bluuebunny/crossref_metadata_2025 huggingface dataset:
A dipole-bound dianion
Authors: Skurski Piotr , Simons Jack
Published: July 2002

The possibility of binding two electrons by the dipole potential of a molecule was examined earlier by us using model potentials. That study suggested that large dipole moments μ=qR and large charge separation distances R (or equivalently large charges q) would be required to achieve binding two electrons. For example, even with a charge q=1.5 a.u. which might be achieved using di- or tri-valent cations, a dipole moment exceeding 15.922 D is needed. The presence of inner-shell electrons even further increases the value of μ that is required because the dipole-bound electrons’ orbital must be orthogonal to and excluded from such inner shells. In the present work, we discuss our efforts to find a real molecule that can actually bind two electrons to a single dipole site. Numerical results are presented for the mono- and dianions of a double 5-member carbon ring system substituted with a Ca atom and three superhalogen −PF5 groups. The dianion of this molecule is found to be geometrically stable and to have a vertical electron detachment energy of ca. 0.8 eV. Its two excess electrons occupy the same fully symmetric a1 molecular orbital localized at the electropositive Ca end of the neutral system as is routinely observed in dipole-bound monoanions. Although our final candidate is chemically unusual, it is hoped that our predictions about it will encourage others to search for more synthetically tractable alternatives.
Asymmetry and rectification in the tunnel current of a nanometer-sized metal-conjugated polymer–metal junction
Authors: Yau S.-T. , Zhang C. , Innis P. C.
Published: July 2002

Electron transport processes of a nanometer metal-conjugated polymer–metal tunnel junction have been probed using a scanning tunneling microscope. The tunnel current of the junction shows two effects. The appearance of an asymmetry in the tunnel current indicates that the junction transport mechanism is different from that for which tunneling occurs directly between two metallic electrodes. Thus, understanding of the asymmetry and hence the transport mechanism demands a detailed description of the metal–polymer interface. By applying the theories of the metal–semiconductor interface to the tunnel junction, we show the presence of an asymmetric electrostatic potential-energy profile, which, together with the metal-induced gap states in the polymer, gives rise to the observed asymmetry in the tunnel current. In some cases, a threshold of anomalously large currents enhances the current asymmetry to give rise to rectification, indicating carrier excitations and carrier multiplication processes in the junction. Our results show that a detailed description of the interface electronic structure is essential to understanding electron transport in devices based on organic molecules.
Response to “Comment on ‘Frequency-dependent polarizabilities, hyperpolarizabilities, and excitation energies from time-dependent density-functional theory based on the quasienergy derivative method’ ” [J. Chem. Phys. 112, 6938 (2000)]
Authors: Aiga Fumihiko , Tada Tsukasa , Yoshimura Reiko
Published: July 2002

We replied to the comment by Banerjee and Harbola on our previous paper [J. Chem. Phys. 111, 2878 (1999)]. As their comment, the basic direction of our previous paper is similar to theirs [Phys. Lett. A 236, 525 (1997) and Eur. Phys. J. D 5, 201 (1999)]. However, there exist the significant differences between them concerning (1) the description of the exchange-correlation quasienergy functional, (2) the universality of the expression of hyperpolarizabilities, (3) the derivation of the expression for the excitation energies and transition moments, and (4) the orbital quasienergy matrix in the coupled-perturbed Kohn–Sham equation.
The singlet–triplet separation in dichlorocarbene: A surprising difference between theory and experiment
Authors: Barden Christopher J. , Schaefer Henry F.
Published: July 2002

The recently reported experimental singlet–triplet energy separation in CCl2, namely 3±3 kcal/mol, lies far below extant theoretical predictions. This problem is investigated here at much higher levels of theory than previously applied. The present theoretical prediction is 19.5±2 kcal/mol.
Intramolecular Coulomb repulsion and anisotropies of the repulsive Coulomb barrier in multiply charged anions
Authors: Wang Xue-Bin , Nicholas John B. , Wang Lai-Sheng
Published: July 2002

Photoelectron spectra of the three isomers of the benzene dicarboxylate dianion (o-, m-, and p-BDC2−) were measured in the gas phase at five photon energies. Detachment features from the carboxylate groups and the π electrons of the ring were clearly observed and distinguished. The electron binding energies were found to increase from the very small value of ∼0.2 eV in o-BDC2− to about 1.0 eV in p-BDC2−, due to the reduced Coulomb repulsion as the two excess charges become farther apart. We found that the repulsive Coulomb barrier (RCB) for detaching electrons from the carboxylates decreases from o-BDC2− to p-BDC2−. However, the RCB for detaching the ring π electrons was found to be significantly higher and remain constant for the three isomers. This distinct anisotropy in the RCB involving different detachment channels is related to the different intramolecular Coulomb repulsions experienced by electrons localized on the carboxylates and the ring. Theoretical calculations were performed to obtain the equilibrium structures of both the dianions and the monoanions and to gain insight into the intramolecular electrostatic interactions. The two carboxylates in m- and p-BDC2− were shown to be in-plane with the ring whereas the strong Coulomb repulsion in o-BDC2− forces the carboxylate groups out of the plane of the ring. The theoretical results clearly show the localized nature of the excess charges on the carboxylates and help us understand the intramolecular Coulomb repulsions within the three dianions.
On the intrinsic behavior of the internal variable in the Finslerian gravitational field
Authors: Ikeda Satoshi
Published: July 2002

