bluuebunny/crossref_metadata_2025 huggingface dataset:
Study of tin- and tin cluster–cyano complexes using anion photoelectron spectroscopy and density functional calculations
Authors: Moravec Vicki D. , Jarrold Caroline Chick
Published: July 2002

The photoelectron spectra of SnCN−, SnCH2CN−, Sn(CN)2−, Sn(CN)(CH2CN)−, Sn2CN−, Sn2CH2CN−, Sn3CN−, Sn3CH2CN−, and Sn4CN− have been obtained and analyzed, and density functional calculations (B3LYP/LANL2DZ and B3LYP/LANL2MB) have been performed on the SnCN, Sn(CN)2, Sn2CN, and Sn3CN anions and neutrals. From the spectra of the singly ligated complexes, the ground and low-lying excited neutral states are inferred to be predominantly ionic (Snx+CN− or Snx+CH2CN−). These states are accessed by detaching an electron from what is nominally a neutral tin atomic or tin cluster orbital in the anionic complex (SnxCN− or SnxCH2CN−). In all cases, the SnxCN− and SnxCH2CN− spectra show similar electronic structure, though in the case of the latter, electronic structure is more vibrationally congested and shifted to lower binding energy. The spectra of SnCN−, Sn(CN)2−, and Sn(CN)(CH2CN)− exhibit a nearly 400 cm−1 vibrational spacing. SnCN/SnCN− and Sn(CN)2/Sn(CN)2− are linear and planar, respectively. The spectra of SnCN− and SnCH2CN− show an approximately 0.3 eV spin-orbit splitting. The spectrum of Sn2CN− shows transitions to two neutral electronic states; the excited state band exhibits a short, partially resolved 190(50) cm−1 vibrational progression. Analysis of the spectrum of Sn2CN− and density functional theory (DFT) calculations suggest planar structures for the anion and two neutral states. The spectra of Sn3CN−, Sn3CH2CN−, and Sn4CN− show multiple, vibrationally congested electronic bands. The electronic structures of all the complexes are described qualitatively in the ionic limit.
Seeded amplification of amplified spontaneous emission in NO
Authors: Ogi Yoshihiro , Sakoda Aya , Tsukiyama Koichi
Published: July 2002

Two techniques are presented for control of cascade-type amplified spontaneous emission (ASE) pathways in the NO Rydberg states. The first method, referred to as switching, is based on destruction of the population inversion required for amplification. When one of the two competing ASE decay paths is prohibited by prepopulating the corresponding lower level, a part of the population in the upper level flows down through the other ASE decay path, resulting in the enhancement of this ASE transition. The second method, called seeding, utilizes the injection of external field. The weak ASE radiation generated in a seeder cell travels collinearly with pump beams, acting as seeder light for the inverted medium in a main cell. By extracting desired seeder wavelengths with optical filtering, amplification of the selected electronic transition is realized. In addition, selective enhancement between the rotational transitions belonging to the same inter-Rydberg system is achieved by taking advantage of their different polarization properties. Finally, the combined use of switching and seeding, also providing rotational selectivity, is described.
On the control of the production of hydrogen atom 2s–2p resonance hybrids through the use of competitive one- and two-photon transitions from the ground state
Authors: Jagatap B. N. , Meath William J.
Published: July 2002

The control of the formation of dipolar hydrogen atom 2s–2p hybrid states, through varying the relative phase δ of two lasers inducing simultaneous one- and two-photon transitions from the ground state, is discussed by using time-dependent perturbation theory. Numerical examples are presented that illustrate how the populations of the hybrid states can be controlled by varying δ. The perturbative calculations are augmented by various exact finite basis set, and full split operator/fast Fourier transform, solutions to the time-dependent wave equation for the problem.
The spectral forms of transient ESR spectra of radical pairs and the origin of the antiphase structure
Authors: Neufeld A. A. , Pedersen J. Boiden
Published: July 2002

We show that transient electron spin resonance (ESR) spectra of short lived radical pairs can be written formally as a superposition of Lorentzian-like lines and the corresponding dispersive lines. The coefficients to these spectral components depend strongly on the frequency and amplitude of the microwave (mw) field and consequently a variety of spectral forms may result. The coefficients, and thus the spectral form, are determined by the interradical interaction induced rate of change of the longitudinal and transversal electron spin polarization. The longitudinal polarization is responsible for the well known chemically induced dynamic electron polarization (CIDEP) which changes the intensity of the lines without affecting the line shape. The transversal polarization is shown to be responsible for the antiphase structure (APS) in accordance with our previous proposition [J. Chem. Phys. 109, 8743 (1998)]. A simple one re-encounter model calculation illustrates and explains qualitatively most of the observed APS characteristics. Numerical calculations are used to discuss anomalously large APS splitting.
Absolute cross section for the formation of Si(1S) atoms following electron impact dissociation of SiH4
Authors: Abramzon N. , Martus K. E. , Becker K.
Published: July 2002

