bluuebunny/crossref_metadata_2025 huggingface dataset:
Response to “Comment on ‘The surplus function approach’ ” [J. Chem. Phys. 112, 455 (2000)]
Authors: Huang Hongxin
Published: July 2002

The existence of integral (Hi¯) in the surplus function variational quantum Monte Carlo approach is discussed and a method is proposed for avoiding the infinity in the calculation of Hi¯. A rigid model of nucleus was adopted to avoid the infinity appearance of r−i. Discussion of a new solution for Schrödinger’s equation of hydrogen atom, which may make the calculation of the Hi¯ value more accurate is also presented.
Molecular dynamics study of benzene–benzene and benzene–potassium ion interactions using polarizable potential models
Authors: Dang Liem X.
Published: July 2002

We have constructed a polarizable potential model for benzene using molecular dynamics techniques. The atomic site polarizabilities for carbon and hydrogen were taken from the recent work of Applequist [J. Phys. Chem. 97, 6016 (1993)], which reproduced the experimental molecular polarizability of the benzene molecule very accurately. Our model describes well the available experimental data such as the structure and thermodynamic properties of liquid benzene and the equilibrium properties of the liquid/vapor interface of benzene. The lowest minimum-energy structure of the benzene dimer predicted by our model has a T-shape with a potential energy of −2.5 kcal/mol. This value agrees with the experimentally obtained value (−2.4±0.4 kcal/mol), which was determined from a high-precision ionization measurement. The cyclic minimum-energy structures are found for both the benzene trimer and tetramer clusters. The computed density profile shows that the interface is not sharp at a microscopic level and has a thickness about 5 Å at 300 K. The calculated surface tension is 25±2 dyn/cm, which is in excellent agreement with the experimentally obtained value of 28 dyn/cm. The results of our model also compare well with the corresponding results for benzene obtained by Jorgensen and Severance [J. Am. Chem. Soc. 112, 4768 (1990)], who used nonpolarizable potential parameters. We also report the details of our study of K+(C6H6)n=1–6 clusters. We found that the polarization effects were quite significant in these systems.
Photoelectron spectroscopy of copper cyanide cluster anions: On the possibility of linear and ring structures
Authors: Negishi Yuichi , Yasuike Tomokazu , Hayakawa Fumitaka , Kizawa Miki , Yabushita Satoshi , Nakajima Atsushi , Kaya Koji
Published: July 2002

The electronic properties of copper cyanide cluster anions [Cun(CN)m−; n=1–6, m=1–6] were studied using photoelectron spectroscopy (PES) with a magnetic-bottle type electron spectrometer. Both the anions and the cations of the Cun(CN)m cluster were generated by laser vaporization of a molded copper cyanide rod in a He carrier gas. In the mass spectra, abundant clusters were produced at the composition of (n,m)=(n,n+1;n=1−6) and (n,n;n=4 and 5) for the anions, whereas more abundant clusters were observed at (n, n−1; n=1−9) for the cations. The stability of Cun(CN)n+1− and Cun(CN)n−1+ clusters is attributed to their electronic structure, where ionic Cu+ and CN− are linked alternately in a linear geometry. The PES spectra of the Cun(CN)m− anions show that the (n,n+1) clusters exhibit an extremely large EA of above 4.5 eV, while the EA’s of the less abundant (n,n) clusters increase monotonously with cluster size from 1.3 eV (n=1) to 3.12 eV (n=6), except for n=4 and 5. Together with theoretical calculations by the density functional theory (DFT), two different linear isomers have been found for (n,n) clusters, where CN takes a opposite direction toward Cu. For Cu4(CN)4− and Cu5(CN)5−, moreover, the PES spectra show two components of distinctly different peak shape, suggesting that a ring isomer should coexist with the linear ones.
What to see and what not to see in three-photon absorption: (3+1) REMPI of HBr
Authors: Kvaran Ágúst , Waage Benedikt G. , Wang Huasheng
Published: July 2002

Hönl–London type approximation expressions are derived for transition strengths of the Ω′=0,1,2,3, ←Ω″=0 (Σ, Π, Δ and Φ←Σ) three-photon transitions for diatomic molecules belonging to Hund’s case (a) and intermediate (a)–(b) coupling schemes. These are used to demonstrate what may be seen and what may not be seen in three-photon absorption spectra. The forms are used to simulate room temperature (3+1)REMPI spectra of HBr, for different electronic transitions. The analysis as well as comparison with (2+1)REMPI spectra is used to demonstrate the usefulness of three-photon absorption spectroscopy to identify excited states and to derive spectroscopic parameters. A Rydberg state, not observed in single or two-photon absorption, with band origin 82 837 cm−1 was identified and analyzed for the first time. It was assigned as the L1Φ(3) ((σ2π3)5dδ)) state, (0,0) band.
Phonon spectra in model carbon nanotubes
Authors: Sokhan V. P. , Nicholson D. , Quirke N.
Published: July 2002

Using classical molecular dynamics simulation and the empirical bond-order Tersoff–Brenner potential for the carbon–carbon interaction the phonon density of states of single-wall carbon nanotubes (SWNT) of various chiralities has been studied as a function of temperature and nanotube diameter. The calculated frequencies of the radial breathing mode (RBM) are in excellent agreement with results of an empirical force constant model and in good agreement with ab initio and tight-binding calculations. This allows us to assign low-frequency resonance enhanced Raman modes observed in SWNT bundles.
Nontrivial zeros of the Racah quadrupole invariant
Authors: Brudno Simcha , Louck James D.
Published: July 2002

