rb2+, and Cs2+.
Phase stability of solid clusters
Authors: Berry R. S. , Smirnov B. M.
Published: July 2002

A solid cluster of 923 atoms bound by pairwise Morse interactions is the model for analyzing thermodynamic properties and phase equilibria in moderately small systems. The range of the potential is chosen so that the free energies of the icosahedral and face-centered cubic (fcc) structures are similar, enough so to allow a phase change between them. Statistical parameters of the cluster are determined for the two structures from their configurational entropies and pair interaction energies. The heat capacity and entropy of this cluster are calculated for conditions in the region of the phase change between the two solid forms, as well as away from this region. The configurational contribution to the thermodynamic properties is small relative to the vibrational contribution, but dominates the differences between free energies of the two phases. The configurational contributions to the thermodynamic properties become relatively more important for liquid clusters.
Reflectance anisotropy spectroscopy of oriented films of semiconducting polymers
Authors: Miller E. K. , Hingerl K. , Brabec C. J. , Heeger A. J. , Sariciftci N. S.
Published: July 2002

We present reflectance anisotropy spectroscopy (RAS) data for aligned films of luminescent conjugated polymers. Ultrathin films (5–10 nm) spin-cast onto friction-deposited poly-tetrafluoroethylene (PTFE) show birefringence and dichroism indicating alignment of the polymer chains with the PTFE axis. The observed dichroism agrees very well with recently published polarized ultraviolet absorption spectra. In particular, the spectrum of a derivative of poly (para-phenylene) shows the onset of a perpendicular-polarized absorption feature at 5 eV, consistent with recent theoretical predictions. Thick films, prepared by gel-processing in polyethylene (PE), also show characteristic optical anisotropy, and the RAS results are interpreted in terms of the ellipsometric functions, Ψ and Δ.
Surface self-diffusion of hydrogen on Cu(100): A quantum kinetic equation approach
Authors: Pouthier V. , Light J. C.
Published: July 2002

The self-diffusion of hydrogen on the (100) copper surface is investigated using a quantum kinetic equation approach. The dynamics of the adatom is described with a multiple-band model and the surface phonons represent the thermal bath responsible for the diffusion mechanism. Using the Wigner distribution formalism, the diffusive motion of the adatom is characterized in terms of the correlation functions of the adatom–phonon interaction. The diffusion coefficient exhibits two terms related to phonon mediated tunneling (incoherent part) and to dephasing limited coherent motion (coherent part). The competition between these two contributions induced a transition from a thermally activated regime to an almost temperature independent regime at a crossover temperature T*. A numerical analysis is performed using a well-established semiempirical potential to describe the adatom–surface interaction and a slab calculation to characterize the surface phonons. These calculations show that two-phonon processes represent the relevant contribution involved in the adatom–phonon coupling. The temperature dependence of the diffusion constant is thus presented and the relative contribution of the incoherent versus the coherent part is analyzed. Both contributions exhibit a change of behavior around 100 K from an exponential to a power law temperature dependence as the temperature decreases. This change is due to the confinement of the motion of the adatom in the ground energy band at low temperature. The incoherent part is shown to be the dominant contribution at high temperature and is characterized by an activation energy and a prefactor equal to ΔE=0.49±0.01 eV and D0≈2.44×10−3 cm2/s, respectively. At low temperature, the power law dependence of the two contributions is different since the coherent part increases slowly as the temperature decreases whereas the incoherent part decreases. The crossover temperature is estimated to be equal to T*=125 K. Below T*, the coherent part becomes the main contribution and the diffusion constant exhibits an almost temperature independent behavior.
Ionization energies of hyperlithiated and electronically segregated isomers of Lin(OH)n−1 (n=2–5) clusters
Authors: Tanaka Hiromasa , Yokoyama Keiichi , Kudo Hiroshi
Published: July 2002

Density functional theory (DFT) calculations at the Becke three parameter hybrid functional with the Lee–Yang–Parr nonlocal correlation functional (B3LYP)/6-311+G(d,p) level are performed to study the stability and structures of lithium-excess lithium hydroxide clusters Lin(OH)n−1 (n=2–5). These small clusters are stable toward the dissociation to liberate one lithium atom and each of the clusters has structural isomers differing in the stability. The result of calculations implies that the most stable isomer of the clusters with n=2 and 3 have a “hyperlithiated” electronic structure, in which the excess electron fully delocalizes over all of the lithium atoms in the cluster, while the most stable isomer of the clusters with n=4 and 5 in which the excess electron localizes on a specific site has a “segregated” electronic structure composed of the metallic and ionic parts. Vertical ionization energies of the isomers of these clusters calculated by ab initio MO theory at the coupled cluster singles and doubles calculation including a perturbational estimate of the triples excitations [CCSD(T)] and second-order perturbation theory Mo/ller–Plesset (MP2)/6-311+G(d,p) levels depend on the structure; e.g., around 5 eV for the planar isomers, approximately 4.2 eV for the “Li-tail” isomers with one terminal lithium atom, and 3.5 eV or less for the other isomers. The structure dependence of ionization energies reflects a feature of the singly occupied molecular orbital (SOMO) which accommodates the excess electron.
H
1
nuclear magnetic resonance spin-lattice relaxation, C13 magic-angle-spinning nuclear magnetic resonance spectroscopy, differential scanning calorimetry, and x-ray diffraction of two polymorphs of 2,6-di-tert-butylnaphthalene
Authors: Beckmann Peter A. , Burbank Kendra S. , Clemo Katharine M. , Slonaker Erin N. , Averill Kristin , Dybowski Cecil , Figueroa Joshua S. , Glatfelter Alicia , Koch Stephanie , Liable-Sands Louise M. , Rheingold Arnold L.
Published: July 2002