A combination of electron scattering and laser-induced fluorescence (LIF) techniques was used in the experimental determination of the absolute cross section for the formation of Si(1S) ground-state atoms following the neutral molecular dissociation of SiH4 by electron impact for energies from 20 eV to 100 eV. Electron impact on SiH4 produces—among other species—Si(1S) ground-state atoms which are detected by pumping the Si(3p)2 1S→(3p)(4s)1P transition at 390 nm with a tunable dye laser and recording the subsequent Si(3p)(4s)1P→(3p)2 1D fluorescence at 288 nm. We found a peak cross section for the formation of Si(1S) atoms from SiH4 of 4.5×10−17 cm2 at an impact energy of 60 eV. When compared to the previously determined total SiH4 neutral dissociation cross section obtained from measurements in a constant-flow plasma reactor [Perrin et al., Chem. Phys. 73, 383 (1982)], we find a branching ratio of about 0.037 for the formation of Si(1S) atoms in the electron-impact induced neutral dissociation of SiH4. The absolute calibration of our measured dissociation cross section was made relative to the cross section for the formation of N2+(X) ground-state ions produced by electron impact on N2 which was previously measured in the same apparatus using the same experimental technique. This cross section is known to within ±10% and can serve as a benchmark for the calibration of neutral dissociation cross sections as discussed previously [Abramzon et al., J. Phys. B 32, L247 (1999)]. © 2000 American Institute of Physics.
The Fock wave function as classified by the supergroup chain U(N/M)⊃OSp(N/M)⊃O(N)×Sp(M)
Authors: Han Qi-Zhi , Sun Hong-Zhou , Zhang Mei , Feng Da Hsuan
Published: July 2002

The wave functions for bosons and fermions, classified according to the supergroup chain U(N/M)⊃OSp(N/M)⊃O(N)×Sp(M)⊃⋅ ⋅ ⋅, are given in this paper. The method presented here adheres closely to the standard raising and lowering method commonly used in quantum mechanics. When the so-called star representation [n} is decomposed into the irreducible representation of the OSp(N/M), one obtains a reducible, but not completely reducible, representation of the OSp(N/M). This decomposition is quite different from a regular Lie group chain and has very interesting physical implications.
Superunitary reduction of the orthosymplectic supertableaux
Authors: Gourdin Michel
Published: July 2002

The supertableaux of the orthosymplectic groups OSP(2ν‖2p) and OSP(2ν+1‖2p) are decomposed in sums of supertableaux of the superunitary group SU(ν‖p).
Logarithmic corrections to the uncertainty principle and infinitude of the number of bound states of N-particle systems
Authors: Perez J. Fernando , Coutinho F. A. B. , Malta C. P.
Published: July 2002

It is shown that critical long-distance behavior for a two-body potential, defining the finiteness or infinitude of the number of negative eigenvalues of Schrödinger operators in ν dimensions, is given by vk(r)=−((ν−2)/2r)2−1/(2r ln r)2 +⋅⋅⋅−1/(2r ln r⋅ln ln r ⋅⋅⋅ ln(k)r)2, where k=0,1,... for ν≠2 and k=1,2,... if ν=2. This result is a consequence of logarithmic corrections to an inequality known as the uncertainty principle. If the continuum threshold in the N-body problem is defined by a two-cluster breakup the results presented generate corrections to the existing sufficient conditions for the existence of infinitely many bound states.
Prolongation structures and Lie algebra real forms
Authors: Radford Chris
Published: July 2002

A technique useful as an aid for finding finite-dimensional representations of a Wahlquist–Estabrook prolongation algebra is introduced. The technique is illustrated with an examination of equations of the form ∂2za/∂x1 ∂x2=fa(zb).
Dimensional reduction of invariant linear connections and tensor fields on multidimensional space-time
Authors: Nikolova Lora , Rizov V. A.
Published: July 2002

Let the compact Lie group G act smoothly on the C∞ manifold S with a single orbit type G/H, where H is a closed subgroup of G, and let N(H)/H be a Lie group [N(H) denotes the normalizer of H in G]. Assuming a given connection in the fiber bundle S → M, where M=S/G is the orbit space (to be identified with the physical space-time) and N(H)/H is the structure (gauge) group, the G-invariant tensor fields and linear connections on S are analyzed. A kind of ‘‘dimensional reduction’’ for these objects is established: every field corresponds uniquely to a field on M, and the linear connection defines uniquely a set of fields and a linear connection on M.
Particlelike solutions to nonlinear classical real scalar field theories
Authors: Okolowski J. A. , Slomiana M.
Published: July 2002

A classical Lorentz-covariant nonlinear model scalar field theory, which admits an exact, closed-form, spatially localized, nonsingular solution, is considered. This solution corresponds to a dynamically unstable extended ‘‘particle’’ of finite positive ‘‘rest mass.’’ An approximate two-particle solution is constructed, and the associated effective two-particle Lagrangian is derived by means of a Rayleigh–Ritz procedure.
Duality and orthogonal transitivity in dimensional reduction
Authors: Carter Brandon
Published: July 2002

Conditions under which a symmetry group action can be expected to be orthogonally transitive are investigated within the generalized Kaluza–Klein framework in terms of the dimensional reduction scheme whereby a higher-dimensional space is regarded as a bundle over a lower-dimensional basespace formed as its quotient with respect to the surfaces over which the group action is transitive, so that orthogonal transitivity is interpretable as meaning the existence of a section that is everywhere orthogonal to the fibers. It is shown that if a certain comoving source condition is satisfied locally, then the system admits a dual reformulation whereby trivectors are introduced in place of the usual gauge-potential covectors, and that under these circumstances (but not otherwise) orthogonal transitivity will hold subject to suitable global boundary conditions provided appropriate local signature inequalities are satisfied everywhere, the simplest (but not the only) possibility being that in which both the metric and the relevant coupling matrix are positive definite.
Relativistic Schrödinger equations
Authors: Bel L. , Ruiz E.
Published: July 2002

