Covariant quantization of the superstring

After reviewing the Green-Schwarz superstring using the approach of Siegel, the superstring is covariantly quantized by constructing a BRST operator from the fermionic constraints and a bosonic pure spinor ghost variable. Physical massless vertex operators are constructed and, for the first time, N-point tree amplitudes are computed in a manifestly ten-dimensional super-Poincare covariant manner. Quantization can be generalized to curved supergravity backgrounds and the vertex operator for fluctuations around AdS(5) x S-5 is explicitly constructed.

A Hodge dual for soldered bundles

In order to account for all possible contractions allowed by the presence of the solder form, a generalized Hodge dual is defined for the case of soldered bundles. Although for curvature the generalized dual coincides with the usual one, for torsion it gives a completely new dual definition. Starting from the standard form of a gauge Lagrangian for the translation group, the generalized Hodge dual yields precisely the Lagrangian of the teleparallel equivalent of general relativity, and consequently also the Einstein-Hilbert Lagrangian of general relativity.

Extended 2D generalized dilaton gravity theories

We show that an anomaly-free description of matter in (1+1) dimensions requires a deformation of the 2D relativity principle, which introduces a non-trivial centre in the 2D Poincare algebra. Then we work out the reduced phase space of the anomaly-free 2D relativistic particle, in order to show that it lives in a noncommutative 2D Minkowski space. Moreover, we build a Gaussian wave packet to show that a Planck length is well defined in two dimensions. In order to provide a gravitational interpretation for this noncommutativity, we propose to extend the usual 2D generalized dilaton gravity models by a specific Maxwell component, which guages the extra symmetry associated with the centre of the 2D Poincare algebra. In addition, we show that this extension is a high energy correction to the unextended dilaton theories that can affect the topology of spacetime. Further, we couple a test particle to the general extended dilaton models with the purpose of showing that they predict a noncommutativity in curved spacetime, which is locally described by a Moyal star product in the low energy limit. We also conjecture a probable generalization of this result, which provides strong evidence that the noncommutativity is described by a certain star product which is not of the Moyal type at high energies. Finally, we prove that the extended dilaton theories can be formulated as Poisson-Sigma models based on a nonlinear deformation of the extended Poincare algebra.

Path integral quantization of generalized quantum electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Generalized neighbor-interaction models induced by nonlinear lattices

It is shown that the tight-binding approximation of the nonlinear Schrodinger equation with a periodic linear potential and periodic in space nonlinearity coefficient gives rise to a number of nonlinear lattices with complex, both linear and nonlinear, neighbor interactions. The obtained lattices present nonstandard possibilities, among which we mention a quasilinear regime, where the pulse dynamics obeys essentially the linear Schrodinger equation. We analyze the properties of such models both in connection to their modulational stability, as well as in regard to the existence and stability of their localized solitary wave solutions.

The canonical structure of Podolsky's generalized electrodynamics on the null-plane

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Renormalizability of generalized quantum electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

A generalized alternating-direction implicit scheme for incompressible magnetohydrodynamic viscous flows at low magnetic Reynolds number

This paper presents numerical simulations of incompressible fluid flows in the presence of a magnetic field at low magnetic Reynolds number. The equations governing the flow are the Navier-Stokes equations of fluid motion coupled with Maxwell's equations of electromagnetics. The study of fluid flows under the influence of a magnetic field and with no free electric charges or electric fields is known as magnetohydrodynamics. The magnetohydrodynamics approximation is considered for the formulation of the non-dimensional problem and for the characterization of similarity parameters. A finite-difference technique is used to discretize the equations. In particular, an extension of the generalized Peaceman and Rachford alternating-direction implicit (ADI) scheme for simulating two-dimensional fluid flows is presented. The discretized conservation equations are solved in stream function-vorticity formulation. We compare the ADI and generalized ADI schemes, and show that the latter is more efficient in simulating low Reynolds number and magnetic Reynolds number problems. Numerical results demonstrating the applicability of this technique are also presented. The simulation of incompressible magneto hydrodynamic fluid flows is illustrated by numerical solution for two-dimensional cases. (c) 2007 Elsevier B.V. All rights reserved.