A structural extension of the gravitational field is attempted in reference to the theory of Finsler spaces: The vector y is attached to each point x as the internal variable and the intrinsic behavior of y is reflected in the whole spatial structure.
A path-integral–Riemann-space approach to the electromagnetic wedge diffraction problem
Authors: Ziolkowski Richard W.
Published: July 2002

A path integral constructed over a particular Riemann space is developed and applied to two-dimensional wedge problems. This path-integral–Riemann-space (PIRS) approach recovers the exact solutions of the heat conduction and the corresponding electromagnetic wedge problems. A high-frequency asymptotic evaluation of the PIRS electromagnetic wedge solution returns the standard geometrical theory of diffraction (GTD) results. Ramifications of this approach and its relationships with known path-integral methods are examined.
Large-N solution of the Klein–Gordon equation
Authors: Chatterjee Ashok
Published: July 2002

An iterative 1/N expansion scheme is developed to solve the Klein–Gordon equation to obtain the energy spectrum of a scalar particle in a spherically symmetric potential. For the Coulomb potential, this approach is shown to yield the exact results.
Four-dimensional boson field theory. II. Existence
Authors: Baker George A.
Published: July 2002

The existence of the continuum, quantum field theory found by Baker and Johnson [G. A. Baker, Jr. and J. D. Johnson, J. Phys. A 18, L261 (1985)] to be nontrivial is proved rigorously. It is proved to satisfy all usual requirements of such a field theory, except rotational invariance. Currently known information is consistent with rotational invariance however. Most of the usual properties of other known Euclidean boson quantum field theories hold here, in a somewhat weakened form. Summability of the sufficiently strongly ultraviolet cutoff bare coupling constant perturbation series is proved as well as a nonzero radius of convergence for high-temperature expansions of the corresponding continuous-spin Ising model. The description of the theory by these two series methods is shown to be equivalent. The field theory is probably not asymptotically free.
On the exceptional equivalence of complex Dirac spinors and complex space-time vectors
Authors: Nash Patrick L.
Published: July 2002

It is well known that there exists an equivalence of R8 vectors and spinors, which has its roots in the rotational symmetry of the Dynkin diagram for D4. We endow R8 with a real action of ∼(SO(4,4)), and restrict to ∼(SO(3,1)). Under this restriction the R8 spinor decomposes into the direct sum of two real Dirac spinors, while the R8 vector decomposes into a real space-time vector plus four real scalars. The equivalence is preserved under this restriction; it is shown that it is realized in the (exceptional) equivalence of a complex Dirac spinor and a complex space-time vector.
Dynamic-group approach to the x2+λx2/(1+g
x2) potential
Authors: Fack V. , De Meyer H. , Vanden Berghe G.
Published: July 2002

A modified operator method based upon the SO (2,1) dynamic group is applied to the one-dimensional anharmonic oscillator potential V(x)=x2+λx2/(1+gx2). A tilting transformation is carried out in order to improve the rate of convergence of the algebraic perturbation series. Very accurate results are obtained for the energy eigenvalues and for the wave functions especially in the case of small g-values.
The unboundedness of the gravitational partition function
Authors: Broda B.
Published: July 2002

The unboundedness of the gravitational partition function Z is formally established. First the Euclidean path integral representation for Z, in terms of the renormalized effective action Seffren, is derived. Next it is shown that for ‘‘strong’’ fields, Seffren is unbounded from below. The possible influence of the space-time topology is taken into account.
Principal five-dimensional subalgebras of Lie superalgebras
Authors: Van der Jeugt Joris
Published: July 2002

The analog of sl(2) for Lie superalgebras is osp(1,2), a five-dimensional superalgebra. All basic classical Lie superalgebras L that contain a principal five-dimensional osp(1,2) subalgebra are classified. Moreover, the decomposition of the standard representation and of the adjoint representation of L into irreducible components of the principal osp(1,2) subalgebra is given.
Cohomology in connection space, family index theorem, and Abelian gauge structure
Authors: Hou Bo-Yu , Zhang Yao-Zhong
Published: July 2002

Using the natural connection form on a principal bundle P(M,G) and the bundle 𝔄(𝔄/𝒢,𝒢) a systematic derivation of the double-cohomological series constituted by the exterior differential d on space-time M and arbitrary, horizontal, and vertical variations in connection space is given. The relationship between these cohomologies and the family index theorem is clarified. The formalism is then used to analyze Abelian gauge structure inside non-Abelian gauge theory. The pertinent functional U(1) connection form, curvature form, and three-form ‘‘curvature’’ are identified and computed, and are related to the θ vacuum, anomalous commutation relation, and Jacobi identity, respectively. Some of the results differ from those obtained by Wu and Zee [Nucl. Phys. B 258, 157 (1985)] and Niemi and Semenoff [Phys. Rev. Lett. 55, 227 (1985)] and the results of this paperrecover theirs under certain conditions. Finally the generalization of the formalism to a nontrivial principal bundle by introduction of a fixed background connection form is discussed.
Series representations for calculations in quantum statistics. III
Authors: Barker William A.
Published: July 2002