It is shown that a class of nontrivial zeros of the Racah quadrupole invariant operator is given by two orbits of the group action of an infinite discrete subgroup of the proper two-dimensional Lorentz group SO(1,1) on the hyperbola 4x2−3y2= (11)/(4) .
Confinement of quarks and gluons in gauge quantum field theory
Authors: Völkel A. H.
Published: July 2002

A SU(3)-gauge quantum field theory with a quark triplet, an antiquark triplet, and a self-conjugate gluon octet as basic fields is investigated. In virtue of a nontrivial coupling between the representation of the translation group and the SU(3)-color charge of the basic fields it is proved: (i) The basic quark, antiquark, and gluon fields are confined. (ii) Every state vector of the physical Hilbert space is a SU(3)-color singlet state. (iii) Poincaré invariance holds in the physical Hilbert space. These results rest on a nonstandard transformation law of the basic fields with respect to translations. Its meaning within the frame of classical Lagrangian field theory for chromodynamics is investigated.
Sums of products of ultraspherical functions
Authors: Rahman Mizan , Shah Mihr J.
Published: July 2002

Analytical expressions for the sum ∑∞n=0(n+λ)[Γ(n+1)Γ(n+2λ)]2 ×Cλn(x)Cλn( y) ×Cλn(z)Dλn(u) are given, where Cλn and Dλn are ultraspherical polynomials and functions of the second kind, respectively, on the sets {‖x‖,‖ y‖,‖z‖<1, u>1} and {‖x‖,‖ y‖,‖z‖,‖u‖<1}.
Infinitesimal null isotropy and Robertson–Walker metrics
Authors: Koch-Sen Lisa
Published: July 2002

The concept of infinitesimal null isotropy is defined for a Lorentz manifold, in terms of null sectional curvature (as defined by Harris). It is shown that infinitesimal null isotropy is equivalent to infinitesimal spatial isotropy (as defined by Karcher), and that a null-isotropic space for which null sectional curvature is infinitesimally spatially constant must have a Robertson–Walker metric.
Three-dimensional inverse scattering: Plasma and variable velocity wave equations
Authors: Rose James H. , Cheney Margaret , DeFacio Brian
Published: July 2002

Exact equations governing three-dimensional time-domain inverse scattering are derived for the plasma wave equation and the variable velocity classical wave equation. This derivation was announced for the plasma wave equation in a short note by the authors. That work was motivated by Newton’s three-dimensional generalization of Marchenko’s equation. This paper gives the details of the new derivation and extends it to the classical wave equation. For the time domain derivation in this paper, the scattering region is assumed to have compact support and smoothly joins the surrounding three-dimensional infinite medium. The derivation contains the following ingredients: (1) a representation of the solution at a point in terms of its values on a large sphere, (2) the far-field form of the Green’s function, (3) causality, and (4) information carried in the wave front of the solution. The derivation of the classical wave inverse scattering equation requires that the velocity in the scattering region be less than that of the surrounding medium. This condition is natural, for example, in the scalar wave model of electromagnetic scattering from dielectric nonconducting bodies in free space. Finally, an experiment to verify the inverse scattering equations is proposed.
From spinor structure to magnetic monopoles
Authors: Bugajska Krystyna
Published: July 2002

Starting with a spinor structure over a space-time, to which a more fundamental character is ascribed than to the vector structure, an affine-metric geometry of the space-time. The U(1) bundle of electromagnetism appears naturally in this approach. A ‘‘sublocal’’ action of the U(1) on the spinor structure is found. Any field of timelike directions creates a ‘‘field’’ of magnetic monopoles.
Skeleton inequalities and mean field properties for lattice spin systems
Authors: Hara Takashi , Hattori Tetsuya , Tasaki Hal
Published: July 2002

We present a proof of skeleton inequalities for ferromagnetic lattice spin systems with potential V(φ2)=(a/2)φ2+∑Mn=2{λ2n/ (2n)!}φ2n (a real, λ2n≥0) generalizing the Brydges–Fröhlich–Sokal and Bovier–Felder methods. As an application of the inequalities, we prove that, for sufficiently soft systems in d>4 dimensions, critical exponents γ, α , and Δ4 take their mean-field values (i.e., γ=1, α=0, and Δ4= (3)/(2) ).
A multitype random sequential process. III. The case of constant target area
Authors: Mellein B.
Published: July 2002

We consider the static properties of a sequential process where the compartments of a 1×n lattice space are filled irreversibly with particles of integral random length α (α-bell particles, α-mers; 1≤q≤α≤r, r≥2). While, in a previous model, filling was assumed to be random on the occasionally accessible (yet unoccupied) part of the lattice (shrinking target area), particle placing is now assumed to be random on the entire array at any time (constant target area) and subject to the condition of no overlap, i.e., particles striking already filled sites will be rejected. The occupation statistics of the lattice in the jammed state is analyzed by means of three random variables, (i) the total number of empty sites, (ii) the number of α-bell particles forming part of the saturation coverage (α=q,...,r), and (iii) the number of vacancies of m sites (m=0,1,...,q−1). Recursion relationships are obtained for the expectation values of these random variables and their behavior for n→∞ is studied. The results are used to describe the size distribution of adsorbed particles on infinite arrays.
Perturbation theory for polyacetylene-type kink dynamics model with acoustic phonon effects
Authors: Leblanc Y. , Matsumoto H. , Umezawa H.
Published: July 2002

