THERMODYNAMICS OF A WEAKLY INTERACTING BOSE-EINSTEIN GAS

The one-loop effective potential for nonrelativistic bosuns with a del ta function repulsive potential is calculated for a given chemical pot ential using functional methods. After renormalization and at zero tem perature it reproduces the standard ground state energy and pressure a s function of the particle density. At finite temperatures it is found necessary to include ring corrections to the one-loop result in order to satisfy the Goldstone theorem. II is natural to introduce an effec tive chemical potential directly related to the order parameter and wh ich uniformly decreases with increasing temperatures. This is in contr ast to the ordinary chemical potential which peaks at the critical tem perature. The resulting thermodynamics in the condensed phase at very low temperatures is found to be the same as in the Bogoliubov approxim ation where the degrees of freedom are given by the Goldstone bosons. At higher temperatures the ring corrections dominate and result in a c ritical temperature unaffected by the interaction. (C) 1998 Academic P ress.