A Proof of Luttinger Theorem

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.

7 pages

References in corpus (2)

• Topological approach to Luttinger's theorem and the Fermi surface of a Kondo lattice
• Perturbation Theory around Non-Nested Fermi Surfaces I. Keeping the Fermi Surface Fixed

Cited by in corpus (6)

• Absence of Luttinger's Theorem due to Zeros in the Single-Particle Green Function
• Breakdown of Luttinger's theorem in two-orbital Mott insulators
• Luttinger sum rule for finite systems of correlated electrons
• Luttinger theorem and imbalanced Fermi systems
• On the Luttinger theorem concerning number of particles in the ground states of systems of interacting fermions
• A phenomenological description on an incoherent Fermi liquid near optimal doping in high T_{c} cuprates