Using a quasirealistic generalized continuum Takayama–Liu–Maki (TLM) model including acoustic phonon effects, perturbation theory is applied and a formal method for computing the kink of the TLM model with its perturbative corrections due to acoustic phonon interaction effects is presented. It is found that acoustic effects induce the motion of the soliton. The kink is then constrained to propagate along the molecular chain with a fixed velocity of magnitude close to that of the acoustic phonon velocity. No static solution is consistent with perturbation theory.
On unifying electromagnetism and gravitation without curvature
Authors: Schütze Dieter
Published: July 2002

This paper is devoted to a five-dimensional unification of the gravitational theory of Hayashi and Shirafuji with electromagnetism. Interference effects are found between gravitational contributions of matter spin and electromagnetism. This unification becomes the classical Kaluza–Klein theory if contributions of the torsion tensor related with spin are neglected.
Practical pretheories of QED. II. Choosing the interaction
Authors: Yoakam M. C.
Published: July 2002

An interaction of the j⋅A form is introduced. The Coester transformation, which connects the Proca and the Coester fields, is extended to the pretheory boson fields when the boson mass counterterms are absent. The Fermi transformation, used to make the Lorentz condition stationary in the weak-convergence limit, is shown to be extendable to the pretheories (sans the freedom of commutator choice, which is usually associated with it). The familiar consequences of including a Fermi transformation (the Heisenberg picture images of the spinor fields do not transform as spinors) are retained, but a suitable limitation on the choice of the spinor charge and mass counterterms will allow the Heisenberg picture forms which are bilinear in the spinor operators to retain their transformation properties. In particular, familiar choices for Lint require that the spinor fields be expressed in the intermediate-Heisenberg picture. The introduction of boson mass counterterms into the practical pretheories is shown to give infinite gauge shifts which are independent of the zero-mass limit. Sufficient conditions for a modified Fermi operator are presented, and an ‘‘obvious’’ candidate is eliminated.
Quantum theory of particles of indefinite mass: Spin- 1/2
Authors: Hostler Levere
Published: July 2002

The quantum theory of particles of indefinite mass investigated earlier by Hostler [J. Math. Phys. 21, 2461 (1980); 22, 2307 (1981)] is adapted to apply to spin- 1/2 particles. The proposed wave equation is { 1/2  Π⋅(1+iσ)⋅Π+(1/i)(∂/∂λ)} φ=0, Πμ=pμ−eAμ, in which φ is a 2×1 Pauli spinor and σ is a spin tensor whose Lorentz components are 2×2 Pauli spin matrices. Particle scattering by an external c-number static field is computed within the framework of the new formalism, and agreement with the known physics of a charged spin- 1/2 particle is obtained for this special case.
Fermi states of Bose systems in three space dimensions. II. The solvable version of the Hubbard model
Authors: Garbaczewski Piotr
Published: July 2002

An exact spectral solution of the Hubbard problem on the tetrahedron is given. It is demonstrated that it provides at the same time a partial spectral solution for the Bose version of this (Fermi) model. A remarkable relationship of the Hamiltonians HB=HF+(1−P)HB(1−P) is established, where P is a projection in the state space of the interacting Bose system. This partial observation is then extended to the spatial lattice composed of the four-site Hubbard cells, which interact due to the superimposed perturbation of the hopping type, affecting all sites of the lattice; H=∑(i j) ∑σ=± bi j c*iσ cjσ+U ∑i ni+ni− being the corresponding Hamiltonian. It is thus demonstrated that the joint Bose–Fermi spectral problem (previously established in 1+1 dimensions) makes sense in 1+3 dimensions as well.
On combinatoric determination of SU(n) weight multiplicities
Authors: Schmidt Jeffrey R.
Published: July 2002

A combinatoric method for evaluating the inner multiplicity of a central weight is given using results from the theory of distributions. A formula for special cases is derived, and a recursive algorithm is presented for the general problem.
On the zeros of eigenfunctions of polynomial differential operators
Authors: Buendia E. , Dehesa J. S. , Sanchez-Buendia M. A.
Published: July 2002

It is shown that for polynomial eigenfunctions of an ordinary polynomial differential operator with coefficients depending only on the independent variable it is possible to determine the density of nodes around the mean without solving the corresponding eigenvalue problem. This is done by means of the first few moments, which can be directly expressed in terms of the above-mentioned coefficients. Also, very simple expressions for the asymptotic values (i.e., when the degree of the polynomial becomes very large) of these quantities are found. For illustration, these results are applied to various orthogonal polynomials, which satisfy ordinary differential equations of second, fourth, and/or sixth order.
A note on the classification of the zeros of angular momentum coefficients
Authors: Srinivasa Rao K.
Published: July 2002

Closed form expressions for polynomial or ‘‘nontrivial’’ zeros of degree one of the Clebsch–Gordan (3-j) and the Racah (6-j) coefficients are presented and a conjecture regarding closed form formulas for the same is made.
Solutions to wave equations on black hole geometries. II
Authors: Couch W. E.
Published: July 2002