Approximations for the generalized temperature integral: a method based on quadrature rules

The generalized temperature integral I(m, x) appears in non-isothermal kinetic analysis when the frequency factor depends on the temperature. A procedure based on Gaussian quadrature to obtain analytical approximations for the integral I(m, x) was proposed. The results showed good agreement between the obtained approximation values and those obtained by numerical integration. Unless other approximations found in literature, the methodology presented in this paper can be easily generalized in order to obtain approximations with the maximum of accurate.

Hq(4) symmetry: the linear q-harmonic oscillator based on generalized irreps of the q-deformed Heisenberg algebra

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

QUANTUM BROWNIAN PARTICLE AND MEMORY EFFECTS

The quantum Brownian particle, immersed in a heat bath, is described by a statistical operator whose evolution is ruled by a generalized master equation (GME). The heat bath's degrees of freedom are considered to be either white-noise or colored-noise correlated, while the GME is considered under either the Markov or non-Markov approaches. The comparisons between these considerations are fully developed, and their physical meaning is discussed.

Virasoro constraints and flavor-topology duality in QCD

We derive Virasoro constraints for the zero momentum part of the QCD-like partition functions in the sector of topological charge v. The constraints depend on the topological charge only through the combination N-f +betav/2 where the value of the Dyson index beta is determined by the reality type of the fermions. This duality between flavor and topology is inherited by the small-mass expansion of the partition function and all spectral sum rules of inverse powers of the eigenvalues of the Dirac operator. For the special case beta =2 but arbitrary topological charge the Virasoro constraints are solved uniquely by a generalized Kontsevich model with the potential V(X) = 1/X.

HIGHER-DERIVATIVE SCHWINGER MODEL

Using the operator formalism, we obtain the bosonic representation for the free fermion field satisfying an equation of motion with higher-order derivatives. Then, we consider the operator solution of a generalized Schwinger model with higher-derivative coupling. Since the increasing of the derivative order implies the introduction of an equivalent number of extra fermionic degrees of freedom, the mass acquired by the gauge field is bigger than the one for the standard two-dimensional QED. An analysis of the problem from the functional integration point of view corroborates the findings of canonical quantization, and corrects certain results previously announced in the literature on the basis of Fujikawa's technique.

Using error bounds to compare aggregated generalized transportation models

A comparative study of aggregation error bounds for the generalized transportation problem is presented. A priori and a posteriori error bounds were derived and a computational study was performed to (a) test the correlation between the a priori, the a posteriori, and the actual error and (b) quantify the difference of the error bounds from the actual error. Based on the results we conclude that calculating the a priori error bound can be considered as a useful strategy to select the appropriate aggregation level. The a posteriori error bound provides a good quantitative measure of the actual error.

REDUCTION OF TODA LATTICE HIERARCHY TO GENERALIZED KDV HIERARCHIES AND THE 2-MATRIX MODEL

Toda lattice hierarchy and the associated matrix formulation of the 2M-boson KP hierarchies provide a framework for the Drinfeld-Sokolov reduction scheme realized through Hamiltonian action within the second KP Poisson bracket. By working with free currents, which Abelianize the second KP Hamiltonian structure, we are able to obtain a unified formalism for the reduced SL(M + 1, M - k) KdV hierarchies interpolating between the ordinary KP and KdV hierarchies. The corresponding Lax operators are given as superdeterminants of graded SL(M + 1, M - k) matrices in the diagonal gauge and we describe their bracket structure and field content. In particular, we provide explicit free field representations of the associated W(M, M - k) Poisson bracket algebras generalising the familiar nonlinear W-M+1 algebra. Discrete Backlund transformations for SL(M + 1, M - k) KdV are generated naturally from lattice translations in the underlying Toda-like hierarchy. As an application we demonstrate the equivalence of the two-matrix string model to the SL(M + 1, 1) KdV hierarchy.