Radiative corrections to the Casimir effect for the massive scalar field

We compute the $O(\lambda)$ correction to the Casimir energy for the massive $\lambda\phi^4$ model confined between a pair of parallel plates. The calculations are made with Dirichlet and Neumann boundary conditions. The correction is shown to be sensitive to the boundary conditions, except in the zero mass limit, in which case our results agree with those found in the literature.Comment: 6 pages. Work presented at the XXIII Brazilian National Meeting on Particles and Fields (Aguas de Lindoia, Brazil, 15-19 Oct 2002). Also available at http://www.sbf1.if.usp.br/eventos/enfpc/xxiii/procs/RES142.pd

Dynamical Breakdown of Symmetry in a (2+1) Dimensional Model Containing the Chern-Simons Field

We study the vacuum stability of a model of massless scalar and fermionic fields minimally coupled to a Chern-Simons field. The classical Lagrangian only involves dimensionless parameters, and the model can be thought as a (2+1) dimensional analog of the Coleman-Weinberg model. By calculating the effective potential, we show that dynamical symmetry breakdown occurs in the two-loop approximation. The vacuum becomes asymmetric and mass generation, for the boson and fermion fields takes place. Renormalization group arguments are used to clarify some aspects of the solution.Comment: Minor modifications in the text and figure