Methods from the author’s previous work and the classes of solutions which they produce are extended to the wave equations which govern the massive scalar field and the massless spin- 1/2 field on the Kerr–Newman geometry and the massless fields of spin 1 and 2 on the Kerr geometry. The solutions found are exact and expressed in simple closed forms in terms of elementary functions, but they only exist when appropriate constraints hold on some of the black hole parameters and on the frequency of the field in some cases. The behavior on the horizon, at null infinity, and with respect to the angular variables is analyzed for some example solutions. For the examples studied, it is found that the ones having radial behavior of a normal mode are not free of angular singularities. An exact relation is established between the scalar wave equation on the extreme Kerr–Newman geometry and the Whittaker–Hill equation.
Nontrivial zeros of weight 1 3j and 6j coefficients: Relation to Diophantine equations of equal sums of like powers
Authors: Brudno Simcha , Louck James D.
Published: July 2002

The nontrivial zeros of weight 1 3j and 6j coefficients given previously are shown to be the set of all such zeros. The relation of these zeros to the solutions of well-known Diophantine equations is also discussed.
Canonical map approach to channeling stability in crystals
Authors: Sáenz A. W.
Published: July 2002

We state and prove rigorous mathematical results on the orbital stability of certain rectilinear trajectories of sufficiently energetic particles subjected to appropriate periodic potentials. This is done in the context of nontrivial classical Hamiltonian models, nonrelativistic and relativistic, in two space dimensions. The main steps involved in the proofs are the derivation of the asymptotic form of certain canonical maps in the plane in the limit of large particle energies and the application of a version of Moser’s twist theorem. When suitably specialized, these results establish rigorously for the first time that the pertinent straight-line channeling trajectories of fast particles in two-dimensional rigid crystal lattices have this stability property under reasonable conditions on the crystal potential.
Locally operating realizations of transformation Lie groups
Authors: Cariñena Jose F. , Del Olmo Mariano A. , Santander Mariano
Published: July 2002

Using the Mackey theory of induced representations, a systematic study of the locally operating multiplier realizations of a connected Lie group G that acts transitively on a space-time manifold is presented. We obtain a mathematical characterization of the locally operating multiplier realizations and a reduction of the problem of multiplier locally operating realizations to linear ones via a splitting group G‘;m for G. In this way the locally operating multiplier realizations are obtained by induction from finite-dimensional linear representations of a well-determined subgroup of Ḡ. Some examples, such as the two-dimensional Euclidean group, the Galilei group, and the one-dimensional Newton–Hooke group, are given.
Scalar formalism for non-Abelian gauge theory
Authors: Hostler Levere C.
Published: July 2002

The gauge field theory of an N-dimensional multiplet of spin- 1/2 particles is investigated using the Klein–Gordon-type wave equation {Π ⋅ (1+iσ) ⋅ Π+m2}Φ=0, Πμ≡∂/∂ixμ−eAμ, investigated before by a number of authors, to describe the fermions. Here Φ is a 2×1 Pauli spinor, and σ repesents a Lorentz spin tensor whose components σμν are ordinary 2×2 Pauli spin matrices. Feynman rules for the scalar formalism for non-Abelian gauge theory are derived starting from the conventional field theory of the multiplet and converting it to the new description. The equivalence of the new and the old formalism for arbitrary radiative processes is thereby established. The conversion to the scalar formalism is accomplished in a novel way by working in terms of the path integral representation of the generating functional of the vacuum τ-functions, τ(2,1, ⋅⋅⋅ 3 ⋅⋅⋅)≡〈0−‖T(Ψin(2) Ψ̄in(1) ⋅⋅⋅ Aμ(3)in ⋅⋅⋅ S)‖0−〉, where Ψin is a Heisenberg operator belonging to a 4N×1 Dirac wave function of the multiplet. The Feynman rules obtained generalize earlier results for the Abelian case of quantum electrodynamics.
Invariant operators for the n-dimensional super-Poincaré algebra and the decomposition of the scalar superfield
Authors: Finkelstein R. , Villasante M.
Published: July 2002

An analysis of supersymmetric Kaluza–Klein theories is begun by obtaining the Casimir operators for the super-Poincaré algebra in any number of dimensions. The knowledge of these operators is used to decompose the general scalar superfield in 11 dimensions into its irreducible parts. The irreducible superfields are expressed as products of Grassmann–Hermite functions and Grassmann–Bargmann–Wigner multispinor fields. Some Lagrangians for these superfields are written down. The formulation is off shell but global.
The group-theoretical treatment of aberrating systems. I. Aligned lens systems in third aberration order
Authors: Navarro-Saad Miguel , Wolf Kurt Bernardo
Published: July 2002

The constituents of a lens system, i.e., slabs of homogeneous transparent material and the refracting surfaces between them, considered to third aberration order, are associated to elements of a nine-parameter aberration group. Three parameters correspond to Gaussian systems and six to group-classified aberrations. The group multiplication operation (through matrix-cum-vector algebra) corresponds to their concatenation, and the linear group action on an eight-dimensional homogeneous space corresponds to the nonlinear action of the system on the optical phase space. This leads to economical computation algorithms that may be extended to aberrating systems of higher order.
Statistical filter theory and the O’Doherty–Anstey effect: Dependence on offset
Authors: Lerche I.
Published: July 2002

