Correct functional-integral expressions for partition functions in the coherent-state representation

The grand canonical partition functions in the quantum statistics for boson and fermion systems are rederived in the coherent-state representation and given correct functional-integral expressions. For free systems, the funct ional integrals are easily evaluated by means of the stationary-phase metho d. For interacting systems, either the partition functions or the Green's f unctions can be calculated perturbatively with the aid of the generating fu nctionals defined in the coherent-state representation. (C) 2000 Published by Elsevier Science B.V. All rights reserved.