In two previous papers [J. Math. Phys. 27, 1 (1986) (I); 28, ▪ ▪ ▪ (1987) (II)] simple mathematical procedures are developed for averaging the particle energy ε, raised to any power p≥1 over Maxwell–Boltzmann, Bose–Einstein, and Fermi–Dirac distributions. In I, the particle energy is treated nonrelativistically: ε=p2/2m. In II, the particle energy is treated ultrarelativistically: ε=pc. Here, the particle energy is treated relativistically ε2=p2c2+m20c4. For each distribution function, expressions are obtained for the chemical potential, internal energy, and heat capacity for two cases: (kT/m0c2)2≪1 and (m0c2/kT)2≪1.
Some aspects of the isogroup of the self-dual Yang–Mills system
Authors: Papachristou C. J. , Harrison B. Kent
Published: July 2002

A generalized isovector formalism is used to derive the isovectors and isogroup of the self-dual Yang–Mills (SDYM) equation in the so-called J formulation. In particular, the infinitesimal ‘‘hidden symmetry’’ transformation, a linear system, and a well-known Bäcklund transformation of the SDYM equation are derived in the process. Thus symmetry and integrability aspects of the SDYM system appear in natural relationship to each other within the framework of the isovector approach.
The invariant density for a class of discrete-time maps involving an arbitrary monotonic function operator and an integer parameter
Authors: Grosjean C. C.
Published: July 2002

When xt and xt+1 represent two random variables, each belonging to a real interval [0,1] and being related by a first-order difference equation xt+1=F(xt), called a discrete-time map, the probability density distribution connected with xt can be translated into that associated with xt+1. This yields an evolution equation by means of which one can construct an infinite sequence {wt(x)‖t∈N, x∈[0,1]} starting from an integrable function w0(x) normalized to unity on [0,1]. The question of the convergence of the sequence toward a so-called invariant density function w(x) as t→+∞ and the problem of finding this limit were examined by a number of authors, mostly studying isolated cases. The present paper solves the problem for a class of discrete-time maps characterized by xt+1 =f(‖sn[l sn−1f−1(xt)]‖), l∈{2,3,...}, whereby f is a real, continuous, monotonically increasing function mapping [0,1] onto itself and sn is the usual symbol for the sinelike Jacobian elliptic function with modulus k∈[0,1] (including the sine function). Convergence is proven under very general conditions on w0(x) and an explicit formula to calculate w(x) is established. Some properties of w(x) are discussed. A necessary and sufficient condition for the symmetry of w(x) about x= 1/2 is obtained and attention is also devoted to the inverse problem, leading to a reformulation of the discrete-time map of the type cited above which corresponds to a given invariant density. The examples of practical application considered here cover almost all special cases which were treated in the literature thus far, as well as new cases.
Component states of a composite quaternionic system
Authors: Nash C. G. , Joshi G. C.
Published: July 2002

The problem of finding component states given a composite state is examined for quaternionic quantum mechanics. It is shown that under very loose conditions the component state is forced to be complex.
Nonorientable one-loop amplitudes for the bosonic open string: Electrostatics on a Möbius strip
Authors: Rodrigues João P.
Published: July 2002

The partition function, N-point scalar, and four-point vector nonorientable one-loop amplitudes for the bosonic open string in the critical dimension are obtained using a first quantized path integral treatment of Polyakov’s string that assumes scale independence.
A power counting formula for short distance singularities in quantum field theory
Authors: Hurd T. R.
Published: July 2002

A power counting formula for the short distance singularities in quantum field theory is presented. This configuration space version of Weinberg’s theorem applies to any renormalized Feynman amplitude, and is proved by a simple extension of the tree expansion method.
Gravitational instability in a multicomponent cosmological medium
Authors: Mathai A. M. , Haubold H. J. , Mücket J. P. , Gottlöber S. , Müller V.
Published: July 2002

A systematic approach to exact solutions for the evolution of small density inhomogeneities of a two-component and in special cases for a three-component cosmological medium is presented. In general, there exists just one increasing perturbation mode. Expressing the solutions of the respective differential equations in terms of Meijer’s G function [Proc. Nederl. Akad. Wetensch. A 49, 344 (1946)] various exact and asymptotic formulas for the perturbation modes are derived.
The inverse problem concerning symmetries of ordinary differential equations
Authors: Gonzalez-Gascon F. , González-López A.
Published: July 2002

It is shown that for any local Lie group G of transformations in R×Rn there exist differential systems of the form x(m=f(t,x,...,x(m−1), which are symmetrical under G. The order m_ of these systems is related to r_, the number of essential parameters of G.
Quantum systems with external electromagnetic fields: The large mass asymptotics
Authors: Papiez L. , Osborn T. A. , Molzahn F. H.
Published: July 2002

The large mass asymptotics of the quantum evolution problem for a system of charged particles that mutually interact through scalar fields and couple to an arbitrary time-varying external electromagnetic field is rigorously described. If K(x,t; y,s;m) denotes the coordinate space propagator (time evolution kernel) of this system, the singular perturbation behavior of K as mass m→∞ is expressed in terms of a gauge invariant asymptotic expansion. In terms of the external fields and interparticle interactions, this expansion provides a nonperturbative approximation for the propagator K that is valid for all particle coordinates x, y and for finite time displacements t−s. For the class of analytic scalar and vector fields that are defined as Fourier transforms of time-dependent measures, the existence of this asymptotic series for K in powers of (m)−1 is established for both real and complex masses. Explicit bounds for the error term are obtained and a manifestly gauge invariant transport recurrence relation is derived that uniquely determines all the coefficient functions of the asymptotic series. The small time asymptotic expansion of K is shown to be embedded within the large mass expansion.
Coherent states over symplectic homogeneous spaces
Authors: De Bièvre S.
Published: July 2002

