A proof of Luttinger's theoremA. 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.
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