bluuebunny/crossref_metadata_2025 huggingface dataset:
Free bosonic string field theory without supplementary fields
Authors: Embacher Franz
Published: July 2002

A covariant local action for free bosonic string fields is constructed without the use of supplementary fields. The open string case is treated in detail. Up to a mathematical conjecture that is likely to hold it is shown that the Virasoro constraints arise as a special choice of gauge. The kinetic operator turns out to be extremely simple, the gauge transformation law arising rather implicitly. The case of closed strings is briefly discussed.
Nonperturbative solutions of nonlinear differential equations using continued fractions
Authors: Ditto William L. , Pickett Thomas J.
Published: July 2002

A new approach to the solution of nonlinear differential equations of mathematical physics is presented. Continued fractions are exploited to convert a power series of a solution into a closed form expression that yields an excellent approximation to the exact solution. These solutions contain the appropriate number of arbitrary constants to accommodate boundary conditions. The method is also shown to be capable of generating certain exact solutions. Evidence is provided for the conjecture that the known exact solutions are members of families of exact solutions.
Field quantization for pure and mixed states and its classical limit
Authors: Ajanapon Pimon
Published: July 2002

The path-integral formulation of quantum mechanics in terms of the density matrix proposed in a previous paper is here extended to quantum field theory. The corresponding classical field equation is derived as the deterministic classical limit by imposing an appropriate mixed-state initial condition. Relativistic invariance is insured by construction of ten generators of the inhomogeneous Lorentz group.
On the time evolution operator for time-dependent quadratic Hamiltonians
Authors: Fernández Francisco M.
Published: July 2002

The Schrödinger equation with a time-dependent quadratic Hamiltonian is investigated. The time-evolution operator is written as a product of exponential operators determined by the Heisenberg equations of motion. This product operator is shown to be global in the occupation number representation when the Hamiltonian is Hermitian. The success of some physical applications of the product-form representation is explained.
Lagrangian and Hamiltonian many-time equations
Authors: Lusanna Luca
Published: July 2002

The Lagrangian and Hamiltonian many-time equations are derived for a finite-dimensional system with an arbitray number of primary and secondary first-class constraints. Assuming that all the secondary constraints are generators of gauge transformations, the general form of the Lagrangian gauge algebra is given.
Induced representations for SIM (d−1,1) and scaling of massless fields in even-dimensional spaces
Authors: Bhansali Vineer
Published: July 2002

Using an invariant operator in the enveloping algebra of SIM (d−1,1) (the similitude subgroup of the conformal group in d dimensions), conformal invariance, and the recent result for the eigenvalue of a generalized ‘‘helicity’’ operator, the eigenvalue of massless fields under scale transformations is computed in higher even dimensions.
An extension of Szegö’s theorem
Authors: Morita T.
Published: July 2002

An extension of Szegö’s theorem, Theorem 1 in the text, is proved by using the elementary theory of complex functions and the Wiener–Lévy theorem.
Spherically symmetric solutions admitting a spacelike self-similar motion
Authors: Sussman Roberto A.
Published: July 2002

Global properties and causal structure are considered for spherically symmetric, perfect fluid solutions admiting a self-similar motion orthogonal to the four-velocity. The fluid admits a stiff equation of state. The momentum-energy tensor is equivalent to that of a free massless scalar field. All solutions have center singularities, some of which are timelike. In the latter cases, there are regions with negative density covered by Cauchy horizons. Regular boundaries at infinity display an asymptotically Minkowski behavior. Models of ‘‘vacuum bubbles’’ arise by performing a C1 matching with a section of Minkowski space-time along the Cauchy horizon. Generalizations associated with a nonzero cosmological constant are briefly examined.
Strengths of naked singularities in radiation collapse with nonlinear mass functions
Authors: Joshi P. S. , Dwivedi I. H.
Published: July 2002

The structure of naked singularity for a nonlinear mass function in Vaidya solutions for collapse of imploding radiation is examined here. The singularity is shown to be a scalar polynomial singularity even though RabKaKb does not diverge sufficiently fast along any singular geodesic.
Symmetry breaking and restoration in models with extended Higgs sectors
Authors: Farris Timothy H. , Kephart Thomas W.
Published: July 2002

The finite temperature behavior of the scalar sector of models with U(1) and/or SU(2) gauge symmetries beyond the standard model is investigated. As the temperature decreases, complicated patterns of symmetry breaking and restoration appear in a model with U3(1) gauge symmetry. The results will be generalized to include an arbitrary number of U(1) and/or SU(2) factors, deriving expressions for the vacuum expectation values and masses of the scalar fields and the phase transition temperatures, to make contact with flipped model phenomenology.
The SU(u,v)-group path integration
Authors: Grosche Christian
Published: July 2002

Path integration over the SU(u,v) group manifolds, in particular SU(n) and SU(n−1,1), are calculated in an appropriate polar coordinate representation, giving explicitly their set of harmonic functions of all irreducible representations and the corresponding energy spectrum. A path integral identity for multidimensional generalizations of the Pöschl–Teller potential is also stated.
Equivalence and s-equivalence of vector-tensor Lagrangians
Authors: López M. C. , Noriega R. J. , Schifini C. G.
Published: July 2002