A generalization of the Perelomov procedure for the construction of coherent states is proposed. The new procedure is used to construct systems of coherent states in the carrier spaces of unitary irreducible representations of groups G=S∅V, where V is a vector space and S⊂GL(V). The coherent states are shown to be labeled by the points in cotangent bundles T*𝒪* of orbits 𝒪* of S in V*, the dual of V; it is proven that T*𝒪* is a symplectic homogeneous space of G. The generalized procedure for the construction of coherent states presented in this paper is shown to encompass as special cases the constructions known in the literature for the coherent states of the Weyl–Heisenberg, the ‘‘ax+b,’’ and the Galilei and Poincaré groups. Moreover, completely new sets of coherent states are constructed for the Euclidean group E(n), where the Perelomov construction fails.
Group cocycles, line bundles, and anomalies
Authors: Blau Matthias
Published: July 2002

The relation between complex line bundles and certain group cocycles is explored in general to obtain explicit formulae for the transition functions and curvature of the determinant line bundle DET of a family of Dirac operators coupled to Yang–Mills fields. A covariant derivative on sections of DET is constructed which realizes the curvature and ‘‘minimally couples’’ to the integrated anomaly which thus appears as a ‘‘functional magnetic field’’ on gauge orbit space. The transcription of group cohomological (cocycles) into geometrical (line bundles) information is refined in such a way that the relevant cohomology groups can be computed in many cases, giving insight into the classification of lifts of principal group actions.
A Kerr object embedded in a gravitational field. II
Authors: Krori K. D. , Bhattacharjee R.
Published: July 2002

Starting with a Weyl solution representing an axially symmetric gravitational field as the seed metric, a generalized Kerr solution is generated by the Belinskii–Zakharov technique [Sov. Phys. JETP 48, 985 (1978); 50, 1 (1980)]. This solution may be interpreted as a Kerr metric embedded in a gravitational field.
N=2 superprojective transformations and the nilpotent invariant
Authors: Nogueira P.
Published: July 2002

The nilpotent quantity that is invariant under the N=2 superprojective transformations is constructed. Also commented on is the parametrization of such transformations.
Semiclassical quantization for Coulomb systems on a hypersphere
Authors: Kvitsinsky Andrei A. , Kostrykin Vadim V.
Published: July 2002

As an approach to the highly excited states of a Coulomb three-body system, a Schrödinger operator on a hypersphere of radius ρ, the hyperradius of the system, is considered. A corresponding spectral problem is studied in the limit ρ→∞, which is interpreted as semiclassical. For two particular models, the semiclassical quantization rules for eigenvalues along with the WKB-type approximations for eigenfunctions are obtained. One of the models imitates a heliumlike atom in the Wannier region.
Separation of variables for the Dirac equation in an extended class of Lorentzian metrics with local rotational symmetry
Authors: Iyer B. R. , Kamran N.
Published: July 2002

The question of the separability of the Dirac equation in metrics with local rotational symmetry is reexamined by adapting the analysis of Kamran and McLenaghan [J. Math. Phys. 25, 1019 (1984)] for the metrics admitting a two-dimensional Abelian local isometry group acting orthogonally transitively. This generalized treatment, which involves the choice of a suitable system of local coordinates and spinor frame, allows one to establish the separability of the Dirac equation within the class of metrics for which the previous analysis of Iyer and Vishveshwara [J. Math. Phys. 26, 1034 (1985)] had left the question of separability open.
On the isovectors of the principal chiral model
Authors: Hu Zhi-Jin
Published: July 2002

In this paper the principal chiral model with isovector techniques is dealt with [B. K. Harrison and F. B. Estabrook, J. Math. Phys. 12, 653 (1971); C. J. Papachristou and B. K. Harrison, J. Math. Phys. 28, 1261 (1987)]. Due to the ‘‘on shell’’ property of the symmetry related to integrability [M. L. Ge and Y. S. Wu, Phys. Lett. B 108, 411 (1982), L. L. Chau, M. L. Ge, and Y. S. Wu, Phys. Rev. D 25, 1086 (1982); B. Y. Hou, M. L. Ge, and Y. S. Wu, Phys. Rev. D 24, 2238 (1981)], the linear system is derived from the internal part of the isogroup after the determining equation is localized. When the geometric part of the derived isovectors is analyzed, a set of operators acting on space-time are found, which make up an infinite-dimensional invariant algebra of the principal chiral model.
A covariant extrapolation of the noncovariant two particle Wheeler–Feynman Hamiltonian from the Todorov equation and Dirac’s constraint mechanics
Authors: Crater Horace , Yang Dujiu
Published: July 2002

