Casimir energy for a scalar field with a frequency dependent boundary condition

We consider the vacuum energy for a scalar field subject to a frequency dependent boundary condition. The effect of a frequency cut-off is described in terms of an {\it incomplete} $\zeta$-function. The use of the Debye asymptotic expansion for Bessel functions allows to determine the dominant (volume, area, >...) terms in the Casimir energy. The possible interest of this kind of models for dielectric media (and its application to sonoluminescence) is also discussed.Comment: 7 pages, RevTeX. Version to appear in PRD (Introduction enlarged, references added

Magnetic Corrections to π{\pi}-π{\pi} Scattering Lengths in the Linear Sigma Model

In this article we consider the magnetic corrections to ${\pi}$-${\pi}$ scattering lengths in the frame of the linear sigma model. For this we consider all the one loop corrections in the s, t and u channels, associate to the insertion of a Schwinger propagator for charged pions, working in the region of small values of the magnetic field. Our calculation relies on an appropriate expansion for the propagator. It turns out that the leading scattering length, $l = 0$ in the S-channel, increases for an increasing value of the magnetic field, in the isospin $I = 2$ case whereas the opposite effect is found for the $I = 0$ case. The isospin symmetry is valid because the insertion of the magnetic field occurs through the absolute value of the electric charges. The channel $I = 1$ does not receive any corrections. These results, for the channels $I = 0$ and $I = 2$ are opposite with respect to the thermal corrections found previously in the literature.Comment: 6 pages. arXiv admin note: text overlap with arXiv:0801.2176; new references were added; to appear in Phys. Rev.

Vacuum instability by a chromoelectric field in 2 + 1-dimensions

The problem of vacuum instability and creation of pairs by external fields SU(2) is studied. The effective mass operator has complex eigenvalues implying decay and pair creation. We consider a constant external chromoelectric field and a region in the parameter space where the vaccum becomes unstable and decays in pairs. Although the calculation is done in SU(2) color group it is also valid for SU(3).Comment: 5 pages, 1 figure, to appear in Physical Review

Two-flavor condensates in chiral dynamics: temperature and isospin density effects

Isospin density and thermal corrections for several condensates are discussed, at the one-loop level, in the frame of chiral dynamics with pionic degrees of freedom. The evolution of such objects give an additional insight into the condensed-pion phase transition, that occurs basically when |\mui|>m_\pi, being |\mui| the isospin chemical potential. Calculations are done in both phases, showing a good agreement with lattice results for such condensates.Comment: 9 pages, 10 figure

Gauge dependence ambiguity and chemical potential in thermal U(1) theory

In this letter we explore the dependence on the gauge fixing condition of several quantities in the U(1) Higgs model at finite temperature and chemical potential. We compute the effective potential at the one loop level, using a gauge fixing condition that depends on $\mu$ and which allows to decouple the contributions of the different fields in the model. In this way we get the mass spectrum and the characterization of the phase transition, pointing out in each case how these quantities depend on the gauge fixing parameter $\xi$. When $\mu$ vanishes, we agree with previous results if $\xi=0$. The gauge dependence problem is also analyzed from the perspective of the Nielsen identities.Comment: fourteen pages, we add an analysis of the problem from the perspective of Nielsen identities, to be published in Modern Letters Physics