Phase invariant perturbation scheme in Bose-Einstein condensed states

Abstract

In the Bose-Einstein condensation of a dilute alkaline atomic gas trapped in a magnetic potential, one has to deal with a strongly space- (and time-) dependent order parameter, which violates the phase symmetry. In this case, certain relations are required among propagators and vertices, known as Ward-Takahashi identities. In this paper, we show that a systematic self-consistent perturbation scheme can be developed even with a space-time order parameter in such a way as to satisfy the requirement of phase symmetry. The key procedure is that the information concerning the full order parameter, which is self-consistently determined, is included in the unperturbed Hamiltonian.