A representation of the Poincaré group by means of operators acting on the function space of the nonrelativistic quantum mechanics is introduced. The conditions that the Hamiltonian of an interacting particle system must verify in order to define a relativistic invariant Schrödinger equation are found out. The relation with usual quantum constraint theories is also studied.
On generalized coherent states with maximal symmetry for the harmonic oscillator
Authors: Beckers J. , Debergh N.
Published: July 2002

Generalized coherent states for the one-dimensional harmonic oscillator with maximal symmetry, i.e., admitting the semidirect sum so(2,1) ⧠ h(2) as the largest invariance Lie algebra pointed out by Niederer are constructed. The normalization of such states as well as their completeness property are determined and discussed. They are also analyzed in the subcontexts of the so(2,1) algebra and of the Heisenberg h(2) algebra. General considerations on Heisenberg relations, on minimal dispersions, and on quantum mechanical entropies are presented in connection with the uncertainty principle.
On the modification of the Stark states of hydrogen by a weak ac electric field
Authors: Florescu Viorica , Patrascu Suzana
Published: July 2002

A derivation is presented for the compact integral representation that describes the first-order perturbed wavefunction of an electron in a fixed Coulomb field and in a harmonic uniform electric field, for the case of an initial stationary Stark state with the symmetry axis along the electric field.
Dirac quantization of massive spin-one particles in an external symmetrical tensor field
Authors: Darkhosh Teymour
Published: July 2002

Dirac’s method is used to quantize massive spin-one particles interacting with an external symmetric tensor field. It is shown that Dirac equations of motion are identical to Euler–Lagrange equations and that φ0, the 0th component of the unknown field, is the only component that depends on the external field. Furthermore, Dirac commutators of the field and the Lorentz generators are calculated. It is shown that the field components except φ0 transform like components of a free field, and that φ0 transforms like a field component in an external potential.
Embedding of a Demianski cavity with small rotation parameter in a perturbation of a Friedmann universe with cosmological constant
Authors: Aguirregabiria J. M. , Chamorro A. , Etxebarria J. R. , Rivas M.
Published: July 2002

The problem of embedding a Demianski cavity with small rotation parameter in an appropriate rotational perturbation of a pressureless Friedmann universe with a Λ term is considered. The relation between the coordinate change introduced by Schücking [Z. Phys. 137, 595 (1954)] for this kind of problems and that used for the simple model of Oppenheimer and Snyder [Phys. Rev. 56, 455 (1939)] for gravitational collapse is also discussed.
Sectional curvature and tidal accelerations
Authors: Beem John K. , Parker Phillip E.
Published: July 2002

Sectional curvature is related to tidal accelerations for small objects of nonzero rest mass. Generically, the magnification of tidal accelerations due to high speed goes as the square of the magnification of energy. However, some space-times have directions with bounded increases in tidal accelerations for relativistic speeds. These investigations also yield a characterization of null directions that fail to satisfy the generic condition used in singularity theorems. For Ricci flat four-dimensional space-times, tidally nondestructive directions are characterized as repeated principal null directions.
Block-diagonalization in second quantization
Authors: Tarantelli A. , Cederbaum L. S.
Published: July 2002

The unitary matrix that brings a Hermitian H into block-diagonal form can be uniquely determined under very simple and transparent conditions. Int his work the block-diagonalization problem is investigated in the framework of the second quantization formalism. Starting with an operator Ḩ which in any n-particle Fock space has a well-defined matrix representation an attemt was made to answer the question whether the transformation matrices T which can be separately given in the various n-particle spaces can be considered matrix representations of the same operator. T̂. Interestingly, the very important result was reached that the block-diagonalization operator T̂ exists and is unique. As a particular example, attention was concentrated on the case of an operator Ĥ given by a one-particle operator. In this case the block-diagonalization operator can be constructed and given in explicit from. This approach is applied to the theory of Green’s functions where the block-diagonalization of the Hamiltonian has interesting consequences that are illustrated in some details.
Criteria for the Kato smoothness with respect to a dispersive N-body Schrödinger operator
Authors: Derezinski Jan
Published: July 2002

The operators of the form H=ω(D)+∑va(πax), which are a natural generalization of N-body Schrödinger operators, are studied. Certain criteria are presented that allow one to verify if a given pseudodifferential operator is Kato smooth with respect to H.
General exact solution for homogeneous time-dependent self-gravitating perfect fluids
Authors: Gaete Patricio , Hojman Roberto
Published: July 2002

A procedure to obtain the general exact solution of Einstein equations for a self-gravitating spherically symmetric static perfect fluid obeying an arbitrary equation of state is applied to time-dependent Kantowski–Sachs line elements (with spherical, planar, and hyperbolic symmetry). As in the static case, the solution is generated by an arbitrary function of the independent variable and its first derivative. To illustrate the results, the whole family of (plane-symmetric) solutions with a ‘‘gamma-law’’ equation of state is explicitly obtained in terms of simple known functions. It is also shown that, while in the static plane-symmetric line element, every metric is in one to one correspondence with a ‘‘partner metric’’ (both originated from the same generatrix function); in this case every generatrix function uniquely determines one metric.
Modified Zassenhaus formula and Stratonovich stochastic integrals
Authors: Sen Zhao Zu
Published: July 2002