A semirelativistic expansion in powers of 1/c2 is canonically matched through order (1/c4) of the two-particle total Hamiltonian of Wheeler–Feynman vector and scalar electrodynamics to a similar expansion of the center of momentum (c.m.) total energy of two interacting particles obtained from covariant generalized mass shell constraints derived with the use of the classical Todorov equation and Dirac’s Hamiltonian constraint mechanics. This determines through order 1/c4 the direct interaction used in the covariant Todorov constraint equation. We show that these interactions are momentum independent in spite of the extensive and complicated momentum dependence of the potential energy terms in the Wheeler–Feynman Hamiltonian. The invariant expressions for the relativistic reduced mass and energy of the fictitious particle of relative motion used in the Todorov equation are also dynamically determined through this order by this same procedure. The resultant covariant Todorov equation then not only reproduces the noncovariant Wheeler–Feynman dynamics through order 1/c4 but also implicitly provides a rather simple covariant extrapolation of it to all orders of 1/c2.
Unimodular theory of gravity and the cosmological constant
Authors: Ng Y. Jack , van Dam H.
Published: July 2002

The unimodular theory of gravity with a constrained determinant gμν is equivalent to general relativity with an arbitrary cosmological constant Λ. Within this framework Λ appears as an integration constant unrelated to any parameters in the Lagrangian. In a quantum theory the state vector of the universe is thus expected to be a superposition of states with different values of Λ. Following Hawking’s argument one concludes that the fully renormalized Λ=0 completely dominates other contributions to the integral over Λ in the vacuum functional. In this scenario of the unimodular theory of gravity the cosmological constant problem is solved. Furthermore, this formulation naturally provides an external (cosmic) time for time ordering of measurements so that the quantum version of the unimodular theory can have a normal ‘‘Schrödinger’’ form of time development, giving a simpler interpretation to the equation of the universe.
Relations between universal scaling constants for the circle map near the golden mean
Authors: Delbourgo R. , Kenny Brian G.
Published: July 2002

The two-frequency quasiperiodic route to chaos is believed to be modeled by the critical circle map and the universal behavior of the scaling constants α and δ is determined by the order z of the inflection point. We have numerically determined α(z) and δ(z) as a function of this order. Using the renormalization group equations, we have succeeded in obtaining approximate analytical relations for α and δ that agree quite well with the data. In the limit as z→∞, we argue that ‖δ‖→1/ρ3=4.236 and δ/αz→1, in good agreement with the numerical computations.
On the superalgebras built from SO(3) tensor operators
Authors: Minnaert Pierre , Mozrzymas Marek
Published: July 2002

A study is made of the superalgebra structures of the sets of SO(3) tensor operators TLM(j,j) and TLM(j,j′). It is shown that for each set of operators there exist natural splittings in two subsets that form, respectively, the even and odd parts of a superalgebra. The superalgebras built in this way are: gl(j‖j+1) for integer j, gl(j+1/2‖j+1/2) for half-odd integer j, gl(2j+1‖2j′+1) for all j and j′, the orthosymplectic superalgebras, P(2j+1) and Q(2j+1) for all j, gl(j+j′+1‖j+j′+1) [or gl(j+j′‖j+j′+2)] for j and j′ both integers with j+j′ odd (or even) and gl(j+j′+1‖j+j′+1) for j and j′ both half-odd integers.
Dyson’s correlation functions and graded symmetry
Authors: Guhr Thomas
Published: July 2002

A new derivation of Dyson’s k-level correlation functions of the Gaussian unitary ensemble (GUE) is given. The method uses matrices with graded symmetry. The number of integrations needed for the ensemble average becomes independent of the level number N. For arbitrary level number N, the k-level correlation function is expressed as an integral involving the eigenvalues of a 2k×2k graded matrix. The limit of infinitely many levels N→∞ is calculated by a simple saddle-point approximation of this integral, avoiding the introduction of Hermite polynomials and oscillator wave functions.
Non-Abelian group quantization and quantum kinematic invariants of some noncompact Lie groups
Authors: Krause J.
Published: July 2002

The formalism of non-Abelian group quantization is briefly revisited, within the regular representation of noncompact Lie groups. It is shown that some of such r-dimensional groups have a set of r basic quantum-kinematic invariants, which substantially differ from the traditional invariants. The relation of the traditional invariants of the Lie algebra with the new quantum-kinematic invariants is also briefly examined. This paper contains two miscellaneous examples of quantum-kinematic invariant operators.
Central extensions of sphere groups
Authors: Dowker J. S.
Published: July 2002

Closed forms for the central extensions of the infinite dimensional Lie algebras of smooth maps from two- and three-spheres to compact Lie groups are given.
A rational interaction: Lower bound on the number of I-PI graphs without tadpoles
Authors: DaCosta G. A. T. F.
Published: July 2002

A lower bound on the number of I-PI connected graphs without tadpoles that will be important in the proof of the divergence of the perturbation series of a model with rational interaction is obtained.
Novel solution of the one-dimensional quantum-mechanical harmonic oscillator
Authors: Fradkin David M.
Published: July 2002

The classical solution is used as a variable for the one-dimensional quantum-mechanical oscillator, and this leads to a separable differential equation solvable in closed form which yields a set of new quantum mechanical solutions, not energy eigenfunctions, that have the property of being localized. These new solutions are shown to be eigenfunctions of a time-independent position operator. The operator algebra of that operator and an analogous momentum operator is given, as well as the relationship of the eigenfunctions to the energy eigenfunction set. The new eigenfunctions, which are not square integrable but possess a δ-function normalization, themselves represent wavepackets that at times corresponding to when the classical position is at an extremum collapse to Dirac δ functions.
Orbit–orbit branching rules between simple low-rank algebras and equal-rank subalgebras
Authors: Gingras F. , Patera J. , Sharp R. T.
Published: July 2002

