bluuebunny/crossref_metadata_2025 huggingface dataset:
The perturbed cubic Schrödinger equation: Selection mechanism, resonant limits, and spatial chaos
Authors: Newton Paul K.
Published: July 2002

Separable solutions of the perturbed cubic Schrödinger equation that are sinusoidal in time with frequency Ωε are considered. Two processes associated with the integrable limit ε→0 are demonstrated. The first will be called a selection mechanism and is demonstrated for Ginzburg–Landau-type perturbations. The second is a resonant limit process and will be demonstrated for perturbations containing spatial driving terms of wave number q. Spatially chaotic behavior is studied in the limits Ωε→0, q→0 and Ωε→∞, q→∞ such that q/Ωαε =const.
Symmetries for the super modified KdV equation
Authors: Kersten P. H. M.
Published: July 2002

Higher-order or generalized symmetries for the super modified KdV equation are constructed. Moreover, by the introduction of graded potentials nonlocal symmetries are obtained, one of them leading to the recursion operator for symmetries in a straightforward way.
Signals in nonlinear electrodynamics invariant under duality rotations
Authors: Salazar Ibarguen Humberto , García A. , Plebanski J.
Published: July 2002

The signal propagation in nonlinear electrodynamics when an arbitrary Einstein–Born–Infeld theory is invariant under duality rotations is discussed. The quasimetric defining the characteristic surfaces that depend on the structural function is obtained. The propagation of nonlinear photons is also briefly discussed.
Universality and integrability of the nonlinear evolution PDE’s describing N-wave interactions
Authors: Calogero F.
Published: July 2002

The universality of the equations describing N-wave interactions is demonstrated by deriving them from a very large class of nonlinear evolution equations (essentially all those whose linear part is dispersive). Various forms of these equations are displayed. The fact that these ‘‘universal’’ nonlinear evolution equations obtain, by an appropriate asymptotic limit, from such a large class of nonlinear evolution equations, suggests that they should be integrable; since for this it is sufficient that the large class from which they are obtainable contain just one integrable equation. This expectation is validated in several cases, by deriving the equations from known integrable equations. In this manner an explanation may be provided of the (already known) integrable nature of certain equations; and new integrable equations may be obtained. Both S-integrable and C-integrable equations are discussed, namely both equations integrable via an appropriate spectral transform and solvable via an appropriate change of variables. In this paper the treatment is limited to equations in 1+1 dimensions.
Construction of the eigenstates for the quantum nonlinear Schrödinger model with the most general supermatrices
Authors: Zhou Yu-Kui , Yun Guo-Hun
Published: July 2002

A quantum nonlinear Schrödinger model with the most general supermatrices, having a structure (n−i, i)×(m−j, j), is studied by using the quantum inverse scattering method. The scattering states and bound states of the model are constructed.
Symmetries of space-time and geodesic symmetries
Authors: Del-Castillo-Negrete Diego , Hojman Sergio
Published: July 2002

It is shown how to construct symmetries of the geodesic equation starting from space-time symmetries. The constants of motion associated with space-time symmetries are recovered and a few new ones are found using non-Noetherian conservation theorems. Explicit examples are presented.
Remarks on a system of coupled nonlinear wave equations
Authors: Krishnan E. V.
Published: July 2002

It is shown that a generalized system of coupled KdV-MKdV equation exhibits solitary wave solutions. It has been shown that an increase in nonlinearity in one variable in a particular fashion does not affect the existence of solitary wave solutions. The periodic traveling wave solutions of the system have also been investigated.
Generalized polyspheroidal periodic functions and the quantum inverse scattering method
Authors: Kuznetsov Vadim B.
Published: July 2002

Bounded and π-periodic eigenfunctions of the operator d2/dv2+[2(μ−ν +(μ+ν+1)cos 2v)/sin 2v] (d/dv)+8ξ cos 2v+4γ2 sin2 2v are studied. These solutions are new special functions, particular cases of which will be the spheroidal, the Coulomb spheroidal, and the hyperspheroidal harmonics. The algebraic technique due to the quantum inverse scattering method is applied to obtain the three-term recursion relations for the coefficients of eigenfunctions expansion at the Jacobi polynomials series and hence the suitable equation (the continued fraction is equal to zero) for eigenvalues. The special functions considered generalize the Truskova polyspheroidal periodic functions (γ=0).
On obtaining the scattering potential and its moments in the partial wave Born approximation
Authors: Mavromatis H. A. , Al-Jalal A. M.
Published: July 2002

Mathematical techniques are used to invert the the partial wave Born approximation. Two expressions are obtained for the scattering potential. Additionally simple expressions are given for various moments of this scattering potential. These results are illustrated by some analytic examples. Finally a few numerical calculations are performed using both ‘‘Born approximation’’ and ‘‘experimental’’ phase shifts in the relevant expressions.
Stochastic calculus and Schrödinger semigroups admitting a ground state
Authors: Pantić Dražen
Published: July 2002