The modified Zassenhaus formula is used instead of the naive Zassenhaus formula to derive the path integral in Gaveau–Schulman’s formulation. This derivation leads to a Stratonovich stochastic integral naturally and straightforwardly.
Quantum field theory of p-forms in curved space-time
Authors: Folacci A.
Published: July 2002

It is developed, in a curved four-dimensional space-time, the quantum field theory of p-forms. In particular, from the Ward–Lichnerowicz identityG(p)a1...ap   b1′... bp′;ap+G(p−1)a1...ap−1    [b1′... bp−1;bp′]=0 it is shown how to treat the complications that appear in the quantum theory of p-forms because of the phenomenon of ghosts for ghosts. In addition, the expression of the renormalized stress-energy tensor associated to a p-form for a Hadamard state in an arbitrary gravitational background is given.
Stochastic quantization of a dissipative dynamical system and its hydrodynamical interpretation
Authors: Hajra K.
Published: July 2002

In the framework of stochastic quantization the quantum theory of an open system is envisaged here. A hydrodynamical model has been suggested for the motion of a quantum particle in the presence of frictional dissipative force. Finally, a comparison is made between quantum conservative and nonconservative systems.
A big-bang cylindrically symmetric radiation universe
Authors: Davidson W.
Published: July 2002

A new nonstationary cylindrically symmetric solution to Einstein’s equations is given for a perfect fluid. The solution has a time singularity (t=0) at which the pressure p and density μ are equal to +∞ throughout the radial coordinate range 0≤r<∞, but for t>0 the model is well behaved. The fluid has the equation of state p= (1)/(3) μ, and for any fixed t>0 both p and μ are finite, decreasing monotonically to zero as r increases through the range 0≤r<∞. At any fixed r (0≤r<∞) both p and μ decrease steadily to zero as t increases through the range 0≤t<∞. The motion is irrotational, with shear, expansion and acceleration while the solution is algebraically general of Petrov type I.
Reasons for a physical field to obey linear partial differential equations
Authors: Audretsch Jürgen , Lämmerzahl Claus
Published: July 2002

Fields showing a deterministic evolution, which is linear and local, can be described by a linear system of partial differential equations.
Singular perturbation theory applied to magnetohydrostatic equilibria: Proof of convergence
Authors: Kopp A. , Schindler K.
Published: July 2002

Magnetohydrostatic equilibria with two relevant length scales are considered. Their ratio Ε is assumed to be small. Regular solutions in the sense of singular perturbation theory are discussed and the magnetic flux function A (2-D case) and Euler potentials α, β (3-D case) are shown that can be expanded into convergent power series in Ε. This ensures further the existence of weakly 2-D and 3-D equilibria within a bounded domain.
Derivation of the Wess–Zumino term for the chiral Schwinger model using Dirac bracket formalism
Authors: Wotzasek C.
Published: July 2002

The Wess–Zumino term, in the context of the anomalous chiral Schwinger model, is derived using the Dirac formulation for constrained system. The guideline of this construction is the iterative transformation of second-class constraints into first-class ones with the addition of appropriated counter terms in the Lagrangian.
Normally ordered Bose–Fermi operator realization of the SU(N/M) group
Authors: Fan Hong-yi , Weng Hai-guang
Published: July 2002

The technique of integration within an ordered product, which is now generalized to the supersymmetric case, together with the boson–fermion coherent states, is used to derive the normally ordered Bose–Fermi operator realization of the group SU(N/M). The mapping of the SU(N/M) fundamental representation in classical complex number–Grassmann number space into the realization in Hilbert space is manifestly shown in our formalism. The corresponding antinormally ordered realization is also discussed.
High-frequency asymptotic solution of the wave equation in an inhomogeneous medium
Authors: Robinson Sam L.
Published: July 2002

An explicit integral representation is obtained in the Ε→0 limit of the solution of the wave equation utt=c(x)2Δu on Rn (n≤3) with initial data of the form u(x,0)=f(x)e𝒾S(x)/Ε. Estimates are given with respect to the energy norm and the representation is valid for any finite time interval. Away from caustics, the integral is asymptotically evaluated and it is found that the solution is determined by time-dependent geometrical optics.
On the geometric quantization of Poisson manifolds
Authors: Vaisman Izu
Published: July 2002

In a paper by Huebschmann [J. Reine Angew. Math. 408, 57 (1990)], the geometric quantization of Poisson manifolds appears as a particular case of the quantization of Poisson algebras. Here, this quantization is presented straightforwardly. The results include a geometric prequantization integrality condition and its discussion in particular cases such as Dirac brackets, an adaptation of the notion of a polarization and a construction of a quantum Hilbert space, and a computational example. In the last section of the paper the general prequantization representations in the sense of Urwin [Adv. Math. 50, 126 (1983)] are described for the Poisson and Jacobi manifolds.
On the structure of absolute steady states in sandpile type of cellular automata: The geometrical aspect
Authors: Chung S. K. , Chau H. F.
Published: July 2002

It is proved that all bounded subsets of ℛn with nonempty interior are cutable. Also found is an if and only if classification of when a nontrivial absolute steady state (ASS) of the sandpile-type cellular automata model will exist. The classification helps one to narrow down the geometrical structure of the ASS and is applicable to both Abelian and non-Abelian models. It is important for the future studies of self-organized criticality.
Why do soliton equations come in hierarchies?
Authors: Yordanov Russi G.
Published: July 2002