It will be proven that if a gauge-invariant Lagrangian density having the local form L=L(gij;Ai;Ai,j) is such that its Euler–Lagrange equations Ei(L)=0 have the same set of solutions as Ei(L0)=0, where L0=g1/2FijFij, then L and cL0 are equivalent for same constant c, i.e., Ei(L)=Ei(cL0). From a previous result it follows that L=cL0+D+eg1/2, where D is a divergence and e is a constant.
Complex confocal involutive systems associated with the solutions of the AKNS evolution equations
Authors: Gu Zhuquan
Published: July 2002

In this paper, the complex involutive systems associated with the Ablowitz, Kaup, Newell, and Segur (AKNS) evolution equations are discussed. By means of the complex representations of the standard symplectic form and the standard Poisson bracket on the real space R2n, using the equivalent relations between the Hamiltonian canonical equations, it is proved that the complex involutive systems are exactly finite-dimensional completely integrable systems in the Liouville sense. Therefore, by mapping nonlinearly from the involutive solutions of the compatible Hamiltonian canonical equations to the AKNS evolution equations, the representations of the solutions of the AKNS evolution equations are obtained.
Existence of the massive SO(3) vortices
Authors: Yang Yisong
Published: July 2002

In the massive SO(3) gauge field theory, a critical choice of the configuration ansatz leads to a system of the Bogomol’nyi type equations governing the unstable modes of the model. A ’t Hooft periodic condition implies the quantization of the flux lines confined in a cell domain if a certain class of solutions exist. The present paper establishes an existence theorem for such solutions via a constrained variational principle. These solutions exhibit the analogous properties of the vortex-like solutions predicted in the theory of type II superconductivity by Abrikosov.
U(n) generator matrix elements using orthogonal Gel’fand basis states
Authors: Ponnapalli P. S. , Schlesinger M. , Kent R. D.
Published: July 2002

A matrix element factorization scheme in the Gel’fand basis is presented. In lieu of the standard orthonormal Gel’fand basis, a related orthogonal basis set is employed. This leads to algebraic expressions that are purely rational, no square roots are involved in the calculations, thereby affording considerable simplification of one- and two-body generator matrix elements. These techniques are illustrated through numerous example calculations.
Invariant projection of the energy-momentum tensors for field theories in spaces with affine connection and metric
Authors: Manoff S.
Published: July 2002

The invariant projections of the generalized canonical, symmetric, and variational energy-momentum tensor and their divergences are investigated in spaces with affine connection and metric. Connections between the obtained quantities are found on the basis of the generalized covariant Bianchi-type identities and the covariant Euler–Lagrange equations. It can be shown that the weak principle of equivalence can be considered as a corollary of the Euler–Lagrange equations for a given field theory.
Inhomogeneous differential realization, boson–fermion realization of Lie superalgebras and their indecomposable representations
Authors: Fu Hong-Chen
Published: July 2002

An inhomogeneous differential realization (IHDR) of Lie superalgebras, which plays an important role in the search for quasi-exactly solvable problems (QESP) of quantum mechanics, is studied. The corresponding inhomogeneous boson–fermion realization (IHBFR) of Lie superalgebras is obtained. By making use of the IHBFR, a new kind of indecomposable and irreducible representations of Lie superalgebras is studied on the universal enveloping algebra of Heisenberg–Weyl superalgebra, and on its subspaces and quotient spaces. The finite dimensional representations of Lie superalgebras are naturally obtained on the subspaces of Fock space. As examples, the IHDR of Lie superalgebra spl(m,1) is given, and the indecomposable and irreducible representations of Lie superalgebra su(2,1) are studied in detail.
High-order K-space linear response of a noninteracting Fermion system in an external potential
Authors: Li Shiwei , Percus J. K.
Published: July 2002

The one-body density matrix of a noninteracting Fermion system is expressed in terms of a contour integral, and expanded about that of the free particle system. High-order k-space linear response functions of this in an external potential are calculated for one and three dimensions via a functional expansion formulation. The results are compared with those given by the inverse Laplace transform (ILT) method. It is shown that the k-space linear responses in one dimension have a much simpler structure than those in the real space, and can be evaluated systematically. Two special one-body Hamiltonians are used to illustrate the one-dimensional results. The validity of the linear response expansion is addressed in the discussion of these examples.
Quantum deformation of the ladder representations of U(1,1) for ‖q‖=1
Authors: Furlan Paolo , Hadjiivanov Ludmil K. , Todorov Ivan T.
Published: July 2002

Uq(u(1,1)) covariant creation and annihilation operators for q on the unit circle are constructed and the corresponding ladder and singleton representations are considered.
Normal form of a metric admitting a parallel field of planes
Authors: Thompson G.
Published: July 2002

Local coordinate normal forms for two classes of metrics are obtained. The first class is comprised of those metrics that have a field of degenerate, but not necessarily null, planes, thereby extending a result of A. G. Walker. The second class of metrics are Artinian metrics that possess a pair of parallel, complementary, null distributions. This latter class is shown to be equivalent to a certain class of symplectic forms.
General inversion formulas for wavelet transforms
Authors: Holschneider Matthias
Published: July 2002

