Occupation numbers from functional integral

Occupation numbers for non-relativistic interacting particles are discussed within a functional integral formulation. For bosons at zero temperature the Bogoliubov theory breaks down for strong couplings as well as for low-dimensional models. We find that the leading behavior of the occupation numbers for small momentum is governed by a quadratic time derivative in the inverse propagator that is not contained in the Bogoliubov theory. We propose to use a functional renormalization group equation for the occupation numbers in order to implement systematic non-perturbative extensions beyond the Bogoliubov theory. We also discuss interacting fermions, in particular the issue of pseudogaps.