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 Bose-Einstein condensation of non-relativistic gases. This method lends itself very naturally to an interpretation of Bose-Einstein condensation in terms of symmetry breaking. It also allows for the definition of a very elegant regularization technique involving generalizedζ-functions. 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-Einstein condensation in terms of a phase transition with symmetry breaking is given. Finally we present an analysis of Bose-Einstein condensation in a harmonic oscillator confining potential trap, and show how the results of this simple model are in excellent agreement with experiment.
University of Leipzig, Institute of Theoretical Physics, Augustusplatz 10, 04109 Leipzig, Germany.
Klaus
K
Kirsten
Department of Physics, University of Newcastle Upon Tyne, Newcastle Upon Tyne, U.K. NE1 7RU.
David J
DJ
Toms
Bose-Einstein condensation; effective action; symmetry breaking; zeta functions