Presented are some new results concerning distorted Brownian motion, the Ito process associated with the Schrödinger operator with ground state. These results are obtained by means of Malliavin stochastic calculus. Under the condition of continuously differentiable drift coefficient with bounded partial derivatives, it is proved that the image of a bounded function after action of the expectation operator of distorted Brownian motion is twice continuously differentiable. This approach enabled us to prove that distorted Brownian motion has twice continuously differentiable transition densities. With the additional assumption that the drift is bounded, it is proved that the corresponding initial value problem has an infinitely differentiable fundamental solution.
The Ginzburg–Landau equations for superconducting films and the Meissner effect
Authors: Yang Yisong
Published: July 2002

The existence of the solutions at the lowest energy level to the Ginzburg–Landau equations describing superconducting films under the influence of an external magnetic field is proved. The condition obtained for maintaining superconducting states does not involve the Ginzburg–Landau parameter, and, more surprisingly, in this condition both the external magnetic field and the thickness of the film play equal parts. The asymptotic behavior of these solutions for small or large values of the external field is also studied, which qualitatively verifies the Meissner effect and quantitatively reproduces the solution found from the classical London theory.
Decomposition of the enveloping algebra of 𝓈ℓ3
Authors: Flath Daniel E.
Published: July 2002

The adjoint representation of 𝓈ℓ3 on its universal enveloping algebra 𝒰 is explicitly decomposed. The result is expressed as a presentation by generators and relations of the commutant in 𝒰 of the raising operators in 𝓈ℓ3. Application is made to the analysis of the representations End(W) for finite-dimensional simple W.
Nonlinear equations invariant under the Poincaré, similitude, and conformal groups in two-dimensional space-time
Authors: Rideau G. , Winternitz P.
Published: July 2002

All realizations of the Lie algebras p(1,1), sim(1,1), and conf(1,1) are classified under the action of the group of local diffeomorphisms of R3. The result is used to obtain all second-order scalar differential equations, invariant under the corresponding Poincaré, similitude, and conformal groups. The invariant equations are, in general, nonlinear, and the requirement of linearity turns out to be very restrictive. Group invariant solutions of some of the conformally invariant equations are obtained either by quadratures or by a linearizing transformation.
Spherically symmetric black holes in Kaluza–Klein unification
Authors: Cho Y. M. , Park D. H.
Published: July 2002

Exact time-independent spherically symmetric black hole solutions of the (4+3)-dimensional Kaluza–Klein theory are obtained by imposing the isometry group E2 on the unified metric. The solutions include the five-dimensional Dobiasch–Maison–Lee solutions as a special case. The physical implication of the solutions is discussed.
On the dynamics of the radially symmetric Heisenberg ferromagnetic spin system
Authors: Porsezian K. , Lakshmanan M.
Published: July 2002

By considering the geometrical equivalence of the radially symmetric Heisenberg ferromagnetic spin system in n-arbitrary spatial dimensions and the generalized nonlinear Schrödinger equation (GNLSE) with radial symmetry, it is shown that they possess the Painlevé property only for the (n=2) circularly (planar radially) symmetric case. For the circularly symmetric case, suitable (2×2) matrix eigenvalue equations are constructed, involving nonisospectral flows and their gauge equivalence is shown. The connection with inhomogeneous systems and, in particular, the linearly x-dependent system is pointed out. Appropriate Bäcklund transformations (BT) and explicit soliton solutions for both the spin systems and the GNLSEs are also derived.
Bosonization techniques on algebraic curves and conformal field theories
Authors: Ferrari Franco
Published: July 2002

The bosonization of b-c systems is studied with conformal weight λ on Riemann surfaces in which the moduli space is parametrized by the branch points (algebraic curves). Besides being interesting in itself, the problem is related to perturbative string theories and to nonfree conformal field theories on the complex plane with the insertion of certain spin fields called the twist fields. The method of λ-differentials is proposed, which allows a complete treatment of the b-c systems on algebraic curves with local Abelian monodromy group. It can be nevertheless applied also to more general algebraic curves allowing the computation of the Green’s functions and shedding some light about the structure of the twist fields in the general case. The connections between our formalism and the solutions of the Riemann monodromy problem, used to find out the conformal blocks of conformal field theories, are pointed out.
On a double Riemann–Hilbert approach to stimulated Raman scattering
Authors: De Mrityunjoy , Chowdhury A. Roy
Published: July 2002

The inverse problem for stimulated Raman Scattering (SRS) with the help of an extension of usual Riemann-Hilbert methodology is considered. The same problem was previously considered by Kaup and Steudel from the viewpoint of scattering formalism. Actually, the Riemann–Hilbert transform has been used for both the x and t part of the Lax pair separately and it has been called double Riemann–Hilbert approach. When compared with the treatment of Kaup and Steudel, the simplicity of our approach becomes quite evident, although it is not still possible to solve an initial-boundary value problem in the present scheme as done by Kaup and Steudel.
The diffeomorphism group and flat principal bundles
Authors: Albertin Uwe K.
Published: July 2002