This paper considers the effects of multiples, generated at plane bed interfaces, on the characteristics of a mean seismic wave propagating at an angle to the bedding plane. It is found that(a) the multiples produce frequency- and angle-dependent phase shifts to the coherent wave as well as providing an effective attenuation, which is also frequency and angle dependent; (b) a slim angular pencil of monochromatic waves rapidly loses information about its original angular width due to the multiples as the pencil propagates; (c) a seismic pulse, initially traveling at a fixed angle, has both its envelope amplitude and its phase distorted by multiples, and after a short distance of transmission into the medium, the wave shape is nearly completely determined by the generated multiples and is only slightly beholden to the initial pulse shape; (d) the phase and group directions of the mean seismic wave are different than the incident wave’s direction and are canted closer to the horizontal with the group direction being the most highly canted; and (e) lateral spreading information of the mean seismic wave is contained in the cross-correlated response of separated geophones and, in principle, can be extracted from cross-correlated measurements. How the generic response depends on the power spectrum of the reflectivity sequence is illustrated by comparing and contrasting results for a transitional sedimentation pattern with those from a cyclic sedimentation pattern; the former produces both a frequency-dependent time delay and attenuation while the latter produces a pure time delay except in the local vicinity of isolated, but periodic frequencies. Numerical estimates, using parameters believed representative of typical seismic conditions, indicate that all of the effects uncovered are large—in the sense that they fall squarely in the regime where they can be expected to have a significant impact both on the subsurface evolution of seismic waves and on interpretations of subsurface conditions made using surface-received signals.
Extension and replacement bases for semisimple Lie algebras
Authors: Capps Richard H.
Published: July 2002

Two simple prescriptions are given for obtaining sets of orthogonal bases for semisimple Lie algebras. The first method allows one to obtain the irreducible representations of all the simple Lie algebras, starting from SU(2) and Dynkin’s method for constructing representations from simple roots and highest weights. The second method relates algebras of the same rank. Several examples are discussed. A method is given for listing the bases that may be obtained from the prescriptions.
Some integrals involving three modified Bessel functions. I
Authors: Gervois A. , Navelet H.
Published: July 2002

The integrals ∫∞0 t1+μIμ(at)Kν (bt)Kν(ct)dt and ∫∞0t1−νIν(at)Kν (bt)Kν(ct)dt are calculated with the help of the factorization properties of the Appell function F4. Results are given for real parameters a, b, c, both when they are and are not in a triangle configuration.
Some integrals involving three modified Bessel functions. II
Authors: Gervois A. , Navelet H.
Published: July 2002

The integrals ∫∞0Zμ(at)Kν(bt) iKρ(ct)dt, where Zμ=Iμ, Kμ, are calculated, with the help of the factorization properties of the function F4. Results are given for real parameters a, b, c both when they are and are not in a triangle configuration. Some generalizations using derivation with respect to the parameters are considered.
Resolving the singularities in the space of Riemannian geometries
Authors: Fischer Arthur E.
Published: July 2002

A method is described for unfolding the singularities of superspace, 𝒢=ℳ/𝒟, the space of Riemannian geometries of a manifold M. This extended, or unfolded superspace, is described by the projection 𝒢F(M)=(ℳ×F(M))/𝒟→ℳ/𝒟=𝒢, where F(M) is the frame bundle of M. The unfolded space 𝒢F(M) is an infinite-dimensional manifold without singularities. Moreover, as expected, the unfolding of 𝒢F(M) at each geometry [ g0]∈𝒢 is parametrized by the isometry group Ig0(M) of g0. The construction is completely natural, gives complete control and knowledge of the unfolding at each geometry necessary to make 𝒢F(M) a manifold, and is generally covariant with respect to all coordinate transformations. A similar program is outlined, based on the methods of this paper, of desingularizing the moduli space of connections on a principal fiber bundle.
Effective determinism in a classical field theory with spacelike characteristics
Authors: Isenberg J. , Horndeski G.
Published: July 2002

For certain classical field theories, it appears as if spacelike characteristic hypersurfaces can occur in the solutions. In principle, this means that acausal propagation is allowed, and the Cauchy problem breaks down. To investigate if indeed this happens, a class of Kasner-like solutions of a generalized Einstein–Maxwell theory is examined. It is found that the spacelike characteristics almost never form, and when they do, they cause no trouble.
Path integration of the time-dependent forced oscillator with a two-time quadratic action
Authors: Zhang Tian Rong , Cheng Bin Kang
Published: July 2002

Using the prodistribution theory proposed by DeWitt-Morette [C. DeWitt-Morette, Commun. Math. Phys. 28, 47 (1972); C. DeWitt-Morette, A. Maheshwari, and B. Nelson, Phys. Rep. 50, 257 (1979)], the path integration of a time-dependent forced harmonic oscillator with a two-time quadratic action has been given in terms of the solutions of some integrodifferential equations. We then evaluate explicitly both the classical path and the propagator for the specific kernel introduced by Feynman in the polaron problem. Our results include the previous known results as special cases.
Sturmian eigenvalue equations with a Bessel function basis
Authors: Rawitscher G. H. , Delic G.
Published: July 2002

A non-self-adjoint Sturmian eigenvalue equation of the form Av=f, encountered in quantum scattering theory, is solved as a complex general matrix eigenvalue problem. The matrix form is obtained on expansion of the solution in a discrete set of spherical Sturmian–Bessel functions of complex argument. This set of basis functions gives better convergence behavior for both the eigenvalues and eigenfunctions when compared to the results of a Chebyshev polynomial method reported previously.
Hyperfunctions and renormalization
Authors: Nagamachi Shigeaki , Mugibayashi Nobumichi
Published: July 2002