This article is the continuation of a series of articles about group theory and wavelet analysis [A. Grossmann, J. Morlet, and T. Paul, J. Math. Phys. 26, 2473 (1985)]. As is well-known in the case of the afine group, the reconstruction wavelet and the analyzing wavelet need not be identic. In this article it is shown that this holds for arbitrary groups. In addition it is shown that even for nonadmissible analyzing wavelets the wavelet transform may be inverted. Accordingly the image of the wavelet transform can be characterized by many different reproducing kernels.
Band representations and duals of the nonsymmorphic crystallographic plane groups pg and p4gm
Authors: Bacry Henri
Published: July 2002

Duals of the groups pg and p4gm are constructed. (1) The group pg has only one band representation (an elementary one) equivalent to the regular representation. There exists a quasiband representation close to it, of multiplicity two, which separates the branches of the band. Finite groups which approximate pg are discussed. (2) Two elementary band representations associated with the Wyckoff position b of the group p4gm are shown to be nonequivalent although they have the same decomposition in unirreps.
Tensor operators III: Some fundamental tensor operator identities
Authors: Flath Dan , Towber Jacob
Published: July 2002

Let s≥2 and let α=<a1,a2,...,as≳, where s, ai ∈ Z and a1≥a2≥...≥as≥1. Let 1≤t≤s. The method of undetermined coefficients was used to investigate natural transformations Ω:Λα → Λa1 ⊗ Λa2 ⊗... ⊗ Λas and Ωt:Λα → Λ<a1,...,ât,...,as≳ ⊗ Λat. Necessary and sufficient conditions were found on the coefficients defining Ω and sufficient conditions on the coefficients defining Ωt. Explicit formulas for Ω1 and Ωs are given herein.
Hermitian symmetric superspaces of type IV
Authors: Borthwick David , Lesniewski Andrzej , Rinaldi Maurizio
Published: July 2002

A construction of the Hermitian symmetric superspaces which are the supermanifold analogs of the Cartan domains of type IV is presented herein. Natural generalizations of the Jordan triple product and Bergman operator for the superdomains are defined, and their properties are studied.
A ‘‘compact Green function’’ approach to the time-domain direct and inverse problems for a stratified dissipative slab
Authors: He Sailing
Published: July 2002

A new type of Green function approach is introduced for time-domain scattering for a stratified dissipative slab. The new Green functions are defined as mappings from the transmitted field to the split fields (i.e., the right-moving and left-moving fields) at any point within the stratified slab. Unlike the usual Green functions, the present Green functions have compact support in the time variable. The new technique is illustrated for the case of normally incident electromagnetic waves on a stratified slab where the permittivity, permeability, and conductivity vary with the depth. The linear and homogeneous partial differential equations (PDEs) for these ‘‘compact Green functions’’ are derived. The PDEs together with the initial and boundary conditions are well suited for a numerical treatment. Numerical results for the compact Green functions are presented in the direct problem, while in the inverse problem the permittivity and conductivity (or the permeability and conductivity) are reconstructed simultaneously using the reflection and transmission data for the first round trip. The present method is useful and attractive for both the direct and inverse problems due to its simplicity, high speed, and high accuracy in numerical computations.
Canonical formalism of action-at-a-distance electrodynamics and many-particle potential among charged particles
Authors: Ohta Tadayuki , Kimura Toshiei
Published: July 2002

The second post-Coulombian Lagrangian of Wheeler–Feynman electrodynamics for a many-particle system is treated according to a canonical formalism of a singular Lagrangian with higher derivatives. The canonical equations are given in terms of a reduced Hamiltonian with Dirac brackets, but they are transformed to be expressed in terms of ordinary Poisson brackets by redefinition of canonical variables. The reduced Hamiltonian includes a characteristic form of three-particle and four-particle potentials. Finally a direct pathway to the reduced Hamiltonian is presented via first-order formalism of the Maxwell theory with charged particles.
Generation of internal waves in a rotating, stratified fluid: Some symmetry properties
Authors: Kharik V. M.
Published: July 2002

A symmetrization of the mathematical model for a dynamic system is considered, as well as its connections with the symmetry properties of the integral operators, which are used to obtain the classical solution to the Neumann problem with a Sobolev-type equation in the field with singularities. The properties of the single-layer and the double-layer potentials and their physical meaning are examined via Holder norms, as well as an integral transformation applied in the included analysis. The similarities between the considered Sobolev-type equation and Laplace-type equations are discussed. An analysis of the applications of the presented boundary integral method and small-amplitude oscillations in a rotating stratified fluid is included, as well as the estimates for the solutions revealing their physical nature.
Generalized embedding variables for geometrodynamics and space-time diffeomorphisms: Ultralocal coordinate conditions
Authors: Braham Stephen P.
Published: July 2002

The embedding variable approach to geometrodynamics advocated in work by Isham, Kuchař, and Unruh are investigated for a general class of coordinate conditions that mirror the Isham–Kuchař Gaussian condition, but allow for arbitrary algebraic complexity. It is found that the same essential structure present in the ultralocal Gaussian condition is repeated in the general case. The resultant embedding-extended phase space contains a full representation of the Lie algebra of the space-time diffeomorphism group, as well as a consistent pure gravity sector.
Some exact solutions of the Einstein field equations in terms of the self-dual spin connection
Authors: Capovilla Riccardo , Plebański Jerzy
Published: July 2002