Complete orbit–orbit branching rules, or equivalently, reduction of Weyl group orbits, between each simple algebra of rank 3 or less, and its equal-rank subalgebras and between F4 and each of its equal-rank subalgebras are given. The generic case An⊇An−1×U(1), the subjoining F4≳B3×U(1), and E8⊇E6×A2 (first and seventh highest weight labels nonzero) are also treated. Branching rules between rank 4 and 5 simple algebras and E6 and their equal-rank subalgebras are available in a depository.
Realization of the discrete series of unitary representations of Sl(2,R) in terms of creation and annihilation operators
Authors: MacDowell Samuel W.
Published: July 2002

A basis for the Hilbert space of the discrete series of unitary representations of Sl(2,R) is constructed as a complete set of coherent states of pairs of particle–antiparticle creation operators. The integer q specifying an irreducible representation is the eigenvalue of the charge operator. Representations with charges ∓q are equivalent.
Functional calculus of the Borel transform
Authors: Boenkost W. , Constantinescu F.
Published: July 2002

An explicit form is given of the Borel transform B̃ of g■f where g■f(z):=g( f(z)) with f Borel summable and g analytic in f(0) and a detailed study of the singularities in B̃ (in the Borel variable) is made. Examples include g(ξ)=1/ξ, log ξ and eξ. The present paper generalizes results of Boenkost et al. [J. Math. Phys. 29, 1118 (1987)].
A new asymptotic form for the Laguerre polynomials
Authors: Smith A. P.
Published: July 2002

A new asymptotic formula in terms of elementary functions is demonstrated for the Laguerre polynomials Lαn(x) in the limit when all three parameters (n,α,x) become large. This asymptotic limit appears in the problem of obtaining the low-field semiclassical approximation from the full quantum mechanical behavior of a two-dimensional electron gas in a magnetic field.
Solvable nonlinear integrodifferential equations of Boltzmann type. I
Authors: Calogero F.
Published: July 2002

A technique suitable to manufacture solvable nonlinear integrodifferential equations of Boltzmann type is introduced. Some examples of solvable homogeneous one-dimensional Boltzmann-like equations are exhibited.
Hidden symmetries of two-dimensional systems with local degeneracies
Authors: Mayrand Michel , Vinet Luc
Published: July 2002

The energy spectrum of a nonrelativistic particle in radial potentials of the form V(r) = αr 2d−2 − βr d−2 shows one level with a singularly high multiplicity. The two-dimensional problems are focused upon and the constants of motion that generate the symmetries responsible for this local accidental degeneracy are determined. The conserved operators realize an SU(2) algebra and the bound states are seen to fall into either finite, semibounded, or unbounded representations of this algebra. An SO(3,2) module encompassing the eigenstates associated to the whole set of potentials is also identified. It is further shown that there exists a second coordinate system besides the polar one in which the Schrödinger equation separates. Finally, it is indicated how the two-dimensional Coulomb and harmonic oscillator problems arise as special cases.
Degenerations of generalized Krichever–Novikov algebras on tori
Authors: Schlichenmaier Martin
Published: July 2002

Degenerations of Lie algebras of meromorphic vector fields on elliptic curves (i.e., complex tori) which are holomorphic outside a certain set of points (markings) are studied. By an algebraic geometric degeneration process certain subalgebras of Lie algebras of meromorphic vector fields on P1, the Riemann sphere, are obtained. In case of some natural choices of the markings these subalgebras are explicitly determined. It is shown that the number of markings can change.
Vertex operators in Hilbert space
Authors: Boenkost W. , Constantinescu F.
Published: July 2002

Free vertex operators V(γ,z) are introduced as operators in Hilbert space. They are densely defined for ‖z‖<1. Any radially ordered product of vertex operators is defined on a dense subset as an operator product. ∥V(γ,z)Ψ∥ is bound by ∥exp(cN)Ψ∥ for appropriate Ψ, where N is the number operator and c is a positive constant. These results are applied to screened vertex operators.
A factorization method with application to perturbation theory
Authors: Fernández Francisco M. , Castro E. A.
Published: July 2002

A new implementation of perturbation theory is presented for separable problems which is a blend of two previously proposed factorization methods. The resulting technique offers several advantages with respect to the parent methods and yields the perturbation corrections exactly in terms of the quantum numbers of the unperturbed problem through equations in which the unperturbed eigenfunction does not appear explicitly. As an example a perturbed Legendre equation is considered and the application of the approach to other problems of physical interest is discussed.
p-adic superanalysis. II. Supermanifolds and differential operators
Authors: Cianci Roberto , Khrennikov Andrew
Published: July 2002

This article is the second part of a work in which p-adic supermanifold theory is studied; by using the algebraic approach introduced in the first part of this work, p-adic superdifferential maps are introduced and, by restricting attention to the class of strictly differential maps, the foundation of p-adic supermanifold theory is developed herein. In particular it is shown that the superfield expansion theorem is no longer true: a superdifferential odd variables map which is not a polynomial is constructed. Finally, tangent space and Lie derivatives are constructed, and it is shown that no complex-valued fermion field of the p-adic argument could exist.
Optimized multicenter expansions
Authors: Foulis D. L.
Published: July 2002

