A Proof of Luttinger Theorem

TL;DR

This paper provides a rigorous, perturbative proof of Luttinger's theorem for Fermi liquids in two and three dimensions, demonstrating the invariance of quasi-particle density with interaction strength and controlling the thermodynamic limit.

Contribution

It offers a simple, rigorous perturbative proof of Luttinger's theorem applicable to Fermi liquids in multiple dimensions, extending the understanding of quasi-particle behavior.

Findings

Quasi-particle density is independent of interaction strength in finite volume.

The thermodynamic limit is controlled to all orders in perturbation theory.

The proof applies to Fermi liquids in two and three dimensions.

Abstract

A rigorous and simple perturbative proof of Luttinger's theorem is sketched for Fermi liquids in two and three dimensions. It is proved that in the finite volume, the quasi-particle density is independent of the interaction strength. The thermodynamic limit is then controlled to all orders in perturbation theory.