In this article, an identity satisfied by the so-called recursion operator is derived. The identity generates by itself an infinite sequence of Lax pairs, thus ensuring the complete integrability of the corresponding hierarchy of nonlinear evolution equations. It is also shown that this identity yields the familiar property that the squares of eigenfunctions of the associated linear spectral problem satisfy the linearized version of the respective soliton equation.
The N=2 super W4 algebra and its associated generalized Korteweg– de Vries hierarchies
Authors: Yung C. M. , Warner Roland C.
Published: July 2002

The N=2 super W4 algebra is constructed as a certain reduction of the second Gel’fand–Dikii bracket on the dual of the Lie superalgebra of N=1 super pseudodifferential operators. The algebra is put in manifestly N=2 supersymmetric form in terms of three N=2 superfields Φi(X), with Φ1 being the N=2 energy momentum tensor and Φ2 and Φ3 being conformal spin 2 and 3 superfields, respectively. A search for integrable hierarchies of the generalized Korteweg-de Vries (KdV) variety with this algebra as Hamiltonian structure gives three solutions, exactly the same number as for the W2 (super KdV) and W3 (super Boussinesq) cases.
On a countable-dimensional subalgebra of the equivalence algebra for equations v
tt=f(x,v
x)v
xx+g(x,v
x)
Authors: Harin A. O.
Published: July 2002

The analysis of the equations vtt=f(x,vx)vxx+g(x,vx) initiated by Ibragimov et al. [J. Math. Phys 32, 2988 (1991)] is continued. The preliminary group classification of these equations with respect to a countable-dimensional subalgebra of their equivalence algebra is presented. This subalgebra is an extension of the 10-dimensional subalgebra considered by Ibragimov et al. The result of the work is a table of nonequivalent equations possessing an additional symmetry.
On the hidden U(1) gauge symmetry in the nonlinear sigma model
Authors: Wotzasek Clovis , Neves Clifford
Published: July 2002

As shown by Kovner and Rosenstein, the O(N) invariant nonlinear sigma model, which in Dirac’s language of constrained systems presents only second-class type of constraints, possess a hidden U(1) gauge symmetry. The presence of this symmetry is investigated, in this work, with the introduction of a Wess–Zumino term that implements Faddeev’s idea of changing second-class constraints into gauge generating first-class constraints. The resulting theory exhibits the embedding of the O(N) invariant model into a gauge theory which presents an enlarged phase-space with the inclusion of a Wess–Zumino field.
Scattering and inverse scattering for a second-order differential equation
Authors: Aktosun Tuncay
Published: July 2002

The scattering and three inverse scattering problems for (d/dx)[a(x)(dψ/dx)] +k2h(x)ψ=Q(x)ψ on the real axis are considered herein. In the first inverse scattering problem, Q(x) is recovered when a(x), h(x), and the scattering data are given. In the second inverse problem h(x) is recovered when a(x), Q(x), and the scattering data are known. In the third inverse problem, in case Q(x)=0, a(x) is recovered when h(x) and the scattering data are known. The inversion is illustrated with examples.
An embedding of the Poincaré Lie algebra into an extension of the Lie field of SO0(1,4)
Authors: Havlíček M. , Moylan P.
Published: July 2002

The * isomorphism between algebraic extensions of the Lie fields of SO0(1,4) and the Poincaré group are considered herein. It is shown that the principal series of unitary ray representations of SO0(1,4) are associated, via the * isomorphism, with real mass, positive and negative energy representations of the Poincaré Lie algebra with arbitrary spin. Results on the most degenerate exceptional series of SO0(1,4) representations are also given.
The Dirac oscillator and local automorphism invariance
Authors: Crawford James P.
Published: July 2002

The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein–Gordon equation with a potential of the form (ar 2+bL⋅S), where a and b are constants. To obtain the Dirac oscillator, a ‘‘minimal substitution’’ is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, a very unusual feature of the covariant derivative in this case is that the potential is a nontrivial element of the Clifford algebra. A theory which naturally gives rise to gauge potentials which are nontrivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the pure automorphism gauge field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented herein.
Algebraic spinors in Dirac propagators as a directed random walk
Authors: Rodríguez-Romo Suemi
Published: July 2002

The directed random walk representation of the Dirac propagator is presented using different algebraic spinor spaces. In particular, Majorana, Even, Dirac, and Chevalley–Crumeyrolle spinor spaces are used. For these cases, the spin connections were calculated and, from them, the gauge potentials. Moreover, for the Chevalley–Crumeyrolle algebraic spinor space, the use of the Dirac propagator as the inverse of the generator of a Markov process in the McKane–Parisi–Sourlas theorem is suggested.
Loop algebra approach to generalized sine-Gordon equations
Authors: Tafel J. , Wisse A.
Published: July 2002

A modification of the loop algebra approach to completely integrable equations is proposed. Hamilton’s equations are given for a generalized sine-Gordon equation and solutions of this equation are constructed in terms of the Riemann theta functions.
Equivalence between Lagrangian and Hamiltonian BRST formalisms
Authors: Nirov Kh. S. , Razumov A. V.
Published: July 2002

For a wide class of gauge invariant systems, the equivalence between Lagrangian and Hamiltonian BRST formalisms is proven.
p-adic superanalysis. III. The structure of p-adic super-Lie groups
Authors: Cianci Roberto , Khrennikov Andrew
Published: July 2002

