Occupation numbers from functional integral

Occupation numbers for non-relativistic interacting particles are discussed within a functional integral formulation. We concentrate on zero temperature, where 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.