Bosonized Momentum Distribution of a Fermi Gas via Friedrichs Diagrams

Abstract

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.

27 pages, 10 figures

References in corpus (5)

• Correlation Energy of a Weakly Interacting Fermi Gas
• The dilute Fermi gas via Bogoliubov theory
• Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential
• The Gell-Mann$-$Brueckner Formula for the Correlation Energy of the Electron Gas: A Rigorous Upper Bound in the Mean-Field Regime
• Friedrichs Diagrams -- Bosonic and Fermionic