Representations of the semidirect product group D■Diff(M) in the context of fiber bundle theory are studied. Here, D is the group of compactly supported functions and Diff(M) is the group of compactly supported diffeomorphisms of a manifold M. The carrier space is taken as the space of equivariant functions on a flat principal bundle over M where M is multiply connected. Two principal bundles are taken as equivalent if they are related by a gauge transformation. For the U(1) case it is found that the representations are irreducible, and the equivalence classes of representations are in one to one correspondence with the equivalence classes of bundles. Simple examples are discussed.
Properties of second-order ordinary differential equations invariant under time translation and self-similar transformation
Authors: Bouquet S. E. , Feix M. R. , Leach P. G. L.
Published: July 2002

The general form of a second-order ordinary differential equation invariant under time translation and self-similarity is obtained together with its solution in parametric form. Next two representatives of two different families of such equations are studied. In terms of rescaled phase space variables, the first example has a simple physical interpretation and its limit cycle properties and period are easily derived. Similar results are found for the second example, but the physical interpretation is less obvious. The invariant equations are used as a basis to study the asymptotic behavior of related noninvariant equations thereby underlining the critical value nature of the parameters for which a self-similar solution (SSS) exists.
Regular quantum Markov processes
Authors: Gudder S. , Schindler C.
Published: July 2002

In a previous work, quasidiscrete quantum Markov processes were considered. In order to describe certain continuum situations, the concept of a regular quantum Markov process is now developed. First, the general theory of such processes will be presented. Then, methods for constructing these processes will be considered. To accomplish this, the classical construction of measures on trajectory spaces to complex measures is generalized. A class of processes that have an associated family of transition amplitude operators is constructed. The paper concludes with various examples that illustrate the theory.
Complete sets of functions for perturbations of Robertson–Walker cosmologies and spin 1 equations in Robertson–Walker-type space-times
Authors: Kalnins E. G. , Miller W.
Published: July 2002

Crucial to a knowledge of the perturbations of Robertson–Walker cosmological models are complete sets of functions with which to expand such perturbations. For the open Robertson–Walker cosmology an answer to this question is given. In addition some observations concerning explicit solution by separation of variables of wave equations for spin 1 in a Riemannian space having an infinitesimal line element of which the Robertson–Walker models are a special case are made.
Morphology of the period-doubling universal function
Authors: Warner Roland C. , Delbourgo R.
Published: July 2002

Results are presented concerning the structure on the real line of the ‘‘universal function’’ which is the fixed point solution of the Feigenbaum–Cvitanovic renormalization group equation associated with period-doubling chaos in quadratic maps. It is shown that the values which the function takes at its turning points can be algebraically characterized by relation to the infinite cycle associated with the original turning point of the map on the interval. These extrema become increasingly numerous as the argument increases, and their locations can be found progressively using knowledge of the previously determined extrema. As well as providing a simple understanding of the structure of the universal function these simple observations may be of assistance in investigating the convergence or asymptotic behavior of approximations to the universal function, and perhaps in providing a ‘‘corrector’’ step to some of these schemes.
Infrared and vacuum structure in two-dimensional models of local quantum field theory. II. Fermion bosonization
Authors: Morchio G. , Pierotti D. , Strocchi F.
Published: July 2002

A new general treatment of fermion bosonization in two-dimensional quantum field theory is presented. The main feature is that the bosonization is completely achieved in terms of a single massless scalar field in two dimensions without the introduction of ad hoc selection rules and/or spurion operators. This is made possible by the exploitation of the infrared operators associated to the algebra of the massless scalar field. Fermionic charges, chiral charges, fermionic symmetries, θ angles, etc. are shown to follow naturally from charges and symmetries of the scalar field. As an application, the massless Thirring model is discussed.
Symmetries of the octonionic root system of E8
Authors: Koca Mehmet
Published: July 2002

Octonionic root system of E8 is decomposed as the 9 sets of Hurwitz integers, each set satisfying the binary tetrahedral group structure, and the 12 sets of quaternionic units, each set obeying the dicylic group structure of order 12. This fact is used to prove that the automorphism group of the octonionic root system of E7 is the finite subgroup of G2, of order 12 096, an explicit 7×7 matrix realization of which is constructed. Possible use of the octonionic representation of the E6 root system as orbifolds and the relevance of the binary tetrahedral structures with the statistical mechanics models are suggested.
Analytical evaluation of elastic Coulomb integrals
Authors: Arnoldus Henk F. , George Thomas F.
Published: July 2002

Indefinite integrals over the product of two Coulomb wave functions and a factor r−λ−1, λ=1,2,3,..., have been evaluated analytically. The results for these multipole integrals could be expressed again in terms of Coulomb wave functions, except for the electric quadrupole (λ=2) integral at zero angular momentum in both the incident and final channels.
Hamiltonian formalism for nonregular Lagrangian theories in fibered manifolds
Authors: Zakharov O. A.
Published: July 2002

A Hamiltonian formalism corresponding to the nonregular Lagrangian systems on jet bundles is constructed. The notion of a Hamiltonian on the Legendre bundle is introduced. The relation between Lagrangian and Hamiltonian formalisms is investigated.
Krichever–Novikov algebras on Riemann surfaces of genus zero and one with N punctures
Authors: Anzaldo-Meneses A.
Published: July 2002

