Static plane symmetric relativistic fluids and empty repelling singular boundaries

We present a detailed analysis of the general exact solution of Einstein's equation corresponding to a static and plane symmetric distribution of matter with density proportional to pressure. We study the geodesics in it and we show that this simple spacetime exhibits very curious properties. In particular, it has a free of matter repelling singular boundary and all geodesics bounce off it.Comment: 9 pages, 1 figure, accepted for publication in Classical and Quantum Gravit

On spectral types of semialgebraic sets

In this work we prove that a semialgebraic set $M\subset{\mathbb R}^m$ is determined (up to a semialgebraic homeomorphism) by its ring ${\mathcal S}(M)$ of (continuous) semialgebraic functions while its ring ${\mathcal S}^*(M)$ of (continuous) bounded semialgebraic functions only determines $M$ besides a distinguished finite subset $\eta(M)\subset M$. In addition it holds that the rings ${\mathcal S}(M)$ and ${\mathcal S}^*(M)$ are isomorphic if and only if $M$ is compact. On the other hand, their respective maximal spectra $\beta_s M$ and $\beta_s^* M$ endowed with the Zariski topology are always homeomorphic and topologically classify a `large piece' of $M$. The proof of this fact requires a careful analysis of the points of the remainder $\partial M:=\beta_s^* M\setminus M$ associated with formal paths.Comment: 22 page

Noncommutative quantum mechanics and the Aharonov-Casher effect

In this work a new method is developed to investigate the Aharonov-Casher effect in a noncommutative space. It is shown that the holonomy receives non-trivial kinematical corrections.Comment: 8 pages, Plain Tex, to appear in Eur. Phys. J.

On gauge invariant regularization of fermion currents

We compare Schwinger and complex powers methods to construct regularized fermion currents. We show that although both of them are gauge invariant they not always yield the same result.Comment: 10 pages, 1 figur

Duality and bosonization in Schwinger-Keldysh formulation

We present a path-integral bosonization approach for systems out of equilibrium based on a duality transformation of the original Dirac fermion theory combined with the Schwinger-Keldysh time closed contour technique, to handle the non-equilibrium situation. The duality approach to bosonization that we present is valid for $D \geq 2$ space-time dimensions leading for $D=2$ to exact results. In this last case we present the bosonization rules for fermion currents, calculate current-current correlation functions and establish the connection between the fermionic and bosonic distribution functions in a generic, nonequilibrium situation.Comment: 16 pages, 1 figur