The self-dual spin connection is used as primary field variable in the determination of space–time geometries which satisfy the Einstein field equations. We find that the simplest nontrivial Ansatz on the self-dual spin connection produces a space–time of the Kasner-type. In the case of gravitational instantons, an analogous form of the self-dual spin connection is shown to determine conformally flat space–times.
Nonperturbative two-body dynamics in 2+1-dimensional gravity
Authors: Falbo-Kenkel M. K. , Mansouri F.
Published: July 2002

Two-body dynamics in 2+1-dimensional gravity is analyzed from the point of view of the Poincaré gauge theory without the a priori introduction of a metrical space-time. Making use of the nonuniqueness of the phase space variables, point-like spinless sources are coupled to the Chern–Simons–Witten action in two different ways. In both cases, the exact gravity Hamiltonian is obtained, not by relying on metrical notions, but directly as Wilson loop observables. Then, by viewing the two-body system from a particular frame, and performing a multivalued gauge transformation, it is shown that for both types of matter couplings, the relative coordinate moves on a cone with a deficit angle given by the corresponding classical Hamiltonian. Thus, the metrical space-time emerges as a broken phase of the Poincaré gauge theory. For one type of matter coupling, ’t Hooft’s Hamiltonian is obtained in the low-energy limit. It is also shown that ’t Hooft’s method of obtaining the scattering amplitude can be made applicable to the exact Hamiltonians by an appropriate reinterpretation of parameters.
Wiener and Poisson process regularization for coherent-state path integrals
Authors: Alicki Robert , Klauder John R.
Published: July 2002

By introducing a suitable continuous-time regularization into a formal phase-space path integral it follows that the propagator is given by the limit of well-defined functional integrals involving standard stochastic processes and their associated probability measures. Such regularizations require pinning of both coordinate and momenta variables, and automatically lead to coherent-state representations. It is found that each standard independent increment process, involving a superposition of a Wiener and a Poisson process, is associated with a specific, generally non-Gaussian, fiducial vector with which the coherent states are defined.
Celestial spheres, light cones, and cuts
Authors: Low R. J.
Published: July 2002

The embedding of celestial spheres in 𝒩, the space of null geodesics of a strongly causal space–time, ℳ is studied, with particular attention to the contact form on 𝒩. The algebraic topology of the embedding is also considered. Light cone cuts with (partial) Cauchy surfaces are examined, by regarding 𝒩 (or appropriate submanifolds of it) as a bundle over 𝒮 and projecting down. Finally, a means of reconstructing the original space–time (up to a conformal factor in the metric) from the cuts of light cones with a Cauchy surface is given.
The classical limit of ultralocal scalar fields
Authors: Zhu Chengjun , Klauder John R.
Published: July 2002

The classical limit of the quantum theory of ultralocal scalar fields is approached with the help of coherent state techniques. In the limit ℏ→0, it is demonstrated that the coherent state expectation value of the Heisenberg field operators coincide with the solutions of the corresponding classical canonical equations of motion.
Symmetries of type D+D− gravitational instantons
Authors: Goldblatt E.
Published: July 2002

Gravitational instantons are considered important in analyzing such quantum gravitational effects as the evaporation and condensation of black holes and the stability of the vacuum at finite temperature. Unfortunately, not every positive definite solution of the field equations is derivable from the Lorentzian regime by analytic continuation. As a first step in the investigation of these objects, it is proven that all Petrov-type D+D− spaces admit an Abelian, orthogonally transitive, two dimensional group of isometries. This is accomplished by using a Euclidean version of the Newman–Penrose formalism to classify the spaces according to the twist and expansion of their Debever–Penrose vectors. In each class one can then infer the existence of Killing spinors, vectors, and tensors required to yield the result.
Optics, mechanics, and quantization of reparametrization-invariant systems
Authors: Navarro Miguel , Guerrero Julio , Aldaya Victor
Published: July 2002

In this article the dynamics obtained from the Fermat principle is regarded as being the classical theory of light. The action is (first) quantized and it is shown how close one can get to the Maxwell theory. It is shown that quantum geometric optics is not a theory of fields in curved space. Considering classical mechanics to be on the same footing, the parallelism between quantum mechanics and quantum geometric optics is shown. It is shown that, due to the reparametrization-invariance of the classical theories, the dynamics of the quantum theories is given by a Hamiltonian constraint. Some implications of the above analogy in the quantization of true reparametrization-invariant theories are discussed.
Equivariance, BRST symmetry, and superspace
Authors: Niemi Antti J. , Tirkkonen Olav
Published: July 2002

The structure of equivariant cohomology in non-Abelian localization formulas and topological field theories is discussed. Equivariance is formulated in terms of a nilpotent Becchi–Rouet–Stora–Tyutin (BRST) symmetry, and another nilpotent operator which restricts the BRST cohomology onto the equivariant, or basic sector. A superfield formulation is presented and connections to reducible [Batalin–Fradkin–Vilkovisky (BFV)] quantization of topological Yang–Mills theory are discussed.
On a class of ‘‘skewed’’ self-similar and hyperbolic fractals
Authors: Huillet Thierry , Jeannet Bernard
Published: July 2002