Polymorphism, the presence of structurally distinct solid phases of the same chemical species, affords a unique opportunity to evaluate the structural consequences of intermolecular forces. The study of two polymorphs of 2,6-di-tert-butylnaphthalene by single-crystal x-ray diffraction, differential scanning calorimetry (DSC), C13 magic-angle-spinning (MAS) nuclear magnetic resonance (NMR) spectroscopy, and H1 NMR spin-lattice relaxation provides a picture of the differences in structure and dynamics in these materials. The subtle differences in structure, observed with x-ray diffraction and chemical shifts, strikingly affect the dynamics, as reflected in the relaxation measurements. We analyze the dynamics in terms of both discrete sums and continuous distributions of Poisson processes.
n
-Pentanol–helium homogeneous nucleation rates
Authors: Anisimov Michael P. , Hopke Philip K. , Shandakov Sergey D. , Shvets Igor I.
Published: July 2002

An international collaboration to examine the effects of different experimental systems on nucleation measurements has resulted in a series of nucleation experiments on the n-pentanol–helium system. In particular, using a laminar flow diffusion chamber, nucleation rate data were obtained for temperatures between 258 and 266 K and total pressures of 0.10, 0.20, and 0.30 MPa. These results are compared with other data on nucleation measured experimentally using an expansion wave tube, a two-piston expansion chamber, a flow diffusion chamber, and a static diffusion chamber. The influence of the carrier gas pressure on nucleation rates was explored. It was concluded that the critical embryo phase transitions should be detectable in an analogous manner to the recently reported phase transitions in the glycerin–carbon dioxide system. The experimental detection of the melting point is suggested as a critical test for the ability of an experimental system to provide adequate measurements of nucleation rates. For example, the glycerin melting point can be used for these tests. A reference equation for nucleation rates of n-pentanol–helium is proposed as a practical test of any experimental measurement system for total pressures of 0.10, 0.20, and 0.30 MPa. The use of this equation is recommended even if the reference equation is not completely accurate, because it provides a scale for comparison of the results for different research groups and methods.
Application of semirigid vibrating rotor target model to reaction of H+CH4→CH3+H2
Authors: Wang M. L. , Li Yimin , Zhang J. Z. H. , Zhang Dong H.
Published: July 2002

The SVRT (semirigid vibrating rotor target) model is applied to study the reaction of H+CH4→CH3+H2 using time-dependent wave packet (TDWP) method. Applying the basic SVRT model, reliable quantum dynamics calculation for any atom–polyatom reaction can be carried out in four mathematical dimensions (4D) only. In the current study, reaction probability, cross-section, and rate constant are calculated for the title reaction from the ground state of the reagent. The energy dependence of the calculated reaction probability shows oscillatory structures, similar to those observed in the H+H2 reaction. Those structures are generally associated with broad dynamical resonances and are washed out in the energy dependence of integral cross-sections due to summation over partial waves. Our calculated rate constant is in good agreement with experimental measurement. The present results demonstrate that the SVRT model for atom–polyatomic reaction provides a practical and accurate approach for studying chemical reactions involving polyatomic molecules.
Relations between Rydberg-valence interactions in the O2 molecule
Authors: Lewis B. R. , Gibson S. T. , Banerjee S. S. , Lefebvre-Brion H.
Published: July 2002

Using a single-configuration formulation, analytical expressions are derived for the (X 2Πg) nsσg, npπu, and npσu Rydberg-valence interaction matrix elements in O2. In addition, new results from diabatic, coupled-channel deperturbations of experimental data dependent on these interactions are reported for n=3 and 4. Using these results, the large differences in magnitude between the Rydberg-valence couplings for the constituent states of the npπu Rydberg complex that are predicted by the analytical expressions are verified experimentally. Effective values for several two-electron integrals are obtained semiempirically through comparison between analytical expressions and deperturbed experimental values for the Rydberg-state energies and Rydberg-valence couplings, allowing predictions to be made for the spectroscopy of the npπu 1Σu− Rydberg states which have yet to be observed.
Response to “Comment on ‘Four-component relativistic density functional calculations of heavy diatomic molecules’ ” [J. Chem. Phys. 113, 2506 (2000)]
Authors: Varga S. , Fricke B. , Nakamatsu H. , Mukoyama T. , Anton J. , Geschke D. , Heitmann A. , Engel E. , Baştuğ T.
Published: July 2002