This work is the third one of a series of articles in which the foundations of a p-adic supermanifold field theory are proposed. In this article p-adic super-Lie groups are defined and their properties studied; finally, the p-adic groups of matrices are analyzed.
Classical functional Bethe ansatz for SL(N): Separation of variables for the magnetic chain
Authors: Scott D. R. D.
Published: July 2002

It is desirable for one to be able to construct separation variables for systems with SL(N) R matrices or Lax pairs. This article relates and extends the two known methods of construction. The Sklyanin’s functional Bethe ansatz (FBA) [Commun. Math. Phys. 150, 181–191 (1992)] was previously only known for SL(2) and SL(3) (and associated) R matrices. The algebraic geometric method of Adams, Harnad, and Hurtubise [Commun. Math. Phys. 155, 385–413 (1993)] has been shown to work for SL(N) but up until now only for linear Poisson brackets. In this article Sklyanin’s program is advanced by giving the FBA for certain systems with SL(N) R matrices. This is achieved by constructing rational functions 𝒜(u) and ℬ(u) of the matrix elements of T(u), so that, in the generic case, the zeros xi of ℬ(u) are the separation coordinates and the Pi=𝒜(xi) provide their conjugate momenta. It is shown that the separation variables thus defined are the same as those given (as the simultaneous solutions of several equations in two variables) by the other method. The crucial calculation of Adams et al. of the commutation relations is also adapted to the case of quadratic Poisson brackets. The method is illustrated with the magnetic chain and the Gaudin model, and its wider applicability is discussed. No knowledge of algebraic geometry is required.
Quantum integrable systems related with symmetric spaces of the groups U(1,2) and Sp(1,2) and Green functions on these spaces
Authors: Verdiev Yi. A.
Published: July 2002

Some quantum integrable systems related with the groups U(1,2) and Sp(1,2) are considered. The motion of particles in the potentials g1/sinh2 α+g2/cosh2 α and g1′/sin2 θ+g2′/cos2 θ is related with the free motion in symmetric spaces of these groups. The integral representations for the Green functions of a free particle on these spaces are given.
Exact solution of the Dirac equation for a Coulomb and scalar potential in the presence of an Aharonov–Bohm and a magnetic monopole fields
Authors: Villalba Víctor M.
Published: July 2002

In the present paper the problem of a relativistic Dirac electron is analyzed in the presence of a combination of a Coulomb field, a 1/r scalar potential, as well as a Dirac magnetic monopole and an Aharonov–Bohm potential. Using the algebraic method of separation of variables, the Dirac equation expressed in the local rotating diagonal gauge is completely separated in spherical coordinates, and exact solutions are obtained. The energy spectrum is computed and its dependence on the intensity of the Aharonov–Bohm and the magnetic monopole strengths is analyzed.
The q-deformation of quantum mechanics of one degree of freedom
Authors: Maximov V. , Odzijewicz A.
Published: July 2002

The q-quantum mechanics of the one degree of freedom is studied. Among others the holomorphic representation of q-deformed Heisenberg–Weyl algebra and its realization by covariant Berezin symbols is described.
Flat connections and nonlocal conserved quantities in irrational conformal field theory
Authors: Halpern M. B. , Obers N. A.
Published: July 2002

Irrational conformal field theory (ICFT) includes rational conformal field theory as a small subspace, and the affine-Virasoro Ward identities describe the biconformal correlators of ICFT. The Ward identities are reformulated as an equivalent linear partial differential system with flat connections and new nonlocal conserved quantities. As examples of the formulation, the system of flat connections is solved for the coset correlators, the correlators of the affine-Sugawara nests, and the high-level n-point correlators of ICFT.
Thermodynamics of the Stephani Universes
Authors: Quevedo Hernando , Sussman Roberto A.
Published: July 2002

The consistency of the thermodynamics of the most general class of a conformally flat solution with an irrotational perfect fluid source (the Stephani Universes) is examined herein. For the case when the isometry group has dimension r≥2, the Gibbs–Duhem relation is always integrable, but if r<2 it is only integrable for the particular subclass [containing Friedman–Robertson–Walker (FRW) cosmologies] characterized by r=1 and by admitting a conformal motion parallel to the four-velocity. Explicit forms of the state variables and equations of state linking them are provided. These formal thermodynamic relations are determined up to an arbitrary function of time which reduces to the FRW scale factor in the FRW limit of the solutions. It is shown that a formal identification of this free parameter with a FRW scale factor determined by FRW dynamics leads to an unphysical temperature evolution law. If this parameter is not identified with a FRW scale factor, it is possible to find examples of solutions and formal equations of state complying with suitable energy conditions and reasonable asymptotic behavior and temperature laws.
An exterior calculus for exact symplectic manifolds
Authors: Frescura F. A. M. , Lubczonok G.
Published: July 2002

A calculus for exact symplectic manifolds is presented. It consists of the familiar exterior calculus augmented by a set of operations, algebraic and differential, admitted naturally by the exact symplectic structure of the underlying space. The result is a high level calculus that is particularly well suited to deal with problems on this type of manifold. Natural differential operators admitted by an exact symplectic structure are identified. The results are also applied to the de Rham cohomology of this type of manifold.
Isomorphism of dimer configurations and spanning trees on finite square lattices
Authors: Brankov J. G.
Published: July 2002

