Bosonized Momentum Distribution of a Fermi Gas via Friedrichs Diagrams

Recently, Benedikter and the author proved an approximate formula for the momentum distribution of a 3d fermionic gas interacting by a short-range pair potential in the mean-field regime, within a trial state close to the ground state. Here, we derive an exact formula for the momentum distribution in this trial state, using a diagrammatic formalism due to Friedrichs. We further demonstrate how the formula of Benedikter and the author arises from a restriction of the contributing diagrams to those corresponding to a bosonization approximation.