A condition is found so that the Wick-ordered power series of scalar fields in four-dimensional space-time is defined as a Fourier-hyperfunction field, and the derivative coupling model is investigated in the framework of hyperfunction quantum field theory.
Coherent states of the real symplectic group in a complex analytic parametrization. II. Annihilation-operator coherent states
Authors: Quesne C.
Published: July 2002

In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations 〈λd+n/2,..,λ1+n/2〉, encountered in physical applications, are analyzed in detail with special emphasis on those of Sp(4,R) and Sp(6,R). The present paper discusses the annihilation-operator coherent states, i.e., the eigenstates of the noncompact lowering generators corresponding to complex eigenvalues. These states generalize the coherent states introduced by Barut and Girardello for Sp(2,R), and later on extended by Deenen and Quesne to the Sp(2d,R) irreducible representations of the type 〈(λ+n/2)d〉. When λ1,...,λd are not all equal, it was shown by Deenen and Quesne that the eigenvalues do not completely specify the eigenstates of the noncompact lowering generators.

In the present work, their characterization is completed by a set of continuous labels parametrizing the (unitary-operator) coherent states of the maximal compact subgroup U(d). The resulting coherent states are therefore of mixed type, being annihilation-operator coherent states only as regards the noncompact generators. A realization in a subspace of a Bargmann space of analytic functions shows that such coherent states satisfy a unity resolution relation in the representation space of 〈λd +n/2,...,λ1+n/2〉, and therefore may be used as a continuous basis in such space. The analytic functions and the differential operators representing the representation space discrete bases and the Sp(2d,R) generators, respectively, are found in explicit form. It is concluded that the annihilation-operator coherent state representation provides the mathematical foundation for the use of differentiation operators with respect to the noncompact raising generators in symbolic expressions of the Sp(2d,R) generators. This is to be compared with the habit of replacing a boson annihilation operator by a symbolic differentiation with respect to the corresponding creation operator, accounted for by the Bargmann representation of such operators.
Is there action-at-a-distance linear confinement?
Authors: Weiss J.
Published: July 2002

The possilibity of constructing an action-at-a-distance form of linear confinement is demonstrated. Using the Fokker–Wheeler–Feynman action principle, known from classical action-at-a-distance electrodynamics, with an action containing the relativistically invariant two-particle Heaviside step function, equations of motion and appropriate potentials exhibiting the linearity of their behavior are derived. The plausibility of the generators of motion describing dynamics with the linear potentials is verified on the simple circular-orbit model of a two-component system, and the expected energy spectrum in terms of semiclassical quantization is obtained.
Soliton solutions for self-dual SU(N) gauge fields on Euclidean space
Authors: Letelier Patricio S.
Published: July 2002

Axially symmetric soliton solutions for self-dual SU(N) gauge fields on Euclidean four-dimensional flat space are found using an extension of the Belinsky–Zakharov solution generating technique. The new solutions depend at most on N−1 arbitrary solutions of the usual Laplace equations in cylindrical coordinates. The inverse scattering method using the chosen seen solution reduces to the computation of at most N−1 quadratures. The n-soliton solution is written in a determinantal form. Three particular cases of one-soliton solutions for the SU(5) group are exhibited.
Coherent states of the real symplectic group in a complex analytic parametrization. I. Unitary-operator coherent states
Authors: Quesne C.
Published: July 2002

In the present series of papers, the coherent states of Sp(2d,R), corresponding to the positive discrete series irreducible representations 〈λd+n/2,...,λ1+n/2〉 encountered in physical applications, are analyzed in detail with special emphasis on those of Sp(4,R) and Sp(6,R). The present paper discusses the unitary-operator coherent states, as defined by Klauder, Perelomov, and Gilmore. These states are parametrized by the points of the coset space Sp(2d,R)/H, where H is the stability group of the Sp(2d,R) irreducible representation lowest weight state, chosen as the reference state, and depends upon the relative values of λ1,...,λd, subject to the conditions λ1≥λ2≥ ⋅ ⋅ ⋅ ≥λd≥0. A parametrization of Sp(2d,R)/H corresponding to a factorization of the latter into a product of coset spaces Sp(2d,R)/U(d) and U(d)/H is chosen. The overlap of two coherent states is calculated, the action of the Sp(2d,R) generators on the coherent states is determined, and the explicit form of the unity resolution relation satisfied by the coherent states in the representation space of the irreducible representation is obtained. The Hilbert space of analytic functions arising from the coherent state representation is studied in detail. Finally, some applications of the formalism developed in the present paper are outlined. In particular, its relevance to the study of boson realizations of the Sp(2d,R) algebra is stressed.
Quantum kinematics of the harmonic oscillator
Authors: Krause Jorge
Published: July 2002

The formalism of non-Abelian quantum kinematics is applied to the Newtonian symmetry group of the harmonic oscillator. Within the regular ray representation of the group, the Schrödinger operator, as well as two other (new) invariant operators, are obtained as Casimir operators of the extended kinematic algebra. Superselection rules are then introduced, which permit the identification (and the explicit calculation) of the physical states of the system. Next, a complementary ray representation, attached to the space-time realization of the group, casts the Schrödinger operator into the familiar time-dependent space-time differential operator of the harmonic oscillator and thus, by means of the superselection rules, one obtains the time-dependent Schrödinger equation of the sytem. Finally, the evaluation of a Hurwitz invariant integral, over the group manifold, affords the well known Feynman space-time propagator 〈t′,x′‖t,x〉 of the simple harmonic oscillator. Everything comes out from the assumed symmetries of the system. The whole approach is group theoretic and ‘‘relativistic.’’ No classical analog is used in this ‘‘quantization’’ scheme.
Series representations for calculations in quantum statistics
Authors: Barker William A.
Published: July 2002

