Thermofield Dynamics and Casimir Effect for Fermions

H. Queiroz, J. C. da Silva, F. C. Khanna, J. M. C. Malbouisson, M. Revzen, A. E. Santana Instituto de F́ısica, Universidade Federal da Bahia, Campus de Ondina, 40210-340, Salvador, BA, Brazil Centro Federal de Educação Tecnológica da Bahia, Rua Emı́dio Santos, 40000-900, Salvador, BA, Brazil Physics Department, Theoretical Physics Institute, University of Alberta, Edmonton, AB T6G 2J1, Canada TRIUMF, 4004, Westbrook mall, Vancouver, BC V6T 2A3, Canada Department of Physics, Technion Institute of Technology, Haifa, 32000, Israel Instituto de F́ısica, Universidade de Braśılia, 70910-900, Braśılia, DF, Brazil Abstract A generalization of the Bogoliubov transformation is developed to describe a space compactified fermionic field. The method is the fermionic 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 field in a d-dimensional box at finite temperature. As a particular case the Casimir energy and pressure for the field confined in a 3-dimensional parallelepiped box are calculated. It is found that the attractive or repulsive nature of the Casimir pressure on opposite faces changes depending on the relative magnitude of the edges. We also determine the temperature at which the Casimir pressure in a cubic box changes sign and estimate its value when the edge of the cube is of the order of the confining lengths for baryons. PACS: 03.70.+k; 11.10.Wx