We reply to the comment on our paper “Four-component relativistic density functional calculations of heavy diatomic molecules” [J. Chem. Phys. 112, 3499 (2000)] in which the values of our calculated spectroscopic constants for heavy diatomic molecules were reinvestigated. We point out that the improved spectroscopic constants presented by Liu and van Wüllen confirm our basic conclusion that the generalized gradient approximations tend to overcorrect errors of the bond lengths calculated by the local density approximation for molecules with heavy constituents.
On U(1)-gauge fields and their geometrical interpretation
Authors: Beckers J. , Hussin V.
Published: July 2002

The Harnad–Shnider–Vinet study of symmetry properties on gauge fields in terms of invariant connections on principal fiber bundles is reviewed in the simple U(1)-gauge theory. It is extended to the case of invariant electromagnetic fields admitting nontrivial extensions of their symmetry groups. Some specific examples are discussed.
A vector model for electroweak interactions
Authors: Reifler Frank
Published: July 2002

In this paper we present a vector model for the electroweak interactions. The Cartan map gives an isomorphism between Dirac bispinors and an isotropic class of Yang–Mills vector fields. The isotropic Yang–Mills vector fields Fk =Ek +iHk with k=1,2,3, satisfy the condition that the matrix of scalar invariants (Fj ⋅Fk) equals a scalar multiple of the identity matrix. We show that all the bispinor observables commute with the Cartan isomorphism, including all gauge transformations, as well as Lorentz transformations. We derive the Yang–Mills equivalent Dirac equation. As a consequence of the vector model, we obtain a new Lagrangian for electroweak interactions, which is an alternative to the Weinberg–Salam Lagrangian. Moreover, we show that the vector model predicts that the Weinberg angle θw satisfies sin2 θw =0.25, which is close to the measured value of sin2 θw =0.23. The vector model accommodates all the lepton and quark flavors. Furthermore, it predicts the conservation of baryon number and lepton number, as well as electric charge in electroweak interactions. The vector model also gives a new interpretation to antiparticles. In the vector model, an antiparticle is characterized by its opposite baryon number, lepton number, and electric charge; yet both particles and antiparticles propagate forward in time with positive energies.
The structures of generalized noncommutative Toda lattices
Authors: Kupershmidt B. A.
Published: July 2002

Non-Abelian Toda lattices with a finite number of ‘‘above-diagonal’’ variables are related to appropriate Lie algebras of operators and a certain two-cocycle.
Spectral sum rule for time delay in R2
Authors: Osborn T. A. , Sinha K. B. , Bollé D. , Danneels C.
Published: July 2002

A local spectral sum rule for nonrelativistic scattering in two dimensions is derived for the potential class v∈L4/3 (R2). The sum rule relates the integral over all scattering energies of the trace of the time-delay operator for a finite region Σ⊆R2 to the contributions in Σ of the pure point and singularly continuous spectra.
Equivalence of a magnetohydrodynamic fluid and a viscous fluid with heat flux
Authors: Maiti S. R. , Das S. N.
Published: July 2002

In this paper the equivalence between a perfect fluid with electromagnetic field and a viscous fluid with heat flux is considered. Heat flux, shear tensor, and other fluid parameters are readily calculated out of the magnetohydrodynamic fluid parameters.
On the existence of global integral forms on supermanifolds
Authors: Rogers Alice
Published: July 2002

It is shown that the Berezin approach to integration on supermanifolds can be applied to cases where the supermanifold is a twisted extension of a real manifold. This is done by showing that supermanifolds admit a subatlas of coordinate charts with transition functions of a quite restricted kind.
Vacuum states and superselection rules in quantum field theory
Authors: Borek R.
Published: July 2002

Let (A(O),54,α) be a theory of local observables and let A denote the C*-algebra of quasilocal observables. Assume that every representation of A which satisfies the spectrum condition is type I. Then if (π,H) is an irreducible representation of A which satisfies the spectrum condition there exists a unique vacuum state asociated with (π,H) by large spacelike translations.
Tensor product of quantum logics
Authors: Pulmannová Sylvia
Published: July 2002

A quantum logic is the couple (L,M) where L is an orthomodular σ-lattice and M is a strong set of states on L. The Jauch–Piron property in the σ-form is also supposed for any state of M. A ‘‘tensor product’’ of quantum logics is defined. This definition is compared with the definition of a free orthodistributive product of orthomodular σ-lattices. The existence and uniqueness of the tensor product in special cases of Hilbert space quantum logics and one quantum and one classical logic are studied.
A general approach to the systematic derivation of SO(3) shift operator relations. I. Theory
Authors: De Meyer H. , Vanden Berghe G.
Published: July 2002

A new technique is established for the construction of relations between products consisting of two, three, or more SO(3) shift operators, within the framework of the Lie algebras of SO(3) tensor operators constructed out of an underlying single-boson structure.
Convergent expansions for excited glueball masses in 2+1 strongly coupled lattice gauge theories
Authors: O’Carroll Michael
Published: July 2002

