# Necessary and sufficient conditions for the validity of Luttinger’s theorem

@article{Heath2020NecessaryAS,
title={Necessary and sufficient conditions for the validity of Luttinger’s theorem},
author={Joshuah T Heath and Kevin Shawn Bedell},
journal={New Journal of Physics},
year={2020},
volume={22}
}
• Published 3 June 2019
• Mathematics
• New Journal of Physics
Luttinger’s theorem is a major result in many-body physics that states the volume of the Fermi surface is directly proportional to the particle density. In its ‘hard’ form, Luttinger’s theorem implies that the Fermi volume is invariant with respect to interactions (as opposed to a ‘soft’ Luttinger’s theorem, where this invariance is lost). Despite it is simplicity, the conditions on the fermionic self energy under which Luttinger’s theorem is valid remains a matter of debate, with possible…
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