  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 (J. C. da Silva, A.
Matos Neto, F.C. Khanna and A.E. Santana, Phys. Rev. A 66 (2002) 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.
One interesting result is that the attractive or repulsive nature of the
Casimir pressure can change depending on the rate among the sizes. This fact is
analyzed with specific examples.