It is known that the mass spectrum of a strongly coupled (β=2/g2 small) 2+1 Wilson action lattice gauge theory contains a mass m0∼−4 ln β and two excited masses m1, m2∼−6 ln β and that m0+4 ln β has a convergent expansion in powers of β. We show that m1, m2 admit convergent expansions of the form −6 ln β+r(β), where r(β) is analytic at β=0. Furthermore, a finite lattice algorithm is given for determining cn, the nth β=0 Taylor coefficient of r(β). Here, cn only depends on a finite number of β=0 Taylor series coefficients of the plaquette–plaquette, plaquette–double plaquette, and double plaquette–double plaquette truncated correlation functions at a finite number of points. For the gauge group Z2, by duality, m1, m2 map to bound states of the low-temperature Ising model; a possible relation between an increasing number of bound states and roughening is discussed.
A generalization and refinement of Madivanane’s theorem on general involutional transformations
Authors: Lomont J. S.
Published: July 2002

A result of Madivanane on ‘‘quasianticommuting’’ complex square matrices, which are roots of the identity matrix, is generalized to linear operators on infinite-dimensional complex vector spaces. A constant which appears in the result is shown to be nonzero by giving a simple formula for its absolute value. Also, a simple formula for the constant itself is given, which is valid for some cases.
Splitting methods for time-independent wave propagation in random media
Authors: Evans J. W.
Published: July 2002

Time-independent wave propagation is treated in media where the index of refraction contains a random component, but its mean is invariant with respect to translation in some direction distinguishing the wave propagation. Abstract splitting operators are used to decompose the wave field into forward and backward traveling components satisfying a coupled pair of equations. Mode-coupled equations follow directly from these after implementing a specific representation for the abstract splitting operators. Here we indicate a formal solution to these equations, concentrating on the diffusion regime, where we estimate the forward- and backscattering contributions to the mode specific diffusion coefficients. We consider, in detail, random media with uniform (random atmosphere) and square law (stochastic lense) mean refractive indices.
Invariant decomposition of the retarded electromagnetic field
Authors: Graells J. , Martín C. , Codina J. M.
Published: July 2002

The integral representation of the electromagnetic two-form, defined on Minkowski space-time, is studied from a new point of view. The aim of the paper is to obtain an invariant criteria in order to define the radiative field. This criteria generalizes the well-known structureless charge case. We begin with the curvature two-form, because its field equations incorporate the motion of the sources. The gauge theory methods (connection one-forms) are not suited because their field equations do not incorporate the motion of the sources. We obtain an integral solution of the Maxwell equations in the case of a flow of charges in irrotational motion. This solution induces us to propose a new method of solving the problem of the nature of the retarded radiative field. This method is based on a projection tensor operator which, being local, is suited to being implemented on general relativity. We propose the field equations for the pair {electromagnetic field, projection tensor}. These field equations are an algebraic differential first-order system of one-forms, which verifies automatically the integrability conditions.
The harmonic mapping character of Rosen’s bimetric theory of gravity and the geometry of its harmonic mapping space
Authors: Stoeger W. R. , Whitman A. P. , Knill R. J.
Published: July 2002

After showing that Rosen’s bimetric theory of gravity is a harmonic map, the geometry of the ten-dimensional harmonic mapping space (HMS), and of its nine-dimensional symmetric submanifolds, which are the leaves of the codimension one foliation of the HMS, is detailed. Both structures are global affinely symmetric spaces. For each, the metric, connections, and Riemann, Ricci, and scalar curvatures are given. The Killing vectors in each case are also worked out and related to the ‘‘conserved quantities’’ naturally associated with the harmonic mapping character of the theory. The structure of the Rosen HMS is very much like that determined by the DeWitt metric on the six-dimensional Wheeler superspace of all positive definite three-dimensional metrics. It is clear that a slight modification of the Rosen HMS metric will yield the corresponding metric on the space of all four-dimensional metrics of Lorentz signature. Finally, interesting avenues of further research are indicated, particularly with respect to the structure and comparison of Lagrangian-based gravitational theories which are similar to Einstein’s general relativity.
On Utiyama’s invariant theoretical interpretation of interaction
Authors: Grassini Renato
Published: July 2002

An invariant theoretical interpretation of the geometry of interacting particle and gauge fields is pursued. To this end a critical investigation on Utiyama’s interaction theory, both in coordinate and geometrical formulation, is discussed.
Projective corepresentations and invariants of PCT group
Authors: Rudra P.
Published: July 2002

The comultiplicator group and the nonassociated factor systems for the internal symmetry group of parity (P), charge conjugation (C), and time reversal (T) operators have been obtained. It is found that there are 16 nonassociated factor systems for this group. The basic invariants for all irreducible corepresentations for these factor systems have been constructed.
Multispinor symmetries for massless arbitrary spin Fierz–Pauli and Rarita–Schwinger wave equations
Authors: Doughty Noel A. , Collins Graham P.
Published: July 2002