Bases of meromorphic vector fields on compact Riemann surfaces of genus zero and one with an arbitrary number of punctures are given. The structure constants are expressed in terms exclusively of algebraic constants. Generalized graded modules are also considered. Centrally extended algebras of vector fields as well as generalized Heisenberg algebras are constructed. The most simple examples are worked out in some detail.
Exact solutions and the effective equation of state in Kaluza–Klein theory
Authors: Ponce de Leon J. , Wesson P. S.
Published: July 2002

A generalization of the standard class of solutions in the Kaluza–Klein (4+1) gravity, wherein the spherically symmetric metric depends not only on the radius but also on the extra coordinate, is considered. Two new classes of exact solutions of the empty Kaluza–Klein field equations are given. However, it is known that apparently empty solutions of the (4+1) Kaluza–Klein equations can be interpreted as solutions with effective matter properties of the (3+1) Einstein equations. The physical importance of the new solutions is that in this approach the dependency on the extra coordinate allows us to obtain more general equations of state than before, including ones for radiation, dust, vacuum, and stiff matter.
Soul expansion of G∞ superfunctions
Authors: Pestov Vladimir G.
Published: July 2002

Supersmooth, or G∞, superfunctions with coefficients in the Banach-Grassmann Rogers algebra B∞ are described in terms of the soul expansion and the notion of Pringsheim regular real function.
New approach to the determination of eigenvalues and eigenfunctions for a relativistic two-fermion equation
Authors: Barut A. O. , Bracken A. J. , Komy S. , Ünal N.
Published: July 2002

Working directly from a covariant equation for two interacting fermions with equal masses and opposite charges, energy eigenvalues and eigenfunctions are calculated to order α6 and α4, respectively, where α is the fine structure constant. The eigenvalues agree with those determined previously by perturbative techniques, including relativistic, recoil and spin corrections, for all the energy levels of orthopositronium. The eigenvalue problems that arise in the present approach are of Sturm–Liouville-type, but involve one, or two coupled, second-order ordinary differential equations in the radial variable r, with up to four singular points. The method used has two key steps. For values of r of the order of the Bohr radius, the equations are transformed by suitable changes of variable into equations which are equivalent, to the appropriate order of approximation, but which are exactly soluble. The second step involves adjusting the behavior at r=0 of the resultant solutions to match the known behavior of the (unknown) exact eigenfunctions. This approach enables approximate eigenvalues to be determined directly, and corresponding approximate eigenfunctions to be obtained for the first time in simple closed form.
Eigenvalues of Casimir invariants of Uq
(gl(m/n))
Authors: Links J. R. , Zhang R. B.
Published: July 2002

A method is investigated for determining the eigenvalues of the Casimir invariants of the quantum supergroup Uq(gl(m‖n)) when acting on irreducible highest weight representations. This leads to a simple eigenvalue formula expressible in terms of the highest weight labels.
Poisson structure of dynamical systems with three degrees of freedom
Authors: Gümral Hasan , Nutku Yavuz
Published: July 2002

It is shown that the Poisson structure of dynamical systems with three degrees of freedom can be defined in terms of an integrable one-form in three dimensions. Advantage is taken of this fact and the theory of foliations is used in discussing the geometrical structure underlying complete and partial integrability. Techniques for finding Poisson structures are presented and applied to various examples such as the Halphen system which has been studied as the two-monopole problem by Atiyah and Hitchin. It is shown that the Halphen system can be formulated in terms of a flat SL(2,R)-valued connection and belongs to a nontrivial Godbillon–Vey class. On the other hand, for the Euler top and a special case of three-species Lotka–Volterra equations which are contained in the Halphen system as limiting cases, this structure degenerates into the form of globally integrable bi-Hamiltonian structures. The globally integrable bi-Hamiltonian case is a linear and the SL(2,R) structure is a quadratic unfolding of an integrable one-form in 3+1 dimensions. It is shown that the existence of a vector field compatible with the flow is a powerful tool in the investigation of Poisson structure and some new techniques for incorporating arbitrary constants into the Poisson one-form are presented herein. This leads to some extensions, analogous to q extensions, of Poisson structure. The Kermack–McKendrick model and some of its generalizations describing the spread of epidemics, as well as the integrable cases of the Lorenz, Lotka–Volterra, May–Leonard, and Maxwell–Bloch systems admit globally integrable bi-Hamiltonian structure.
Recursion relations in U(N) integral in lattice QCD
Authors: Tanimura N. , Tanimura O.
Published: July 2002

On the basis of the Schwinger–Dyson variational method the recursion relations of the character expansion coefficients of the U(N) gauge action are derived. Three recursion relations that are associated with the Casimir invariants are shown to be enough to determine the coefficients completely.
Spatially homogeneous isotropic models with nonminimally coupled electromagnetic field
Authors: Berman M. S. , Som M. M.
Published: July 2002

In the spatially homogeneous isotropic space–time the consequences of the nonminimal coupling of the electromagnetic vector potential with gravity have been studied. One obtains an equation of state that depends on the scale factor.
Deformations of Poisson algebra in terms of star products and q-deformed mechanics
Authors: Suzuki Takashi
Published: July 2002