One-to-one mappings of the close-packed dimer configurations on a finite square lattice with free boundaries ℒ onto the spanning trees of a related graph (or two-graph) 𝒢 are found. The graph (two-graph) 𝒢 can be constructed from ℒ by: (1) deleting all the vertices of ℒ with arbitrarily fixed parity of the row and column numbers; (2) suppressing all the vertices of degree 2 except those of degree 2 in ℒ; (3) merging all the vertices of degree 1 into a single vertex g. The matrix Kirchhoff theorem reduces the enumeration problem for the spanning trees on 𝒢 to the eigenvalue problem for the discrete Laplacian on the square lattice ℒ′=𝒢 \ g with mixed Dirichlet–Neumann boundary conditions in at least one direction. That fact explains some of the unusual finite-size properties of the dimer model.
On the azimuthal Fourier components of the Green’s function for the Helmholtz equation in three dimensions
Authors: Matviyenko Gregory
Published: July 2002

Many algorithms that compute acoustic or electromagnetic fields scattered by surfaces of revolution require fast evaluation of the azimuthal Fourier components Gm of the Green’s function for the Helmholtz equation in three dimensions. In this article we derive a recurrence relation for the functions Gm and obtain explicit formulas for their partial derivatives. These observations significantly reduce the complexity of the computation of the scattered fields generated by axisymmetric scatterers.
Simplicial quantum gravity in four dimensions and invariants of discretized manifolds
Authors: Williams Ruth M.
Published: July 2002

The use of Regge’s discrete formulation of classical general relativity in attempts at constructing a theory of simplicial quantum gravity is discussed briefly. Recent work on invariants of discretized three-manifolds, which provide a regularized version of the much earlier result of Ponzano and Regge, where the state sum was related to a Feynman path integral with the Regge action, has led to the search for invariants of discretized four-manifolds, which might be the basis for a four-dimensional theory of quantum gravity. This search is described, and recent developments in Regge calculus arising from it are outlined. This paper is based on a talk given at the LMS Durham Symposium on Quantum Concepts in Space and Time, July 1994.
Path integration in two-dimensional topological quantum field theory
Authors: Sawin Stephen
Published: July 2002

A positive, diffeomorphism-invariant generalized measure on the space of metrics of a two-dimensional smooth manifold is constructed. We use the term generalized measure analogously with the generalized measures of Ashtekar and Lewandowski and of Baez. A family of actions is presented which, when integrated against this measure gives the two-dimensional axiomatic topological quantum field theories, or TQFTs, in terms of which Durhuus and Jonsson decompose every two-dimensional unitary TQFT as a direct sum.
Zero curvature formulations of dual hierarchies
Authors: Schiff Jeremy
Published: July 2002

Zero curvature formulations are given for the ‘‘dual hierarchies’’ of standard soliton equation hierarchies, recently introduced by Olver and Rosenau, including the physically interesting Fuchssteiner–Fokas–Camassa–Holm hierarchy.
A temperature and mass dependence of the linear Boltzmann collision operator from group theory point of view
Authors: Saveliev Vladimir
Published: July 2002

The Lie group of the transformations affecting the parameters of the linear Boltzmann collision operator such as temperature of background gas and ratio of masses of colliding particles and molecules is discovered. The group also describes the conservation laws for collisions and main symmetries of the collision operator. New algebraic properties of the collision operator are derived. Transformations acting on the variables and parameters and leaving the linear Boltzmann kinetic equation invariant are found. For the constant collision frequency the integral representation of solutions for nonuniform case in terms of the distribution function of particles drifting in a gas with zero temperature is deduced. The new exact relaxation solutions are obtained too.
The noncommutative constraints on the standard model à la Connes
Authors: Carminati Lionel , Iochum Bruno , Schücker Thomas
Published: July 2002

Noncommutative geometry applied to the standard model of electroweak and strong interactions was shown to produce fuzzy relations among masses and gauge couplings. We refine these relations and show then that they are exhaustive.
The glq(n)-covariant oscillators and q-deformed quantum mechanics in n dimensions
Authors: Chung W.-S.
Published: July 2002

In this paper the coherent state for glq(n)-covariant oscillators is constructed and is shown to satisfy the completeness relation. And the q-analog of quantum mechanics in n dimensions is obtained by using glq(n) oscillators.
The spectrum of Liouville operators and multiparticle Hamiltonians associated to one-particle Hamiltonians with singular continuous spectrum
Authors: Pushnitski A. B.
Published: July 2002

We study the structure of spectrum of the Liouville operator H−=H⊗I−I⊗H and the two-particle Hamiltonian H+=H⊗I+I⊗H in some model situations when the corresponding one-particle Hamiltonian H has singular continuous spectrum. A Hamiltonian H with singular continuous spectrum of Hausdorff dimension one is constructed such that the absolutely continuous spectrum of the operators H− and H+ is empty. On the other hand, we prove the existence of a Hamiltonian H with singular continuous spectrum of Hausdorff dimension zero such that the operators H− and H+ have nonempty absolutely continuous spectrum. Thus the Hausdorff dimension of the support cannot serve as characteristic of the singular measure of a one-body Hamiltonian that determines the spectral type of the corresponding Liouvillians or two-body Hamiltonians.
Weighted class operators: A new approach to tensor operators for compact groups
Authors: Strasburger Aleksander , Orłowski Arkadiusz
Published: July 2002

