ep - t h / 03 11 24 6 v 1 2 5 N ov 2 00 3 Generalized Bogoliubov Transformation , Fermion Field and Casimir Effect in a Box

In this work a generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermion counterpart of the formalism introduced earlier for bosons (052101), and is based on the thermofield dynamics approach. We analyze the energy-momentum tensor for the Casimir effect of a free massless fermion system in a N-dimensional box in contact with a heat bath. As a particular situation we calculate the Casimir energy and pressure for the field in a 3-dimensional box of sizes L 1 , L 2 , L 3. One interesting result is that the attractive or repulsive nature of the Casimir pressure can change depending on the rate