Bogoliubov transformation for quantum fields in (Bbb S1)d × Bbb RD−d topology and applications to the Casimir effect

Abstract

A Bogoliubov transformation accounting simultaneously for spatial compactifica-tion and thermal effects is introduced. The fields are described in a ΓDd = Bbb S11 × ... × Bbb S1d × Bbb RD−d topology, and the Bogoliubov transformation is derived by a generalization of the thermofield dynamics formalism, a real-time finite-temperature quantum field theory. We consider the Casimir effect for Maxwell and Dirac fields and for a non-interacting massless QCD at finite temperature. For the fermion sector in a cubic box, we analyze the temperature at which the Casimir pressure changes its sign from attractive to repulsive. This critical temperature is approximately 200 MeV when the edge of the cube is of the order of the confining lengths (≈ 1 : fm) for quarks in baryons.