  Wick's theorem for the expectation values of products of field operators for
a system of noninteracting fermions or bosons plays an important role in the
perturbative approach to the quantum many body problem. A finite temperature
version holds in the framework of the grand canonical ensemble but not for the
canonical ensemble appropriate for systems with fixed particle number like
ultracold quantum gases in optical lattices. Here we present new formulas for
expectation values of products of field operators in the canonical ensemble
using a method in the spirit of Gaudin's proof of Wick's theorem for the grand
canonical case. The deviations from Wick's theorem are examined quantitatively
for two simple models of noninteracting fermions.