Using star products, deformations of algebra of classical mechanics, i.e., Poisson algebra, are discussed in the framework of phase space, and algebras of q-deformed classical and quantum mechanics are obtained. In order to formulate q-deformed mechanics, enlarged phase space is introduced by attaching internal space on each point of classical phase space. The internal space is the origin of q deformations. Commutation relations between coordinate and momentum in q-deformed classical and quantum mechanics are derived and the q-deformed quantum mechanical free particle is also discussed.
Perturbation theory and locality in the field–antifield formalism
Authors: Gomis Joaquim , París Jordi
Published: July 2002

The Batalin–Vilkovisky formalism is studied in the framework of perturbation theory by analyzing the antibracket Becchi–Rouet–Stora–Tyutin (BRST) cohomology of the proper solution S0. It is concluded that the recursive equations for the complete proper solution S can be solved at any order of perturbation theory. If certain conditions on the classical action and on the gauge generators are imposed the solution can be taken local.
Convergence of an infinite product of Lie transformations
Authors: Gjaja I.
Published: July 2002

Sufficient conditions are given for convergence of a product of Lie transformations generated by homogeneous polynomials of increasing order. It is shown that if the coefficients of the polynomials do not grow more rapidly with order than exponential functions, then there exists a finite domain around the origin for which the infinite product is a convergent transformation.
A generalized parameter imbedding method
Authors: Cheng G. , Kuo T. K.
Published: July 2002

The parameter imbedding method for the Fredholm equation converts it into an initial value problem in its parameter λ. The method is established for general operator equations of the form [I+f̂(λ)]ψ=φ. It is particularly useful for studying spontaneous symmetry breaking problems such as contained in the nonlinear Schwinger–Dyson equation.
More on U
q(su(1,1)) with q a root of unity
Authors: Suzuki Takashi
Published: July 2002

Highest weight representations of Uq(su(1,1)) with q=exp πi/N are investigated. The structures of the irreducible highest weight modules are discussed in detail. The Clebsch–Gordan decomposition for the tensor product of two irreducible representations is discussed. By using the results, a representation of SL(2,R)⊗Uq(su(2)) is also presented in terms of holomorphic sections which also have Uq(su(2)) index. Furthermore, ZN-graded supersymmetry is realized in terms of the representation. An explicit realization of Osp(1‖2) via the highest weight representation of Uq(su(1,1)) with q2=−1 is given.
Representation theory approach to the polynomial solutions of q-difference equations: Uq(sl(3)) and beyond
Authors: Dobrev V. K. , Truini P. , Biedenharn L. C.
Published: July 2002

A new approach to the theory of polynomial solutions of q-difference equations is proposed. The approach is based on the representation theory of simple Lie algebras 𝒢 and their q-deformations and is presented here for Uq(sl(n)). First a q-difference realization of Uq(sl(n)) in terms of n(n−1)/2 commuting variables and depending on n−1 complex representation parameters, ri, is constructed. From this realization lowest weight modules (LWM) are obtained which are studied in detail for the case n=3 (the well-known n=2 case is also recovered). All reducible LWM are found and the polynomial bases of their invariant irreducible subrepresentations are explicitly given. This also gives a classification of the quasi-exactly solvable operators in the present setting. The invariant subspaces are obtained as solutions of certain invariant q-difference equations, i.e., these are kernels of invariant q-difference operators, which are also explicitly given. Such operators were not used until now in the theory of polynomial solutions. Finally, the states in all subrepresentations are depicted graphically via the so-called Newton diagrams.
Instability proof for Einstein–Yang–Mills solitons and black holes with arbitrary gauge groups
Authors: Brodbeck Othmar , Straumann Norbert
Published: July 2002

We prove that static, spherically symmetric, asymptotically flat soliton and black hole solutions of the Einstein–Yang–Mills equations are unstable for arbitrary gauge groups, at least for the ‘‘generic’’ case. This conclusion is derived without explicit knowledge of the possible equilibrium solutions.
On group invariant solutions of the Boltzmann equation
Authors: Bobylev A. V. , Caraffini G. L. , Spiga G.
Published: July 2002

After reviewing the complete Lie group for the full Boltzmann equation, it is shown that projective transformations play a special role in the general case, and the class of invariant solutions giving rise to homoenergetic affine flows is presented. Homoenergetic affine flows in the two-dimensional case [potential U(r)∝r−2] are considered in detail: It is shown that the general solution of this problem can be essentially simplified by projective transformations.
Nonlinear discrete systems with nonanalytic dispersion relations
Authors: Boiti M. , Leon J. , Pempinelli F.
Published: July 2002

A discrete system of coupled waves (with nonanalytic dispersion relation) is derived in the context of the spectral transform theory for the Ablowitz–Ladik spectral problem (discrete version of the Zakharov–Shabat system). This 3-wave evolution problem is a discrete version of the stimulated Raman scattering equations, and it is shown to be solvable for arbitrary boundary value of the two radiation fields and initial value of the medium state. The spectral transform is constructed on the basis of the ∂-approach.
BRST quantization of gauge theory in noncommutative geometry: Matrix derivative approach
Authors: Lee Chang-Yeong , Hwang Dae Sung , Ne’eman Yuval
Published: July 2002