Massless, D( j,0)⊕D(0, j), multispinor fields of arbitrary unmixed spin j are reduced by simple matrix-algebra methods to associated tensors and tensor–spinors. A generalized Majorana condition applied to the multispinors is seen to correspond to reality and Majorana conditions on the associated tensors and tensor–spinors, respectively. The symmetries of the latter are displayed explicitly for arbitrary spin. For spin-1, - (3)/(2) , -2, and - (5)/(2) the free-field gauge-invariant Lagrangian wave equations of Maxwell (spin-1), Rarita–Schwinger (spin- (3)/(2) ), Fierz–Pauli (spin-2), and spin- (5)/(2) are derived directly and in a uniform manner from the simpler equations of the unmixed spin reps strongly suggesting the method is extendable to arbitrary spin. Similar features of massive fields are briefly reviewed.
Asymptotics of the maximum number of repulsive particles on a spherical surface
Authors: Berezin Alexander A.
Published: July 2002

There are N equal particles interacting through a repulsive potential V(r)=A/rβ ( β>0) placed insided the sphere. For  β=1 (Coulomb case) and for all  β<1, the minimum energy configuration will have all N particles on the inner surface of the sphere for any integer N. It is shown that starting from N=13 and for  β>βcrit the minimum energy configuration will have only a fraction of particles on the inner surface while the rest of the particles will hang in the equilibrium inside the volume of the sphere. As far as  β→1+, the maximum number of charges that can be held on the surface has an asymptotic N0∼const/( β−1)2. For const, the gap 6<C<8 was found. The theory may be applicable to, e.g., ‘‘magic numbers’’ in small atomic clusters. Some problems that are not yet solved are listed.
Potential envelopes and the large-N approximation
Authors: Hall Richard L.
Published: July 2002

If E is an eigenvalue of the quantum-mechanical Hamiltonian H= 1/2 Δ+V(r) in N spatial dimensions, then large-N theory, the potential-envelope method, and scale-optimized variational energies all lead to quasiclassical approximations having the same form given by E(α) = minr>0[ 1/2 αr−2+V(r)], where α depends on the quantum numbers and on N. Energy bounds provided by the envelope method allow us to prove that in many cases the large-N results are lower energy estimates. For pure power-law potentials all these energies approach the exact eigenvalue in either of the limits l → ∞ or N → ∞.
Creating and annihilating Lie–Bäcklund transformations of the Federbush model
Authors: Kersten Paul H. M.
Published: July 2002

Using software developed for symbolic integration, infinitesimal symmetries, conserved currents, and first- and second-order Lie–Bäcklund transformations for the Federbush model are established. Moreover four (x,t)-dependent Lie–Bäcklund transformations are constructed leading to infinite hierarchies of Lie–Bäcklund transformations.
The Fourier transform of confining potentials
Authors: Heiss W. D. , Welke G. M.
Published: July 2002

The precise meaning of the Fourier transform of ‖x‖ν is examined. A general expression is given for real positive ν. For odd ν, derivatives of principal value integrals are obtained, while even ν gives rise to derivatives of the delta function.
Action-at-a-distance linear potentials and conformal conservation laws
Authors: Weiss J.
Published: July 2002

As a consequence of invariance under the full conformal group of transformations, 15 proper conserved quantities are derived for the system of two massive particles interacting via classical action-at-a-distance linear potentials that have been found in the preceding paper [J. Weiss, J. Math. Phys. 27, 1015 (1986)] in terms of the step θ function Lagrangian.
Gauge theory of a group of diffeomorphisms. II. The conformal and de Sitter groups
Authors: Lord Eric A.
Published: July 2002

The extension of Hehl’s Poincaré gauge theory to more general groups that include space-time diffeomorphisms is worked out for two particular examples, one corresponding to the action of the conformal group on Minkowski space, and the other to the action of the de Sitter group on de Sitter space, and the effect of these groups on physical fields.
Some problems of spinor and algebraic spinor structures
Authors: Bugajska Krystyna
Published: July 2002

A concrete realization of the Milnor–Lichnerowicz spinor bundle by algebraic spinors is considered in the case when the holonomy group of the Levi-Civita connection is equal to the Crumeyrolle group. Some relationships between the existence of parallel spinor fields on a space-time manifold ℳ and its topological invariants are given.
Some algebras of unbounded operators in an indefinite inner product vector space
Authors: Jakóbczyk Lech
Published: July 2002

A general theory of unbounded representations of *-algebras in the Krein space is formulated. Following the corresponding theory of unbounded representations in the Hilbert space, the connection between states and representations, properties of covariant representations, the notion of irreducibility, and decomposition into irreducible parts are discussed.
Relativistic plasma dispersion functions: Series, integrals, and approximations
Authors: Robinson P. A.
Published: July 2002

A number of results are presented involving the plasma dispersion functions appropriate to waves in weakly relativistic, magnetized, thermal plasmas. These results include generating functions, series, integral forms and interrelations, and several useful approximations.
Geometric space-time perturbation. I. Multiparameter perturbations
Authors: Maia M. D.
Published: July 2002