Probabilistic (recurrent) renewal theory is used herein to describe the geometry of a new class of self-similar distributions in a ‘‘skewed’’ multiplicative mass splitting procedure. It is shown how this model class can account for a deterministic and conservative treelike structure, in connection with recent developments on ‘‘anomalous’’ multiplicative multifractals. Coexistence of both micro- and macroscopic scales in such objects is a consequence of the underlying renewal phenomena being transient, as is shown in a second part of the article. Various ‘‘entropylike’’ measures of the intrinsic disorder prevailing in these structures are proposed.
Constraint field systems in multimomentum canonical variables
Authors: Sardanashvily G.
Published: July 2002

To describe constraint field models, we apply the multimomentum Hamiltonian formalism where momenta correspond to derivatives of fields with respect to all world coordinates, not only time. If a Lagrangian density is degenerate, the Euler–Lagrange equations are underdetermined and need additional gauge-type conditions which remain elusive in general. One gets these conditions automatically as a part of the Hamilton equations, but must consider a family of Hamiltonian forms associated with the same Lagrangian density in order to exhaust solutions of the Euler–Lagrange equations. The case of degenerate quadratic and affine Lagrangian densities is elaborated. As a result, we get the universal procedure of describing constraint field systems.
Radiating sphere in a Kaluza–Klein space–time
Authors: Bhui B. , Basu Madhumita Barua , Chatterjee S.
Published: July 2002

The well-known solution of Vaidya for a radiating sphere in a Kaluza–Klein-type of space–time is extended. The field equations yield a two-parameter solution—either an exactly four-dimensional Vaidya metric with a flat extra space tucked to it or a flat Minkowski space–time. The geodesic trajectories of test particles in this field are studied and some astrophysical consequences due to the presence of the extra space are also briefly discussed.
Topology of the skyrmion bundle
Authors: Gross Christian
Published: July 2002

We compute homotopy and cohomology groups for the Skyrmion bundle, which play an important role in the description of the monopole-induced proton decay within the Skyrme model. By use of spectral sequences, the differential forms on the bundle that allow for the calculation of baryon numbers and for the anomalous action are developed out of the ones on the fiber, and are adapted to the given Maxwell connection.
Matrix representation of higher integer conformal spin symmetries
Authors: Saidi E. H.
Published: July 2002

Using infinite matrices, we construct the generating functional of higher integer conformal spin extensions of the Virasoro algebra and the SU(2) spin 1/2 representation loop algebra. Higher conformal spin symmetries are realized on the set F1/2 of the configurations of the homogeneous Ising chain. This is an infinite-dimensional vector space reducible into subspaces Fm1/2(l), m∈Z, l∈N, completely specified by the site occupation operator number and the degree of the excitations of the chain states. The algebra of the chain transformations is given by the central extension of the algebra of the site state ones. The anomalous term of the generating functional of the higher integer conformal spin extensions of the Virasoro algebra is calculated and a comment on the unitarity is made. Other properties are discussed.
An application of the Peter–Weyl theorem to non-Abelian lattice gauge theory
Authors: Nishino Kazuyoshi
Published: July 2002

This article presents an application of the Peter–Weyl theorem to obtain a new formula for the physical states of the Kogut–Susskind Hamiltonian model. In this formula a physical state is identified with a matrix element of a suitable representation of the infinite product of the gauge group. The Clebsch–Gordan coefficients for the physical states are obtained. A handy formula is deduced for the plaquette term in the Hamiltonian, so that the matrix elements of the Hamiltonian in the physical space for the (2+1)-dimensional SU(2) model can be calculated without using the Wigner–Eckart theorem for tensor operators.
A new method of solution of Hallén’s problem
Authors: Miano G. , Verolino L. , Vaccaro V. G.
Published: July 2002

A wide class of electromagnetic scattering problems can be expressed as a system of dual integral equations. This kind of integral equation, occurring in boundary value problems wherein there is one equation for a certain region and another for the dual domain, is usual in diffraction problems. Considerable attention has been drawn by many researchers in the field of optics, acoustics, scattering of elastic waves, accelerator physics, and antenna theory. Wiener–Hopf techniques enable us to solve such kinds of integral equations when the two regions are contiguous and semi-infinite. Unfortunately Wiener–Hopf techniques do not apply if one of the regions is finite; this is the case for realistic scatterers, such as irises, antennas, and drift tubes in accelerators. In this article a general method for solving such dual integral equations is discussed and applied to a particular case: Hallén’s equation of cylindrical antennas. This method consists of a transformation of the dual integral equations into a Fredholm integral equation of the second kind and then into a linear system of algebraic equations. Comparisons with results obtained by other methods for a wide range of frequencies show the accuracy and the robustness of the proposed one.
Separability and Lax pairs for the two-dimensional Hamiltonian system with a quartic potential
Authors: Romeiras Filipe J.
Published: July 2002