A new approach to multicenter spherical harmonic expansions is presented, which is based on Fourier transform and variational methods. The individual radial functions are optimized simultaneously over all sites at each order of spherical harmonics; and it is conjectured that the resulting expansions, for arbitrary functions in three dimensions, will be more rapidly convergent than any other type. Both iterative and closed-form solutions are developed. The analogous cases for two- and one-dimensional functions are also treated and examples for all three cases are provided. The one-dimensional case is found to be qualitatively different. In a (perhaps) surprising theorem it is proved that, given N≥2 distinct points of R and N (not necessarily equivalent) choices of parity, an arbitrary one-dimensional function may be exactly decomposed as the sum of N functions each having one of the chosen parities at one of the points. The decomposition is not unique.
Inönü–Wigner contraction of Kac–Moody algebras
Authors: Majumdar Parthasarathi
Published: July 2002

Inönü–Wigner contractions of affine Kac–Moody algebras are discussed here. The Sugawara construction for the contracted affine algebra exists only for a fixed value of the level k, which is determined in terms of the dimension of the uncontracted part of the starting Lie algebra, and the quadratic Casimir in the adjoint representation. Further, contractions of the G/H coset spaces are discussed, and an affine translation algebra is obtained, which yields a Virasoro algebra [via a Goddard–Kent–Olive (GKO) construction] with a central charge given by dim(G/H).
Axially symmetric instantons in generalized Yang–Mills theory in 4p dimensions
Authors: Burzlaff J. , Chakrabarti A. , Tchrakian D. H.
Published: July 2002

Axially symmetric gauge field configurations of a certain type are studied in generalized Yang–Mills theory in 4p dimensions (p=2,3,...). For all p, finite action solutions of the generalized self-duality equations with topological charge n=1,2,... are found. It is also shown that the self-duality equations are overdetermined, when other types of axial symmetry are imposed.
Stochastic interpretation of Feynman path integral
Authors: Haba Z.
Published: July 2002

A class of functions ℋnF was chosen, which are boundary values of holomorphic functions. It was shown that if the potential V∈ℋnF and the initial wave function ψ∈ℋnF then the solution of the Schrödinger equation is ψt∈ℋnF. The unitary evolution ψ → ψt can be expressed by an integral with respect to the Wiener measure. To each ψt∈ℋnF is associated a complex Markov process qt fulfilling stochastic Hamilton equations. The time evolution of ψ as well as multitime correlation functions of arbitrary observables in quantum mechanics take the form of expectation values with respect to qt. Some statistical and ergodic aspects of quantum mechanics resulting from the stochastic interpretation of Feynman’s sum over trajectories are discussed.
Generalized deformed algebras F(A1) and their applications
Authors: Pan Feng
Published: July 2002

Generalized deformation of A1 is proposed. Some generalized deformed algebras F(A1) and their unitary representations are discussed in detail. F(A1) involves not only Lie algebras SU(2), SU(1,1), E2 and boson algebra as special cases, but also quantum algebras SUq(2), SUq(1,1), q-boson algebra, and a large class of other nonlinear algebras. It is found that these algebras can be mapped from one type to another by generalized deforming functionals in some cases. Possible applications in physical problems are outlined. Some examples are also given as illustrations.
Group quantization of parametrized systems. II. Pasting Hilbert spaces
Authors: Hájíček P. , Higuchi A. , Tolar J.
Published: July 2002

The method of group quantization described in the preceding paper [J. Math. Phys. 36, 4612 (1995)] is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy model is studied that admits a pair of maximal transversal surfaces intersecting all orbits. The corresponding two quantum mechanics are constructed. The similarity of the canonical group actions in the classical phase spaces on the one hand and in the quantum Hilbert spaces on the other hand suggests how the two Hilbert spaces are to be pasted together. The resulting quantum theory is checked to be equivalent to that constructed directly by means of Dirac’s operator constraint method. The complete system of partial Hamiltonians for any of the two transversal surfaces is chosen and the quantum Schrödinger or Heisenberg pictures of time evolution are constructed.
Completeness of decoherence functionals
Authors: Schreckenberg Stephan
Published: July 2002

The basic ingredients of the ‘‘consistent histories’’ approach to a generalized quantum theory are ‘‘histories’’ and decoherence functionals. The main aim of this program is to find and to study the behavior of consistent sets associated with a particular decoherence functional d. In its recent formulation by Isham [‘‘Quantum logic and the histories approach to quantum theory,’’ J. Math. Phys. 35, 2157–2185 (1994)] it is natural to identify the space 𝒰𝒫 of propositions about histories with an orthoalgebra or lattice. When 𝒰𝒫 is given by the lattice of projectors 𝒫(𝒱) in some Hilbert space 𝒱, consistent sets correspond to certain partitions of the unit operator in 𝒱 into mutually orthogonal projectors {α1,α2,...}, such that the function d(α,α) is a probability distribution on the boolean algebra generated by {α1,α2,...}. Using the classification theorem for decoherence functionals proven in Isham et al. [‘‘The classification of decoherence functionals: An analog of Gleason’s Theorem,’’ J. Math. Phys. 35, 6360–6370 (1994)] we show that in the case where 𝒱 is some separable Hilbert space there exists for each partition of the unit operator into a set of mutually orthogonal projectors, and for any probability distribution p(α) on the corresponding boolean algebra, decoherence functionals d with respect to which this set is consistent and which are such that for the probability functions d(α,α)=p(α) holds.
The spectrum of adiabatic stellar oscillations
Authors: Beyer Horst R.
Published: July 2002

