EFFECTIVE ACTION APPROACH TO BOSE-EINSTEIN CONDENSATION OF IDEAL-GASES

We present a short review of how the effective action formalism, well known in relativistic quantum field theory, can be used to discuss Bos e-Einstein condensation of non-relativistic gases. This method lends i tself very naturally to an interpretation of Bose-Einstein condensatio n in terms of symmetry breaking. It also allows for the definition of a very elegant regularization technique involving generalized zeta-fun ctions. We show how this method can be used to recover the well known results for the free boson gas, as well as the charged boson gas in a constant magnetic field. A general criterion for interpreting Bose-Ein stein condensation in terms of a phase transition with symmetry breaki ng is given. Finally we present an analysis of Bose-Einstein condensat ion in a harmonic oscillator confining potential trap, and show how th e results of this simple model are in excellent agreement with experim ent.