The standard definition of space-time perturbation is reexamined. It is seen that the noninvariance of the metric under identification gauge transformations is a consequence of the adopted zero signature in the fifth dimension of the space of space-times. An n-parameter extension of that definition is proposed, with a (4+n)-dimensional flat space of space-times with a nonsingular metric. It is shown that in the vicinity of a point in the background space-time there is a geometrically defined family of perturbations, which are solutions of the Einstein–Yang–Mills equations.
Nonperturbative confinement in quantum chromodynamics. IV. Improved treatment of Schoenmaker’s equation
Authors: Atkinson D. , Koopmans M.
Published: July 2002

An improved ansatz for the three-gluon vertex function is treated; and it is shown that the gluon propagator has a double pole at the origin of the p2 plane, as well as a tachyon on the spacelike real axis, at least in this approximation.
On a class of 6j coefficients with one multiplicity index for groups SP(2N), SO(2N), and SO(2N+1)
Authors: Cerkaski Marcin
Published: July 2002

An important class of 6j symbols for the groups SP(2N), SO(2N), and SO(2N+1) with one nontrivial multiplicity index is investigated. An appropriate choice of a basis in the multiplicity space is made and the so-called canonical form for 6j symbols is obtained. Their expressions depending on the roots of an Nth-order equation and explicit expressions for some simple class of representations are obtained.
Mathematical structures for long-range dynamics and symmetry breaking
Authors: Morchio G. , Strocchi F.
Published: July 2002

The algebraic dynamics of systems with long-range (instantaneous) interactions requires an enlargement of the (quasi) local algebra which, in most relevant cases, includes variables at infinity that enter in an essential way in the time evolution of local variables. The mathematical structures emerging for the treatment of long-range dynamics are investigated also in connection with spontaneous symmetry breaking.
The Batalin, Fradkin, and Vilkovisky formalism for higher-order theories
Authors: Browning A. D. , McMullan David
Published: July 2002

The generalized Batalin, Fradkin, and Vilkovisky (BFV) formalism was developed as a method for determining the ghost structure for theories, such as gravity and supergravity, whose Hamiltonian formalism has constraints not related to a Lie algebra action. Previously, the classical dynamical content of the BFV description of Yang–Mills theory was investigated. There it was found that this approach had a homological interpretation, derived from the Lie algebra cohomology of the gauge group, which allowed one to understand the construction in terms of the Dirac approach to constrained systems. In this paper the dynamical consequences of the generalized BFV formalism are investigated. It is found that even though one no longer has a Lie algebra structure associated with the constraints, one can still develop a homology theory that reproduces the Dirac analysis and from which the generalized BFV formalism can be derived. Some of the consequences of this approach are discussed.
Time-dependent canonical formalism of thermally dissipative fields and renormalization scheme
Authors: Hardman I. , Umezawa H. , Yamanaka Y.
Published: July 2002

The canonical formalism of thermally dissipative semifree fields in the time-dependent situation is presented. The use of thermal covariant derivatives simplifies the formulation considerably. With this formalism one can unambiguously obtain the interaction Hamiltonian under any thermal situation which together with the free propagator enables perturbative calculations to be performed. The ‘‘on-shell’’ renormalization condition in the time-dependent case is also discussed. The model of a system with a thermal reservoir illustrates how the present formalism works in time-dependent situations.
General exact solutions of Einstein equations for static perfect fluids with spherical symmetry
Authors: Berger Sonia , Hojman Roberto , Santamarina Jorge
Published: July 2002

The gravitational field equations for a spherical symmetric perfect fluid are completely solved. The general analytical solution obtained depends on an arbitrary function of the radial coordinate. As illustrations of the proposed procedure the exterior and interior Schwarzschild solutions are regained.
Infinite-dimensional Lie algebras acting on the solution space of various σ models
Authors: Jacques Michel , Saint-Aubin Yvan
Published: July 2002

Infinite-dimensional Lie algebras of infinitesimal transformations acting on the solution space of various two-dimensional σ models are investigated. The main tools are (i) Takasaki’s interpretation [Commun. Math. Phys. 94, 35 (1984)] of the solutions of the associated linear system in terms of points in an infinite-dimensional Grassmann manifold and (ii) Mikhaïlov’s reduction procedure [Physica D 3, 73 (1981)] for linear systems. Takasaki’s approach leads, for the σ models with values in a Lie group G, to a set of transformations that has the structure of the loop algebra 𝔤⊗R[t,t−1], where 𝔤 is the Lie algebra of G. (This algebra has already been encountered by Dolan [Phys. Rev. Lett. 47, 1371 (1981)] and by Wu [Nucl. Phys. B 211, 160 (1983)] among others.) The σ models with a Wess–Zumino term are also considered; the algebraic structure is found to be the same. Finally, Mikhaïlov’s procedure is used to study the σ models with values in a Riemannian symmetric space (RSS) G/H which is not a Lie group. The algebra in these cases is a subalgebra of the loop algebra found for the principal models but it does not seem to be graded. However, it contains two graded infinite-dimensional subalgebras with the following structure: if 𝔥 and 𝔪 are the two eigenspaces of the involution σ defining the RSS G/H, these two graded subalgebras are 𝔥⊗R[t] and (⊕i∈N𝔥⊗t2i) ⊕(⊕i∈N𝔪⊗t2i+1).
Chiral symmetry breakdown. II. Ansatz for vertex in ultraviolet
Authors: Atkinson D.
Published: July 2002