The two-dimensional Hamiltonian system with a quartic potential is known to be integrable in four cases, that is, for four sets of parameter values. In three of these cases the system is also known to be separable. In this paper, separating variables for the fourth integrable case are obtained, allowing its solution in terms of elliptic functions. Lax pairs with a spectral parameter for the four integrable cases are also obtained.
Natural symmetries of the Yang–Mills equations
Authors: Torre C. G.
Published: July 2002

A natural generalized symmetry of the Yang–Mills equations is defined as an infinitesimal transformation of the Yang–Mills field, built in a local, gauge invariant, and Poincaré invariant fashion from the Yang–Mills field strength and its derivatives to any order, which maps solutions of the field equations to other solutions. On the jet bundle of Yang–Mills connections a spinorial coordinate system is introduced that is adapted to the solution subspace defined by the Yang–Mills equations. In terms of this coordinate system the complete classification of natural symmetries is carried out in a straightforward manner. It is found that all natural symmetries of the Yang–Mills equations stem from the gauge transformations admitted by the equations.
Transformation of the solutions of the Maxwell equations on a Lorentzian manifold by means of a certain class of diffeomorphisms
Authors: Fecko Marián
Published: July 2002

Poincaré invariance of the Maxwell equations in Minkowski space enables one to generate in a usual way new solutions (corresponding to new sources) from a given one by means of the pullback operation. A method is proposed generalizing this to a wider class of diffeomorphisms f:M → M of a Lorentzian manifold (M,g). It results in the simple explicit formulas for obtaining the new field Ff and its source jf from a given pair (F,j). Some applications, e.g., a uniformly rotating or radially pulsating source, are presented.
Improved high-energy bounds on absorptive parts of elastic scattering amplitudes
Authors: Chung B. K. , Kang Y. D.
Published: July 2002

Improved rigorous high-energy upper bounds are established on the absorptive parts of the elastic scattering amplitudes for the momentum-transfer-squared variable t positive and within the Lehmann–Martin ellipse. These bounds are used to set upper bounds on Regge trajectories and also to extend the region in the complex t plane where the amplitudes cannot have zeros. No assumption is made about the high-energy behavior of the total cross sections.
Scattering theory for mesoscopic quantum systems with non-trivial spatial asymptotics in one dimension
Authors: Pötz W.
Published: July 2002

Basic results which are needed for the formulation of a quantitative theory of charge transport in mesoscopic quantum-interference devices are derived. In particular, orthogonality and proper normalization of scattering states for one-dimensional quantum systems with nonzero and periodic potential asymptotics are discussed. Properties of the S-matrix are investigated. Results are obtained within the framework of ordinary linear differential equations by investigation of the spectral resolution of the identity and, alternatively, directly from asymptotic properties of Jost solutions and the theory of generalized functions. Based on the S-matrix and properties of the scattering states, an independent-particle model for the current response of mesoscopic (quasi-) one-dimensional electronic devices may be formulated.
Transient waves in nonstationary media
Authors: Åberg Ingegerd , Kristensson Gerhard , Wall David J. N.
Published: July 2002

This paper treats propagation of transient waves in nonstationary media, which has many applications in, for example, electromagnetics and acoustics. The underlying hyperbolic equation is a general, homogeneous, linear, first-order 2×2 system of equations. The coefficients in this system depend on one spatial coordinate and time. Furthermore, memory effects are modeled by integral kernels, which, in addition to the spatial dependence, are functions of two different time coordinates. These integrals generalize the convolution integrals, frequently used as a model for memory effects in the medium. Specifically, the scattering problem for this system of equations is addressed. This problem is solved by a generalization of the wave splitting concept, originally developed for wave propagation in media which are invariant under time translations, and by an imbedding or a Green’s functions technique. More explicitly, the imbedding equation for the reflection kernel and the Green’s functions (propagator kernels) equations are derived. Special attention is paid to the problem of nonstationary characteristics. A few numerical examples illustrate this problem.
General eigenvalue formula for Casimir invariants of type I quantum superalgebras
Authors: Gould M. D. , Links J. R.
Published: July 2002

Induced invariant forms and the multiplicity labeling problem are investigated for typical summands of the tensor product of an arbitrary finite dimensional irreducible representation and a typical one, for the type I quantum superalgebras. The results are applied to obtain a general eigenvalue formula for Casimir invariants, corresponding to an arbitrary finite dimensional irreducible reference representation.
The Racah–Wigner algebra and coherent tensors
Authors: Rowe D. J. , Repka J.
Published: July 2002

We present a set of tensors which are shift tensors (Wigner tensors) in accordance with the definitions of Biedenharn and Louck and satisfy the coherence conditions of Flath and Towber. Our tensors are defined for all connected compact Lie groups and for finite-dimensional representations of connected reductive Lie groups. Thus, we have a realization of the coherent tensors in a rather general setting. Moreover, this realization enables us to confirm most of the conjectures of Flath and Towber concerning the properties of coherent tensors.
Quantum Boltzmann equation for photons
Authors: Mahan G. D.
Published: July 2002

The quantum Boltzmann equation is derived for photons. The form of the scattering and absorption terms for the case of photon diffusion is discussed in detail. We show how the structure factor of the scattering centers enters into the scattering rate of the photons.
Pseudoclassical model for Weyl particle in 10 dimensions
Authors: Gitman D. M. , Gonçalves A. E.
Published: July 2002

