Luttinger's theorem

In condensed matter physics, Luttinger's theorem[1][2] is a result derived by J. M. Luttinger and J. C. Ward in 1960 that has broad implications in the field of electron transport.

It arises frequently in theoretical models of correlated electrons, such as the high-temperature superconductors, and in photoemission, where a metal's Fermi surface can be directly observed.

Luttinger's theorem states that the volume enclosed by a material's Fermi surface is directly proportional to the particle density.

Specifically, in the interacting case the Fermi surface must be defined according to the criteria that where

is the single-particle Green function in terms of frequency and momentum.