The Becchi–Rouet–Stora–Tyutin (BRST) quantization of a gauge theory in noncommutative geometry is carried out in the ‘‘matrix derivative’’ approach. BRST/anti-BRST transformation rules are obtained by applying the horizontality condition, in the superconnection formalism. A BRST/anti-BRST invariant quantum action is then constructed, using an adaptation of the method devised by Baulieu and Thierry-Mieg for the Yang–Mills case. The resulting quantum action turns out to be the same as that of a gauge theory in the ’t Hooft gauge with spontaneously broken symmetry. Our result shows that only the even part of the supergroup acts as a gauge symmetry, while the odd part effectively provides a global symmetry. We treat the general formalism first, then work out the SU(2/1) and SU(2/2) cases explicitly.
Transformation bracket for 2D hyperspherical harmonics and its applications to few-anyon problems
Authors: Ruan W. Y. , Bao C. G.
Published: July 2002

The transformation bracket of hyperspherical harmonics with different sets of hyperspherical coordinates as arguments has been derived for an arbitrary number of particles with arbitrary masses in two space dimensions. The solution of the four-anyon problem is given as an example to illustrate its applications.
Covariant path integrals on hyperbolic surfaces
Authors: Schaefer Joe
Published: July 2002

DeWitt’s covariant formulation of path integration [B. De Witt, “Dynamical theory in curved spaces. I. A review of the classical and quantum action principles,” Rev. Mod. Phys. 29, 377–397 (1957)] has two practical advantages over the traditional methods of “lattice approximations;” there is no ordering problem, and classical symmetries are manifestly preserved at the quantum level. Applying the spectral theorem for unbounded self-adjoint operators, we provide a rigorous proof of the convergence of certain path integrals on Riemann surfaces of constant curvature −1. The Pauli–DeWitt curvature correction term arises, as in DeWitt’s work. Introducing a Fuchsian group Γ of the first kind, and a continuous, bounded, Γ-automorphic potential V, we obtain a Feynman–Kac formula for the automorphic Schrödinger equation on the Riemann surface Γ\ℍ. We analyze the Wick rotation and prove the strong convergence of the so-called Feynman maps [K. D. Elworthy, Path Integration on Manifolds, Mathematical Aspects of Superspace, edited by Seifert, Clarke, and Rosenblum (Reidel, Boston, 1983), pp. 47–90] on a dense set of states. Finally, we give a new proof of some results in C. Grosche and F. Steiner, “The path integral on the Poincare upper half plane and for Liouville quantum mechanics,” Phys. Lett. A 123, 319–328 (1987).
An exactly solvable two-body problem with retarded interactions and radiation reaction in classical electrodynamics
Authors: Rivera R. , Villarroel D.
Published: July 2002

An exactly solvable two-body problem dealing with the Lorentz–Dirac equation is constructed in this paper. It corresponds to the motion of two identical charges rotating at opposite ends of a diameter, in a fixed circle, at constant angular velocity. The external electromagnetic field that allows this motion consists of a tangential time-independent electric field with a fixed value over the orbit circle, and a homogeneous time-independent magnetic field that points orthogonally to the orbit plane. Because of the geometrical symmetries of the charges’ motion, in this case it is possible to obtain the rate of radiation emitted by the charges directly from the equation of motion. The rate of radiation is also calculated by studying the energy flux across a sphere of a very large radius, using the far retarded fields of the charges. Both calculations lead to the same result, in agreement with energy conservation.
Coupled Korteveg–de Vries hierarchy with sources and its Newton decomposition
Authors: Marciniak Krzysztof
Published: July 2002

A Lax representation for the equations of the coupled Korteveg–de Vries (cKdV) hierarchy with sources is derived from the energy-dependent Schrödinger spectral problem. It is proved that each stationary flow of the cKdV hierarchy with sources can be reparametrized as a system of Newton equations with velocity-independent forces. These Newton systems have a Lagrangian formulation and are completely integrable. The developed decomposition techniques lead to construction of new infinite families of integrable classical mechanical systems.
The Darboux system: Finite-rank constraints and Darboux transformations
Authors: Guil Francisco , Mañas Manuel
Published: July 2002

The exponential solutions of the Darboux equations for conjugate nets is considered. It is shown that rank-one constraints over the right derivatives of invertible operators on an arbitrary linear space give solutions of the Darboux system, which can be understood as a vectorial Darboux transformation of the exponential background. The method is extended further to obtain vectorial Darboux transformations of the Darboux system.
Graphical classification of global SO(n) invariants and independent general invariants
Authors: Ichinose Shoichi , Ikeda Noriaki
Published: July 2002

