Europhys. Lett.
Volume 72, Number 1, October 2005
Page(s) 49 - 54
Section General
Published online 12 August 2005
Europhys. Lett., 72 (1), pp. 49-54 (2005)
DOI: 10.1209/epl/i2005-10188-9

A proof of Luttinger's theorem

A. Praz1, 2, J. Feldman3, H. Knörrer1 and E. Trubowitz1

1  Department of Mathematics, Eidgenössische Technische Hochschule Zürich Zürich, Switzerland
2  Paul Scherrer Institut - Villigen, Switzerland
3  Department of Mathematics, University of British Columbia - Vancouver, Canada

received 7 June 2005; accepted in final form 22 July 2005
published online 12 August 2005

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.

05.30.Fk - Fermion systems and electron gas.
05.10.Cc - Renormalization group methods.
71.10.Ay - Fermi-liquid theory and other phenomenological models.

© EDP Sciences 2005