Functional Integrals for Many-Boson Systems

We express the grand canonical partition function (GCPF) for a system of interacting bosons as a functional integral over one complex function. Our derivation is based on the so-called coherent-state representation [R. J. Glauber, Phys. Rev. 136, 2766 (1963)]. We show how to extract the perturbative expansion of the GCPF and the various Green's functions from our functional-integral representation and we indicate the relevance of our formalism to the theory of superfluidity.