A pseudoclassical model to describe Weyl particle in 10 dimensions is proposed. In the course of quantization both the massless Dirac equation and the Weyl condition are reproduced automatically. The construction can be relevant to Ramond–Neveu–Schwarz strings where the Weyl reduction in the Ramond sector has to be made by hand.
Noncommutative geometry beyond the standard model
Authors: Pris Igor , Schücker Thomas
Published: July 2002

A natural extension of the standard model within noncommutative geometry is presented. The geometry determines its Higgs sector. This determination is fuzzy, but precise enough to be incompatible with experiment.
Long-range scattering in the position representation
Authors: Dereziński J. , Gérard C.
Published: July 2002

For a large class of long-range potentials we prove the asymptotic completeness of modified wave operators constructed using solutions of the eikonal equation −∂tΨ(t,x)=12(∇xΨ(t,x))2+V(x).
Nonlocal quadratic Poisson algebras, monodromy map, and Bogoyavlensky lattices
Authors: Suris Yuri B.
Published: July 2002

A new Lax representation for the Bogoyavlensky lattice is found and its r-matrix interpretation is elaborated. The r-matrix structure turns out to be related to a highly nonlocal quadratic Poisson structure on a direct sum of associative algebras. The theory of such nonlocal structures is developed and the Poisson property of the monodromy map is worked out in the most general situation. Some problems concerning the duality of Lax representations are raised.
Tensoring with small quantized representations
Authors: Jakobsen Hans Plesner
Published: July 2002

We give an elementary proof of the associativity of the reduced tensor product that also works for primitive roots of −1. At the same time, we get a useful understanding of how representations “fuse” into each other.
Vector bundles over configuration spaces of nonidentical particles: Topological potentials and internal degrees of freedom
Authors: Doebner H.-D. , Mann H.-J.
Published: July 2002

We consider configuration spaces of nonidentical pointlike particles. The physically motivated assumption that any two particles cannot be located at the same point in space–time leads to nontrivial topological structure of the configuration space. For a quantum mechanical description of such a system, we classify complex vector bundles over the configuration space and obtain potentials of topological origin, similar to those that occur in the fiber bundle approach to Dirac’s magnetic monopole or in Yang–Mills theory.
Open perturbation and the Riccati equation: Algebraic determination of the quartic anharmonic oscillator energies and eigenfunctions
Authors: Bessis N. , Bessis G.
Published: July 2002

An algebraic procedure is proposed for the analytical solution of Schrödinger equations that can be viewed as a factorizable equation with an additional potential V(x). Once V(x) has been expanded in a series of suitable x-basis functions u=u(x), which are specific to each factorization type, the solution of the Riccati equation associated with the given equation is performed by means of an open perturbation technique, i.e., at each order of the perturbation, an additional balance u-dependent term is introduced so that the resulting equation becomes solvable. Since the unperturbed potential involves the whole given potential and since the balance term is expected to be small, improved results are expected at low orders of the perturbation, even at the zeroth order. The procedure, well adapted to the use of computer algebra, is applied to the solution of the gx4-anharmonic oscillator equation: by means of very simple algebraic manipulations, the trend of the exact values of the energies is rather well reproduced for a large range of values of the coupling constant (g=0.002 to g=20000).
Invariant differential equations and the Adler–Gel’fand–Dikii bracket
Authors: González-López Artemio , Hernández Heredero Rafael , Beffa Gloria Marı́
Published: July 2002

In this paper we find an explicit formula for the most general vector evolution of curves on RPn−1 invariant under the projective action of SL(n,R). When this formula is applied to the projectivization of solution curves of scalar Lax operators with periodic coefficients, one obtains a corresponding evolution in the space of such operators. We conjecture that the formula we have found gives another alternative definition of the second KdV Hamiltonian evolution under appropriate conditions. In other words, both evolutions are identical provided that the vector differential invariant characterizing the SL(n,R)-invariant evolution on the space of projectivized curves is identified with the coefficients of the Hamiltonian pseudo-differential operator. We prove the above facts for n⩽6, and further simplify both evolutions in appropriate coordinates so that one can attempt to prove the equivalence for arbitrary n.
Applications of the Ashtekar gravity to four-dimensional hyperkähler geometry and Yang–Mills instantons
Authors: Hashimoto Yoshitake , Yasui Yukinori , Miyagi Sayuri , Ootsuka Takayoshi
Published: July 2002

The Ashtekar–Jacobson–Smolin–Mason–Newman equations are used to construct the hyperkähler metrics on four-dimensional manifolds. These equations are closely related to anti-self-dual Yang–Mills equations of the infinite-dimensional gauge Lie algebras of all volume-preserving vector fields. Several examples of hyperkähler metrics are presented through the reductions of anti-self-dual connections. For any gauge group anti-self-dual connections on hyperkähler manifolds are constructed using the solutions of both Nahm and Laplace equations.
de Rham cohomology of SO(n) and some related manifolds by supersymmetric quantum mechanics
Authors: Oshima Kazuto
Published: July 2002