An earlier analysis of the Dyson–Schwinger equation for the quark propagator is improved by taking the Slavnov–Taylor identity into account in the ultraviolet. It is found that chiral symmetry breaking occurs above a critical coupling in the Landau gauge; but that this result does not hold in other gauges.
The effect of a one-dimensional potential of finite range on the statistical parameters of an incident ensemble of particles. I. Pure states
Authors: Farina J. E. G.
Published: July 2002

If an ensemble of particles moving parallel to the x axis in the positive direction impinges on a piecewise continuous potential confined to the interval [−a,a] (a>0) it will divide into a transmitted ensemble and a reflected ensemble. It is shown that the classical results for the means, variances, and covariance of position and velocity of the transmitted and reflected ensembles hold in quantum mechanics if the incident state is assumed to be pure and defined by a C∞ wave function whose Fourier transform has bounded, positive support, on which the modulus and argument of the transmission and reflection coefficients are C∞.
Self-energy operator for an electron in an external Coulomb potential. II
Authors: Hostler Levere
Published: July 2002

Relativistic Coulomb Sturmian matrix elements of the operator O≡ln(1−ρ)/ρ, ρ=−[π⋅(1+iσ)⋅π]/m2, in terms of which the self-energy operator for an electron in an external Coulomb potential has been expressed, are studied. The operator O is dealt with on a term by term basis in a Sturmian expansion. Each term of the Sturmian expansion is separated into a part whose matrix elements are analytic functions of Zα, plus a remainder evaluated in closed form by use of the Cauchy residue theorem. All ignorance about the matrix element of the general term in the Sturmian expansion of O is thereby placed entirely in the analytic part, for which an explicit integral representation is derived.
Analytical behavior of the ground-state energy and pinning transitions for a bound polaron
Authors: Löwen H.
Published: July 2002

Spectral properties of a three-dimensional optical polaron, bound in an external potential, are studied. If the associated one-particle Hamiltonian has a bound state, it is proved that the ground-state energy of the polaron and expectation values of the ground state are analytical functions of the coupling parameter α and the potential strength β. Especially in the case of a Coulomb potential, all changes in the polaron state are continuous, disproving claims of several variational calculations. If, on the other hand, the one-particle Hamiltonian has no bound state, the existence of a pinning transition is shown for the polaron. As physically relevant potentials for the pinning transition, a spherical square well and a screened Coulomb potential are considered. Their phase diagrams are given in the effective-mass approximation.
A Grassmann calculus for infinite spin groups
Authors: Palmer John
Published: July 2002

The correlation functions of the two-dimensional Ising model satisfy nonlinear equations both on the lattice (discovered by McCoy and Wu [Nucl. Phys. B 180, 89 (1981)] and Perk [Phys. Lett. A1 79, 3 (1980)]) and in a continuum limit (discovered by Wu, McCoy, Tracy, and Barouch and generalized by Sato, Miwa, and Jimbo [Publ. RIMS 14, 223 (1978)]). In this paper results are presented for infinite spin groups that extend results of Sato, Miwa, and Jimbo [Publ. RIMS 14, 223 (1978)] and lead to normal ordered product formulas for the difference of adjacent Ising spin fields. These product formulas are shown to lead directly to the lattice difference equations for the correlations and are also a key ingredient in the scaling limit analysis.
Conditions for zero not to be an eigenvalue of the Schrödinger operator. II
Authors: Ramm A. G.
Published: July 2002

A condition for zero not to be an eigenvalue of the Shrödinger operator is given.
The solution of the s-wave Bethe–Goldstone equation with a standard hard core potential
Authors: Ong Michael K.
Published: July 2002

This paper extends the results of an earlier article [J. Math. Phys. 27, 1154 (1986)] to include the solution of the s-wave Bethe–Goldstone equation for the interaction of two nucleons characterized by a potential with an infinite repulsive core and a nearby attractive well. The solution again exhibits band-limiting behavior and is obtained in closed form via the prolate spheroidal wave functions. It is shown that the attractive part of the interaction potential perturbs the far-field scattered wave so that healing of the nucleon wave function is achieved only when the attractive part is weak. Finally, asymptotic results for the case of small core radius are also calculated.
The Demazure–Tits subgroup of a simple Lie group
Authors: Michel L. , Patera J. , Sharp R. T.
Published: July 2002

The Demazure–Tits subgroup of a simple Lie group G is the group of invariance of Clebsch–Gordan coefficients tables (assuming an appropriate choice of basis). The structure of the Demazure–Tits subgroups of An, Bn, Cn, Dn, and G2 is described. Orbits of the permutation action of the DT group in any irreducible finite-dimensional representation space of A2, C2, and G2 are decomposed into the sum of irreducible representations of the DT group.
Superalgebras with Grassman-algebra-valued structure constants from superfields
Authors: de Azcárraga José A. , Lukierski Jerzy
Published: July 2002