Weighted class operators, defined by averaging conjugation operators within fixed representation of a compact group against a weight function living on a conjugacy class, are discussed and their connection to the tensor operators is studied. Making extensive use of the theory of induced representations we prove several results for weighted class operators and in particular identify them, for weight functions being suitable matrix elements of the given group, with irreducible tensor operators. The results complement and extend those obtained earlier by the authors [A. Orłowski and A. Strasburger, J. Phys. A 27, 1971–1976 (1994)] and others.
New formulation of the classical path integral with reparametrization invariance
Authors: Thacker W. D.
Published: July 2002

A classical path integral (CPI) provides a functional integral representation of the kernel which propagates phase space density distributions. In this paper a new formulation of the CPI is developed in which time and energy are promoted to dynamical variables. The reparametrization invariance, inherent in this formalism, is handled by means of the Batalin–Fradkin–Vilkovisky method. The path integral action possesses a set of ISp(2) symmetries connected with reparametrization invariance and an additional set of ISp(2) symmetries connected with the symplectic geometry of the extended phase space. Supersymmetry is also present in the CPI action. This formulation of the CPI allows us to study the dependence on energy of the dynamical evolution of Hamiltonian systems. It naturally incorporates the constraints onto the energy surface.
Localized estimates and Cauchy problem for the logarithmic complex Ginzburg–Landau equation
Authors: Ginibre J. , Velo G.
Published: July 2002

We prove that the localization of the L2 and similar estimates for the complex Ginzburg–Landau equation (1), known to hold in the power case g(ρ)∼ρσ, also holds in the logarithmic case g(ρ)∼(Log ρ)ν for large ρ with ν>2: As a consequence, the theory of the Cauchy problem in local spaces given in a previous paper also extends to the logarithmic case.
Attractors for the Davey–Stewartson systems on R2
Authors: Wang Bixiang , Guo Boling
Published: July 2002

In the present paper, we study the long time behavior of solutions for the Davey–Stewartson systems on R2. We first derive the uniform a priori estimates for the solutions of these systems in H1(R2). Then we show the existence of the compact global attractor for the strong topology of H1(R2).
A natural basis of states for the noncommutative sphere and its Moyal bracket
Authors: Gratus J.
Published: July 2002

An infinite-dimensional algebra which is a nondecomposable reducible representation of su(2) is given. This algebra is defined with respect to two real parameters. If one of these parameters is zero, the algebra is the commutative algebra of functions on the sphere, otherwise it is a noncommutative analog. This is an extension of the algebra normally referred to as the (Berezin) quantum sphere or “fuzzy” sphere. A natural indefinite “inner” product and a basis of the algebra orthogonal with respect to it are given. The basis elements are homogeneous polynomials, eigenvectors of a Laplacian, and related to the Hahn polynomials. It is shown that these elements tend to the spherical harmonics for the sphere. A Moyal bracket is constructed and shown to be the standard Moyal bracket for the sphere.
Analytical formulas for Racah coefficients and 6-j symbols of the quantum superalgebra Uq(osp(1|2))
Authors: Minnaert Pierre , Mozrzymas Marek
Published: July 2002

Using the method of projection operators, analytical formulas for Racah coefficients and 6-j symbols of the quantum superalgebra Uq(osp(1|2)) are derived. The formulas obtained by this method are transformed by means of algebraic identities into symmetrical analytical formulas, the form of which are very similar to the classical formulas obtained by Racah and Regge for su(2) Racah coefficients and 6-j symbols. Symmetry properties of Uq(osp(1|2)) Racah coefficients and 6-j symbols following from these analytical formulas are studied. In particular, it is shown that, similarly to the su(2) classical case, in addition to the usual tetrahedral symmetry, 6-j symbols of the quantum superalgebra Uq(osp(1|2)) satisfy a Regge type symmetry.
Spinning particle in six dimensions
Authors: Lyakhovich S. L. , Sharapov A. A. , Shekhter K. M.
Published: July 2002

Massive spinning particle in 6d-Minkowski space is described as a mechanical system with the configuration space R5,1×CP3. The action functional of the model is unambiguously determined by the requirement of identical (off-shell) conservation for the phase-space counterparts of three Casimir operators of the Poincaré group. The model proves to be completely solvable. Its generalization to the constant curvature background is presented. Canonical quantization of the theory leads to the relativistic wave equations for the irreducible 6d fields.
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Toda solitons and the dressing symmetry
Authors: Belich H. , Paunov R.
Published: July 2002

We present an elementary derivation of the solitonlike solutions in the An(1) Toda models which is an alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N-solitons are calculated. This enables us to obtain explicit expression for the element which, by dressing group action, produces a generic soliton solution. In the particular example of monosolitons we suggest a relation to the vertex operator formalism, previously used by Olive, Turok, and Underwood. Our results can also be considered as generalization of the approach to the sine–Gordon solitons, proposed by Babelon and Bernard.
Limits of space–times in five dimensions and their relation to the Segre types
Authors: Paiva F. M. , Rebouças M. J. , Teixeira A. F. F.
Published: July 2002

A limiting diagram for the Segre classification in 5-dimensional space–times is obtained, extending a recent work on limits of the energy–momentum tensor in general relativity. Some of Geroch’s results on limits of space–times in general relativity are also extended to the context of five-dimensional Kaluza–Klein space–times.