The stability analysis for spherically symmetric stellar equilibrium models with respect to ‘‘small’’ adiabatic Lagrangian perturbations leads to the consideration of a class of densely defined, linear symmetric operators in Hilbert space, which are induced by certain singular vector–integro–partial differential operator. The extension properties of these operators as well as the spectral properties of the linear self-adjoint extensions which are chosen by physical boundary conditions are investigated. For this, the equilibrium models are assumed to be polytropic, with a constant adiabatic index only near the center and near the boundary of the star. Among others it is shown that the operators of the class having a polytropic index near the boundary which is ≥1 are in particular essentially self-adjoint and have a closure with a pure point spectrum.
Algebraic framework for quantization of nonultralocal models
Authors: Hlavatý Ladislav
Published: July 2002

Extension of the braid relations to the multiple braided tensor product of algebras that can be used for quantization of nonultralocal models is presented. The Yang–Baxter-type consistency conditions, as well as conditions for the existence of the multiple coproduct (monodromy matrix), which can be used for construction of the conserved quantities, are given. Homogeneous and local algebras are introduced, and simplification of the Yang–Baxter-type conditions for them is shown. The Yang–Baxter-type equations and multiple coproduct conditions for homogeneous and local of order 2 algebras are solved.
New exact solutions of Burgers’s equation—an extension to the direct method of Clarkson and Kruskal
Authors: Hood Simon
Published: July 2002

New exact solutions of Burgers’s equation, which is the simplest evolution equation to embody nonlinearity and dissipation, are obtained. These solutions are obtained by extending the method for finding symmetry reductions due to Clarkson and Kruskal [‘‘New similarity solutions of the Boussinesq equation,’’ J. Math. Phys. 30, 2201–2213 (1989)]. The novel feature of this extended method is that one can seek reductions to a system of ordinary differential equations, rather than the usual single equation and this leads to a wider class of solutions. One is able to complete the calculations necessary for Burgers’s equation in all but a single case (where it is necessary to integrate an Abel equation of the second kind). This indicates that the method is practicable. In contrast it is often the case that new methods are of limited use in practice. In particular, solutions in terms of a class of confluent-hypergeometric functions are computed. By comparison, solutions found by the original method due to Clarkson and Kruskal, and other reduction methods, are in terms of parabolic-cylinder functions or Airy functions, which are special cases of this class.
Integrability, partial integrability, and nonintegrability for systems of ordinary differential equations
Authors: Goriely Alain
Published: July 2002

The integrability of systems of ordinary differential equations with polynomial vector fields is investigated by using the singularity analysis methods. Three types of results are obtained. First, a general relationship between the degrees of first integrals and the so-called Kowalevskaya exponents is derived. Second, it is shown that all solutions of algebraically integrable systems can be expanded in Puiseux series. Third, a new method to study partially integrable systems is studied. These different aspects allow us to study algorithmically the integrability, partial integrability, and nonintegrability of differential systems.
Self-dual Maxwell fields on curved space–times
Authors: Dotti Gustavo , Kozameh Carlos N.
Published: July 2002

We present a manifestly conformally invariant formulation of Maxwell equations on asymptotically flat space–times. It is shown how to construct regular self-dual and antiself-dual fields from suitable radiation data, and the general solution as a sum of fields with both types of duality. The basic variable in this formalism is a scalar field F defined as the phase of the parallel propagator (associated with the Maxwell potential) from interior points to future null infinity along null geodesics. Field equations equivalent to the source free Maxwell’s equations are derived for F. A perturbative solution based on Huygens’ principle is proposed. Exact solutions are found for H-spaces. The use of these results on gravitational lensing is discussed.
The construction of spinor fields on manifolds with smooth degenerate metrics
Authors: Schray Jörg , Dray Tevian , Manogue Corinne A. , Tucker Robin W. , Wang Charles
Published: July 2002

We examine some of the subtleties inherent in formulating a theory of spinors on a manifold with a smooth degenerate metric. We concentrate on the case where the metric is singular on a hypersurface that partitions the manifold into Lorentzian and Euclidean domains. We introduce the notion of a complex spinor fibration to make precise the meaning of continuity of a spinor field and give an express- ion for the components of a local spinor connection that is valid in the absence of a frame of local orthonormal vectors. These considerations enable one to construct a Dirac equation for the discussion of the behavior of spinors in the vicinity of the metric degeneracy. We conclude that the theory contains more freedom than the spacetime Dirac theory and we discuss some of the implications of this for the continuity of conserved currents.
Constructive building of the Lax pair in the non-linear sigma model
Authors: García Ariel O. , Trinchero Roberto C.
Published: July 2002

A derivation of the Lax pair for the (1+1)-dimensional non-linear σ-model is described. Its main benefit is to have a clearer physical origin and to allow the study of a generalization to higher dimensions.