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.