The canonical ensemble revisited: a projection operator approach

Constraining the particle number N in the canonical ensemble hampers the systematic calculation of the partition function Z$_N$ for non-interacting fermions and bosons, unlike in the case of the grand-canonical ensemble. Recently, we have shown that this task can be accomplished by invoking a projection operator that automatically imposes the particle number constraint in the many-particle Hilbert space. As a result, an integral representation is obtained for Z$_N$, as well as for the the two-point and four-point correlation functions. As an illustration, the Helmholtz free energy and the chemical potential are calculated for a two-dimensional electron gas typically residing in the inversion layer of a field-effect transistor.