This paper treats some basic points in general relativity and in its perturbative analysis. Firstly a systematic classification of global SO(n) invariants, which appear in the weak-field expansion of n-dimensional gravitational theories, is presented. Through the analysis, we explain the following points: (a) a graphical representation is introduced to express invariants clearly; (b) every graph of invariants is specified by a set of indices; (c) a number, called weight, is assigned to each invariant. It expresses the symmetry with respect to the suffix-permutation within an invariant. Interesting relations among the weights of invariants are given. Those relations show the consistency and the completeness of the present classification; (d) some reduction procedures are introduced in graphs for the purpose of classifying them. Secondly the above result is applied to the proof of the independence of general invariants with the mass-dimension M6 for the general geometry in a general space dimension. We take a graphical representation for general invariants too. Finally all relations depending on each space-dimension are systematically obtained for 2, 4, and 6 dimensions.
A Dirac sea and thermodynamic equilibrium for the quantized three-wave interaction
Authors: Beals Richard , Sattinger David , Williams Eric
Published: July 2002

The classical version of the three-wave interaction models the creation and destruction of waves; the quantized version models the creation and destruction of particles. The quantum three-wave interaction is described and the Bethe ansatz for the eigenfunctions is given in closed form. The Bethe equations are derived in a rigorous fashion and are shown to have a thermodynamic limit. The Dirac sea of negative energy states is obtained as the infinite density limit. Finite particle/hole excitations are determined and the asymptotic relation of energy and momentum is obtained. The Yang–Yang functional for the relative free energy of finite density excitations is constructed and is shown to be convex and bounded below. The equations of thermal equilibrium are obtained.
Two-body Dirac equations for general covariant interactions and their coupled Schrödinger-like forms
Authors: Long Peter , Crater Horace W.
Published: July 2002

We present new and useful “external potential” forms of the two-body Dirac equations of constraint dynamics for combined scalar, vector, pseudoscalar, pseudovector, and tensor interactions. These equations have potential applications in two-body problems for bound states in meson spectroscopy and phase shift analysis in nucleon–nucleon scattering. Toward this end, we derive their coupled Schrödinger-like forms using matrix techniques and obtain the corresponding radial equations to these forms from scalar and vector spherical harmonic decompositions.
Conditions for regular space-times with compact spatial sections
Authors: Oliveira-Neto G.
Published: July 2002

We apply the holonomy method to study the regularity of space-times whose initially open spatial sections are made compact. We restrict our attention to a set of different expressions of the anti-de Sitter space-time in (2+1)-dimensions. After we have computed the holonomy matrix to this set, we explicitly derive the regularity conditions for two elements of the set. The first expression, relevant to classical cosmology, will be regular if the periods of the compactified directions are 2π. The other expression, relevant to quantum cosmology, will be regular if the cosmological constant has a certain, well defined, discrete spectrum.
q
-deformed star products and Moyal brackets
Authors: Dayi Ömer F.
Published: July 2002

The standard and antistandard ordered operators acting on two-dimensional q-deformed phase space are shown to satisfy algebras which can be called q−W∞. q-star products and q-Moyal brackets corresponding to these algebras are constructed. Some applications like defining q-classical mechanics and q-path integrals are discussed.
On infinite-dimensional algebras of symmetries of the self-dual Yang–Mills equations
Authors: Ivanova T. A.
Published: July 2002

Infinite-dimensional algebras of hidden symmetries of the self-dual Yang–Mills equations are considered. A current-type algebra of symmetries and an affine extension of conformal symmetries introduced recently are discussed using the twistor picture. It is shown that the extended conformal symmetries of the self-dual Yang–Mills equations have a simple description in terms of Ward’s twistor construction.
Algebraic expressions for O(N)⊃O(N−1) reduction factors for the three-rowed irreducible representations
Authors: Sun Hong-zhou , Ruan Dong
Published: July 2002

Using the concept of irreducible tensor basis and the properties of irreducible tensor operator, we give all O(N)⊃O(N−1) reduction factors for (m1m2m30⋅0)⊗(100⋅0).
On the Fay identity for Korteweg–de Vries tau functions and the identity for the Wronskian of squared solutions of Sturm–Liouville equation
Authors: Mishev Yordan P.
Published: July 2002

We show that the well-known identity for the Wronskian of squared solutions of a Sturm–Liouville equation follows from the Fay identity. We also study some odd-order [(2n−1)-order, n=2,3,…] identities which are specific for tau functions, related to the KdV hierarchy.
The generalized thin-sandwich problem and its local solvability
Authors: Giulini Domenico
Published: July 2002

We consider Einstein gravity coupled to matter consisting of a gauge field with any compact gauge group and minimally coupled scalar fields. We investigate under what conditions a free specification of a spatial field configuration and its time derivative allows us to solve the constraints for lapse, shift, and other gauge parameters and hence determine a solution to the field equations (thin-sandwich problem). We establish sufficient conditions under which the thin-sandwich problem can be solved locally in field space.
Large deviations for ideal quantum systems
Authors: Lebowitz Joel L. , Lenci Marco , Spohn Herbert
Published: July 2002

