On q-Deformed Supersymmetric Classical Mechanical Models

Based on the idea of quantum groups and paragrassmann variables, we presenta generalization of supersymmetric classical mechanics with a deformation parameter $q= \exp{\frac{2 \pi i}{k}}$ dealing with the $k =3$ case. The coordinates of the $q$-superspace are a commuting parameter $t$ and a paragrassmann variable $\theta$, where $$. The generator and covariant derivative are obtained, as well as the action for some possible superfields.Comment: No figures, 14 pages, Latex, revised versio

Remarks on Charged Vortices in the Maxwell-Chern-Simons Model

We study vortex-like configuration in Maxwell-Chern-Simons Electrodynamics. Attention is paid to the similarity it shares with the Nielsen-Olesen solutions at large distances. A magnetic symmetry between a point-like and an azimuthal-like current in this framework is also pointed out. Furthermore, we address the issue of a neutral and spinless particle interacting with a charged vortex, and obtain that the Aharonov-Casher-type phase depends upon mass and distance parameters.Comment: New refs. added. Version accepted for publication in Phys. Lett.

Remarks on some vacuum solutions of scalar-tensor cosmological models

We present a class of exact vacuum solutions corresponding to de Sitter and warm inflation models in the framework of scalar-tensor cosmologies. We show that in both cases the field equations reduce to planar dynamical systems with constraints. Then, we carry out a qualitative analysis of the models by examining the phase diagrams of the solutions near the equilibrium points.Comment: 12 pages, 4 figures. To be published in the Brazilian Journal of Physic

Electron-electron interaction in a MCS model with a purely spacelike Lorentz-violating background

One considers a planar Maxwell-Chern-Simons electrodynamics in the presence of a purely spacelike Lorentz-violating background. Once the Dirac sector is properly introduced and coupled to the scalar and the gauge fields, the electron-electron interaction is evaluated as the Fourier transform of the Moller scattering amplitude (derived in the non-relativistic limit). The associated Fourier integrations can not be exactly carried out, but an algebraic solution for the interaction potential is obtained in leading order in (v/s)^2. It is then observed that the scalar potential presents a logarithmic attractive (repulsive) behavior near (far from) the origin. Concerning the gauge potential, it is composed of the pure MCS interaction corrected by background contributions, also responsible for its anisotropic character. It is also verified that such corrections may turn the gauge potential attractive for some parameter values. Such attractiveness remains even in the presence of the centrifugal barrier and gauge invariant A.A term, which constitutes a condition compatible with the formation of Cooper pairs.Comment: 12 pages, 3 figures, Revtex4 style, figures revised; to appear in Phys. Rev. D (2005

Scalar and Spinor Particles in the Spacetime of a Domain Wall in String Theory

We consider scalar and spinor particles in the spacetime of a domain wall in the context of low energy effective string theories, such as the generalized scalar-tensor gravity theories. This class of theories allows for an arbitrary coupling of the wall and the (gravitational) scalar field. First, we derive the metric of a wall in the weak-field approximation and we show that it depends on the wall's surface energy density and on two post-Newtonian parameters. Then, we solve the Klein-Gordon and the Dirac equations in this spacetime. We obtain the spectrum of energy eigenvalues and the current density in the scalar and spinor cases, respectively. We show that these quantities, except in the case of the energy spectrum for a massless spinor particle, depend on the parameters that characterize the scalar-tensor domain wall.Comment: LATEX file, 21 pages, revised version to appear in Phys. Rev.

Toda lattice field theories, discrete W algebras, Toda lattice hierarchies and quantum groups

In analogy with the Liouville case we study the $sl_3$ Toda theory on the lattice and define the relevant quadratic algebra and out of it we recover the discrete $W_3$ algebra. We define an integrable system with respect to the latter and establish the relation with the Toda lattice hierarchy. We compute the the relevant continuum limits. Finally we find the quantum version of the quadratic algebra.Comment: 12 pages, LaTe