We study supersymmetric quantum mechanics on RPn, SO(n), G2, and U(2) to examine Witten’s Morse theory concretely. We confirm the simple instanton picture of the de Rham cohomology that has been given in a previous paper. We use a reflection symmetry of each theory to select the true vacuums. The number of selected vacuums agrees with the de Rham cohomology for each of the above manifolds.
Distortion of a phase space under the Darboux transformation
Authors: Samsonov Boris F.
Published: July 2002

The Darboux transformation operator technique is applied to construct exactly solvable anharmonic singular oscillator potentials and to study their coherent states. Classical system corresponding to a transformed quantum system is constructed with the help of the coherent states technique. It is shown that at classical level the Darboux transformation may be treated as a transformation of Kähler potential, which leads to a distortion of the initial phase space.
Classification of multidimensional inflationary models
Authors: Mignemi S. , Schmidt H.-J.
Published: July 2002

We define under which circumstances two multiwarped product spacetimes can be considered equivalent and then we classify the spaces of constant curvature in the Euclidean and Lorentzian signature. For dimension D=2, we get essentially twelve representations, for D=3 exactly eighteen. More generally, for every even D, 5D+2 cases exist, whereas for every odd D, 5D+3 cases exist. For every D, exactly one half of them has the Euclidean signature. Our definition is well suited for the discussion of multidimensional cosmological models, and our results give a simple algorithm to decide whether a given metric represents the inflationary de Sitter spacetime (in unusual coordinates) or not.
Breakdown of smooth solutions of the three-dimensional Euler–Poisson system
Authors: Brauer Uwe
Published: July 2002

Results concerning the occurrence of (kinematical) singularities obtained by Majda et al. [Commun. Math. Phys. 94, 61–66 (1984)] for the incompressible Euler equations and of Chemin [Commun. Math. Phys. 133, 323–329 (1990)] for the compressible Euler equations are generalized for the compressible Euler–Poisson system. This generalization is applied to two situations of physical interest, namely, either the evolution of a compact body with a freely falling boundary or a cosmological solution with finite, spatially periodic, deviations of a Newtonian, Friedman-like cosmological model. Both situations are briefly reviewed. For the compact body the solutions belong to a special class, introduced by Makino [Patterns and Waves (North-Holland, Amsterdam, 1986), pp. 459–479]. In Sec. III, uniqueness is shown for these and therewith one of the severe disadvantages of these solution is eliminated. In both situations the qualitative behavior is similar to the gravitation free case in the sense that only some of the kinematical quantities of the fluid and the gradient of the matter variable diverge; in other words, no specific “gravitation singularity” appears. The differences between the two situations considered here is that, for technical reasons, a nonlinear function w=M(ϱ) has to be introduced as a new matter variable for the compact body. Because ϱ has compact support the blow-up of grad w in the L∞-norm implies two possibilities, one being that the singularity is in the interior of the body. In that case the blow-up of grad w implies the blow-up of grad ϱ. If, on the other hand, the singularity is near the boundary of the body, then no precise information is available.
BRST symmetries for the tangent gauge group
Authors: Cattaneo Alberto S. , Cotta-Ramusino Paolo , Rinaldi Maurizio
Published: July 2002

For any principal bundle P, one can consider the subspace of the space of connections on its tangent bundle TP given by the tangent bundle TA of the space of connections A on P. The tangent gauge group acts freely on TA. Appropriate BRST operators are introduced for quantum field theories that include as fields elements of TA, as well as tangent vectors to the space of curvatures. As the simplest application, the BRST symmetry of the so-called BF-Yang–Mills theory is described and the relevant gauge fixing conditions are analyzed. A brief account on the topological BF theories is also included and the relevant Batalin–Vilkovisky operator is described.
Generalized annihilation operator coherent states
Authors: Ghosh Gautam
Published: July 2002

A set of generalized coherent states as eigenstates of the annihilation operator is proposed. These states are analytic functions of a complex variable and admit a resolution of identity with positive measure. Guided by the classical action angle transformation and the correspondence principle a formalism is developed for the construction of the annihilation operator for a given Hamiltonian.
Interaction energy of generalized Abelian Higgs vortices
Authors: Arthur K. , Brihaye Y. , Tchrakian D. H.
Published: July 2002

The interaction energy between vortices of the generalized Abelian Higgs vortices is studied numerically. These are the solitons of the p-th member of the hierarchy of MaxwellHiggs systems, the p=1 member of which is the usual Abelian Higgs model. It is found that for all p, these vortices have both attractive and repulsive phases, the strengths of these interactions decreasing successively for increasing p. A detailed comparison of the p=1,2 and p=3 cases is made quantitatively, and an extended model, composed of the p=1 and p=2 members, is studied in some detail and shown to exhibit attractive and repulsive phases.
Addendum: Overcoming dissipative distortions by a waveform restorer and designer [J. Math. Phys. 36, 2324 (1995)]
Authors: Foong S. K.
Published: July 2002

If observation is restricted to just a single point in space, then Kac’s path integral solution of the telegrapher equation, a wave equation with a damping term, gives the same solution for an infinite number of inputs consisting of the solutions of the wave equation without damping. While this was implicit in a previous publication by the author [J. Math. Phys. 36, 2324 (1995)], it is made explicit here along with examples.