We consider a general d-dimensional quantum system of non-interacting particles in a very large (formally infinite) container. We prove that, in equilibrium, the fluctuations in the density of particles in a subdomain Λ of the container are described by a large deviation function related to the pressure of the system. That is, untypical densities occur with a probability exponentially small in the volume of Λ, with the coefficient in the exponent given by the appropriate thermodynamic potential. Furthermore, small fluctuations satisfy the central limit theorem.
Asymptotic dynamical difference between the nonlocal and local Swift–Hohenberg models
Authors: Lin Guoguang , Gao Hongjun , Duan Jinqiao , Ervin Vincent J.
Published: July 2002

In this paper the difference in the asymptotic dynamics between the nonlocal and local two-dimensional Swift–Hohenberg models is investigated. It is shown that the bounds for the dimensions of the global attractors for the nonlocal and local Swift–Hohenberg models differ by an absolute constant, which depends only on the Rayleigh number, and upper and lower bounds of the kernel of the nonlocal nonlinearity. Even when this kernel of the nonlocal operator is a constant function, the dimension bounds of the global attractors still differ by an absolute constant depending on the Rayleigh number.
A finite-dimensional integrable system and the r-matrix method
Authors: Shi Qi-Yan , Zhu Si-Ming
Published: July 2002

The nonlinearization method is used on the soliton hierarchy associated with the 4×4 AKNS eigenvalue problem, from which a new finite-dimensional Hamiltonian system is obtained by nonlinearization of the eigenvalue problem and its ajoint one. A Lax representation is deduced for the system. The Lax operator admits the representation of an r-matrix. The 4N functionally independent and involutive integrals of motion are obtained via the r-matrix, which shows that the system is completely integrable in the Liouville sense.
Equation of state for liquid nitrogen in the high-density limit
Authors: Bardik V. Yu. , Sysoev V. M.
Published: July 2002

Equations of state are proposed for describing the isothermal compression of liquid argon. These equations are derived by the method of integral equations in the statistical theory of the condensed state of matter. The thermophysical data are analyzed for calculating the isotherms and parameters of molecular interaction potential.
Turbulent thermal convection in a finite domain: Part I. Theory
Authors: Sirovich L. , Park H.
Published: July 2002

Determination of the empirical eigenfunctions for turbulent flows, which result from the Karhunen–Loève procedure, is considered in some generality for fully inhomogeneous flows. Group theoretical considerations are shown to lead to considerable increases in an available database. In addition, group representation procedures are shown to lead to substantial simplification. In fact, for the application considered here, a nonmanageable problem is reduced to one that is solvable. The general methods and techniques presented here are applied to the case of Rayleigh–Bénard convection in a finite box. In addition, indication is made of how to apply the procedures to several other cases. Some results of applying the method of empirical eigenfunctions to a numerical simulation of this particular flow [H. Park and L. Sirovich, Phys. Fluids A 2, 1659 (1990)] are presented here.
Convection of a pattern of vorticity through a reacting shock wave
Authors: Jackson T. L. , Kapila A. K. , Hussaini M. Y.
Published: July 2002

The passage of a weak vorticity disturbance through a reactive shock wave, or detonation, is examined by means of a linearized treatment. Of special interest is the effect of chemical heat release on the amplification of vorticity, in particular, and on the disturbance pattern generated downstream of the detonation, in general. It is found that the effect of exothermicity is to amplify the refracted waves. The manner in which the imposed disturbance alters the structure of the detonation itself is also discussed.
Remobilizing surfactant retarded fluid particle interfaces. I. Stress-free conditions at the interfaces of micellar solutions of surfactants with fast sorption kinetics
Authors: Stebe Kathleen J. , Lin Shi-Yow , Maldarelli Charles
Published: July 2002

Surfactant molecules adsorb onto the interfaces of moving fluid particles and are convected to regions in which the surface flow converges. Accumulation of surfactant in these regions creates interfacial tension gradients that retard the surface flow. In this study it is argued theoretically and demonstrated experimentally that fluid movement on the surface of a drop or bubble can remain unhindered in the presence of a single adsorbed surfactant if, relative to the convective rate of transport of adsorbed surfactant along the surface, desorption is fast, and the bulk concentration is high enough so that diffusion away from the particle is fast. For this circumstance, a uniform surface concentration of surfactant is maintained, and no gradients in surface tension arise to retard the surface velocity. The fluid particle flow behaves as it would in the absence of surfactant save that it has a reduced, uniform surface tension. The remobilization of surfactant-laden interfaces of fluid particles is demonstrated experimentally in a three-phase periodic slug flow in a capillary tube in which a train of alternating air and aqueous slugs ride on an annular wetting film of fluorocarbon oil. Surfactant, dissolved in the aqueous slug phase, adsorbs onto and retards the aqueous–oil interface. The hydrodynamics of this flow is such that small changes in the mobility of this interface create large shear rates in the oil layer. This significantly increases the pressure drop required to drive the slug train at constant velocity. Three surface adsorbers are used to demonstrate surface remobilization: The polyethoxy, nonionic surfactants Triton X-100 and Brij-35, which have fast desorption kinetics and do not retard the surface flow at high concentrations and, as a counter example, the desorption hindered protein bovine serum albumin, which is shown to be unable to remobilize an interface even at high concentration.