The mathematical methods used to average a function of energy over the Maxwell–Boltzmann (MB), Bose–Einstein (BE), and Fermi–Dirac(FD) statistics are compared. Blankenbecler’s method converts the FD integrals into a series of differentiations which converge rapidly if the Fermi energy is large compared to kT. The BE integrals may be obtained from the corresponding MB integral by setting the chemical potential equal to zero and multiplying by a slowly converging numerical series. In each case a single integral of general form is used to calculate familiar quantities like chemical potential, energy, and heat capacity.
Hamiltonian particle mechanics on curved space-times—A no-interaction theorem
Authors: De Bièvre Stephan
Published: July 2002

Hamiltonian particle mechanics is formulated on a space-time (M,ℊ). The restrictions imposed by the isometry group G of ℊ on the possible dynamics are analyzed; a no-interaction theorem is obtained on a large class of homogeneous space-times. The results are in particular applied to the de Sitter space-time: here it is proven that a G-invariant dynamics can describe geodesic particle motion only.
Realizing the Berezin integral as a superspace contour integral
Authors: Rogers Alice
Published: July 2002

Integration on supermanifolds, using contours and the covariant differential forms of Kostant [B. Kostant, ‘‘Graded manifolds, graded Lie theory and prequantisation,’’ in Lecture Notes in Mathematics, Vol. 570 (Springer, Berlin, 1977)], is described; the good properties that these integrals naturally acquire are considered. It is then shown that the formal process of integration over even and odd variables introduced by Berezin [F. A. Berezin, The Method of Second Quantization (Academic, New York, 1966)] using partly covariant and partly contravariant forms can be regarded as a special case of these contour integrals over covariant forms.
Surface integrals in lower dimensions from higher-order Chern classes and a class of solutions in three dimensions
Authors: O’Sé D. , Sherry T. N. , Tchrakian D. H.
Published: July 2002

It is shown that surface integrals, involving gauge and Higgs fields, in both odd and even dimensions can be obtained by dimensional reduction from Chern classes in higher dimensions. For odd dimensions, the physically useful dimensional reduction is characterized by ℳN=EN−p×Sp, and for even dimensions by ℳN =EN−p×S2×⋅ ⋅ ⋅×S2 ( 1/2 p times). The existence of a family of field configurations for which these surface integrals in three dimensions exist, and are nonzero, is presented. This family includes a Yang–Mills–Higgs (YMH) system with an algebra-valued Higgs field and one with the Higgs field in the reducible representation adjoint ⊕ scalar.
Minimization of Landau potentials invariant under SO(3)
Authors: Brihaye Yves , Nuyts Jean
Published: July 2002

The absolute minima for Landau potentials corresponding to one irreducible representation of SO(3) of spin up to 4 are computed together with their stability groups. For spin 4 the nonmaximal D4 stability group appears. This is a contribution to the literature about Michel’s conjecture.
Integrals for two-loop calculations in massless QCD
Authors: Kramer G. , Lampe B.
Published: July 2002

Tools that have been developed for the extension of the Sterman–Weinberg formula in two-loop order are presented. They are the essential ingredients for any perturbative two-loop calculation in a massless theory. Introducing dimensional regularization, this paper deals with poles up to fourth order in the dimensional parameters. The virtual two-loop integrations as well as real ones over phase space are studied.
On the generalization of Szafron solutions of Einstein field equations
Authors: Bona C. , Stela J. , Palou P.
Published: July 2002

The explicit form of the solutions of the Einstein field equations corresponding to a perfect fluid in geodesic, hypersurface-orthogonal motion is given with the following restrictions: (i) the comoving hypersurfaces are flat; and (ii) the second fundamental form of these surfaces is degenerate. These results are a natural extension of the metrics previously found by Szafron and co-workers [D. A. Szafron and J. Wainwright, J. Math. Phys. 18, 1668 (1977); D. A. Szafron, ibid. 18, 1673 (1977); D. A. Szafron and C. B. Collins, ibid. 20, 2354 (1979)] as a perfect fluid generalization of the Szekeres dust solutions.
On classical action at a distance theories which contain a cutoff
Authors: Burgers G. J. H. , Van Dam H.
Published: July 2002

It is pointed out that a certain class of classical relativistic action at a distance theories contains a cutoff which eliminates self-interaction of the particles. This cutoff is put in by hand, but one might hope that eventually it may be produced by considerations of space-time in the small. This class of theories is extended from models that closely mimic classical electrodynamics to models that resemble Yang–Mills and gravity.
On unusual statistics and quantum point vortices
Authors: Goldin Gerald A. , Menikoff Ralph , Sharp David H.
Published: July 2002

In an ideal two-dimensional incompressible fluid, θ statistics for a pair of identical quantum point vortices is not well defined.
On a property of a classical solution of the nonlinear mass transport equation u
t=u
x
x/1+u
x 2. II
Authors: Kitada Akihiko , Umehara Hiroyuki
Published: July 2002

