Occupation numbers from functional integral

Understand

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.