Occupation numbers from functional integral

TL;DR

This paper develops a functional integral approach to analyze occupation numbers in non-relativistic interacting particles at zero temperature, highlighting limitations of Bogoliubov theory and proposing a non-perturbative renormalization group method.

Contribution

It introduces a functional renormalization group framework to systematically extend beyond Bogoliubov theory for occupation numbers at zero temperature.

Findings

Quadratic time derivative dominates small momentum behavior

Bogoliubov theory fails for strong couplings and low dimensions

Proposes a systematic non-perturbative approach

Abstract

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.