Universal renormalization of saddle-point integrals for condensed Bose gases

When treating the ground-state contribution exactly, a variant of the saddl e-point method emerges that works even for condensed Bose gases. Results th us obtained, such as canonical partition functions, differ by universal ren ormalization factors from those provided by the conventional but incorrect scheme. The amended method yields the statistical properties of ideal and v ery weakly interacting Bose gases with a fixed number of particles with par ticular simplicity. [S1063-651X(99)13012-5].