A mechanism of smoothing due to evaporation condensation of the roughly perturbed surface of solid is formulated by Mullins [W. W. Mullins, J. Appl. Phys. 28, 333 (1957); 30, 77 (1959)] as a certain Cauchy problem for a nonlinear parabolic equation which describes the evolution of the profile of the surface. In the preceding paper [A. Kitada, J. Math. Phys. 27, 1391 (1986)], through the careful investigations of the Cauchy problem, it was demonstrated that each peak in the initial surface did not increase in height with time. In the present paper, by slightly limiting the set of functions to which the classical solutions of the Cauchy problem belong, it is demonstrated that each peak height decreases with time in the strict sense.
Fractal and nonfractal behavior in Levy flights
Authors: Cheng Zheming , Savit Robert
Published: July 2002

The d-dimentional space-continuous time-discrete Markovian random walk with a distribution of step lengths, which behaves like x−(α+d) with α>0 for large x, is studied. By studying the density–density correlation function of these walks, it is determined under what conditions the walks are fractal and when they are nonfractal. An ensemble average of walks is considered and the lower entropy dimension D of the set of stopovers of the walks in this ensemble is calculated, and D=min{2,α,d} is found. It is also found that the fractal nature of the walks is related to a finite value of the mean first passage time. The crossover of the correlation function from the fractal to nonfractal regimes is studied in detail. Finally, it is conjectured that these results for the lower entropy dimension apply to a wide class of symmetric Markov processes.
Pole term decomposition of the resolvent kernel in Fredholm’s form
Authors: Matsui Yoshiko
Published: July 2002

The resolvent kernel represented by a ratio of two Fredholm’s series can be reformed into a sum of two ratios, only one of which contains Fredholm’s determinant in its denominator. The general results presented are then used to apply Faddeev’s residue prescription in the case of the rank N separable potential for determining those three-body scattering amplitudes in which a two-particle bound state is in the initial and/or final configuration. As a numerical example, the triton binding energy and the doublet scattering length for the Tabakin potential are calculated.
Generalization of the N=1 supersymmetric effective Lagrangian to arbitrary N in the absence of central charges
Authors: El Hassouni A. , Oudrhiri-Safiani E. G. , Saidi E. H.
Published: July 2002

Using nonlinear realization, extended supersymmetry breaking is studied. The N-extended Volkov–Akulov and standard superfields are constructed and the N generalized Wess constraints in the presence of central charges are given. The extended Volkov–Akulov Lagrangian and the N-extended effective Lagrangian are constructed for arbitrary N in the absence of central charges.
Canonical map approach to channeling stability in crystals. II
Authors: Sáenz A. W.
Published: July 2002

A nonrelativistic and a relativistic classical Hamiltonian model of two degrees of freedom are considered describing the plane motion of a particle in a potential V(x1,x2)[(x1,x2) =Cartesian coordinates]. Suppose V(x1,x2) is real analytic in its arguments in a neighborhood of the line x2=0, one-periodic in x1 there, and such that the average value of ∂V(x1,0)/∂x2 vanishes. It is proved that, under these conditions and provided that the particle energy E is sufficiently large, there exist for all time two distinguished solutions, one satisfying the equations of motion of the nonrelativistic model and the other those of the relativistic model, whose corresponding configuration-space orbits are one-periodic in x1 and approach the line x2=0 as E→∞. The main theorem is that these solutions are (future) orbitally stable at large enough E if V satisfies the above conditions, as well as natural requirements of linear and nonlinear stability. To prove their existence, one uses a well-known theorem, for which a new and simpler proof is provided, and properties of certain natural canonical maps appropriate to these respective models. It is shown that such solutions are orbitally stable by reducing the maps in question to Birkhoff canonical form and then applying a version of the Moser twist theorem. The approach used here greatly lightens the labor of deriving key estimates for the above maps, these estimates being needed to effect this reduction. The present stability theorem is physically interesting because it is the first rigorous statement on the orbital stability of certain channeling motions of fast charged particles in rigid two-dimensional lattices, within the context of models of the stated degree of generality.
Local Green’s function. I
Authors: Wang Renchuan
Published: July 2002

The local Green’s function is used in many physical problems. In this paper, the properties of the local Green’s function are studied, and it is proved that the N×N local Green’s function can represent the results of the full N1×N1 Green’s function, where N is small (or at least finite) and N1 is large (or infinite). The accuracy of cutting the general Green’s function into the local Green’s function is also discussed.
Local Green’s function. III
Authors: Wang Renchuan
Published: July 2002

In this paper a way of solving for the local Green’s function by means of a projection operator method is presented. Both a procedure for attacking the problem and a general formula for calculation are obtained. It is also proved that the calculation can be done with a finite number of basis functions. A short discussion of the accuracy is also presented.
Tunneling in one-dimensional ideal barriers
Authors: Kowalski Jacek M. , Fry John L.
Published: July 2002

General properties of the transmission coefficient of an ideal, one-dimensional potential barrier of arbitrary shape are studied. It is proved that an arbitrary symmetric barrier is perfectly transparent for at least one energy in each energy band of the related band problem, where the barrier potential is periodically continued on the whole real axis. Recursion relations are obtained for transmission coefficients of barriers consisting of 2k structural units. They are used in a simple proof showing that transmission coefficients of finite barriers composed of m identical arbitrary structural units have chaotic behavior for almost all energies for m→∞ in each energy band. There exists, however, becoming more dense with m, a countable set of energies in each energy band where finite repeated barriers are perfectly transparent. The results are illustrated by a numerical example.