Generalized Lie algebras and superalgebras with generators and structure constants taking values in a Grassmann algebra are introduced. Such algebraic structures describe the equal time algebras in the superfield formalism. As an example, the equal time commutators and anticommutators among bilinears made out of the D=1 quantum superfields describing the supersymmetric harmonic oscillator are considered.
Comments on the paper ‘‘On the WKBJ approximation’’ [J. Math. Phys. 2
8, 556 (1987)]
Authors: Fröman Nanny , Fröman Per Olof
Published: July 2002

Attention is drawn to the fact that the ‘‘standard form for the generalized WKBJ approximation’’ of El Sawi [J. Math. Phys. 28, 556 (1987)] already had been derived by N. Fröman [Ark. Fys. 32, 541 (1966)].
The 2ω-dimensional light-cone integrals with momentum shift
Authors: Suzuki A. T.
Published: July 2002

A class of light-cone integrals typical to one-loop calculations in the two-component formalism is considered. For the particular cases considered, convergence is verified though the results cannot be expressed as a finite sum of elementary functions.
On a parametrization method for the semiclassical vacuum problem. I
Authors: Castagnino Mario , Laciana Carlos
Published: July 2002

A formalism to study the semiclassical vacuum problem is introduced. Using this formalism we try to satisfy two competitive natural hypotheses: H1, the vacuum definition must assure the absorption of the infinities, coming from the vacuum expectation value of the energy-momentum tensor of the matter fields, in the bare constants of the gravitational classic action; H2, the vacuum must be the ground state. It is proved that the system of equations yielded by these two hypotheses is, in general, incompatible. With this formalism, the vacuum problem in curved space-time is stated. It is hoped that this formalism could eventually be used to solve the problem.
Spinors in periodic self-dual gauge field backgrounds
Authors: Chakrabarti A.
Published: July 2002

Normalizable zero modes of the Dirac operator are constructed for a class of self-dual, periodic SU(2) gauge field backgrounds characterized by two independent integer invariants. The integers are (ST/8π2), where ST is the action over one period T, and the asymptotic winding number (q) in R3, the solutions reducing to static ‘‘monopoles’’ for large spatial distances independently of the time. The spinor solutions are obtained for the simplest class of the hierarchy presented in Chakrabarti [Phys. Rev. D 35, 696 (1987)], corresponding to q=1 and ST=8π2⋅2n (n=1,2,3,...). The full number of zero modes for such backgrounds is ((ST/8π2)−q)=(2n−1). They are all constructed explicitly. It is shown how these results can be obtained through a simple scaling limit by starting with special classes of instantons with finite action over R4. A derivation of ST is also given.
Classification of the space-times admitting a constant curvature synchronization
Authors: Bona C. , Coll B.
Published: July 2002

A constant curvature synchronization is a foliation of the space-time by spacelike hypersurfaces which are spaces of constant curvature for the induced metric. The classification of the space-times admitting such a synchronization is given according to the dimension and structure of all the isometry groups that can act with orbits tangent to it.
Infinite-dimensional homogeneous manifolds with translational symmetry and nonlinear partial differential equations
Authors: Szmigielski J.
Published: July 2002

A construction relating scale invariant, nonlinear partial differential equations and the orbits of the group of translations on infinite-dimensional homogeneous manifolds is proposed. It presupposes that the homogeneous manifold M has translations and scale transformations among its automorphisms. This assumption is made to ensure that the set of orbits of the group of translations is invariant under scale transformations. What is important is that the proposed construction provides a way of inducing scale covariance of derived nonlinear equations for which the set of orbits can be identified with a set of solutions of these equations. Application to the derivation of the potential KdV and the sine–Gordon equation yields as an important intermediate result the construction of their respective Lax pairs out of the commuting vectors tangent to the orbits. In yet another application, an infinite-dimensional, scale-invariant Riccati equation is derived. The latter is known to be related to the potential KP equation. The orbit leading to the Riccati equation is then computed in different charts. The transition functions between charts are shown to generate the nonlinear term in the potential KP equation. Also, the relation to the Zakharov–Shabat dressing method is briefly discussed.
Invariant conformal vectors in space-times admitting a group of G3 of motions acting on spacelike orbits S2
Authors: Bona C.
Published: July 2002

The paper deals with four-dimensional space-times admitting locally a three-dimensional group of motions G3 acting on two-dimensional spacelike orbits S2. The local existence problem for conformal vectors invariant under G3 is shown to be equivalent to the local existence problem for Killing vectors of a given two-dimensional pseudo-Riemannian metric g. This problem is explicitly solved in terms of the Gaussian curvature R of g and two of its scalar differential concomitants. The results are applied to the case of dust-filled space-times, where an exhaustive list of metrics has been obtained by using the algebraic computing language smp. The metrics are either homogeneous, self-similar, or Friedmann models.