What's the difference between a Luttinger surface and a Fermi surface?

[SadScholar]

I'm trying to learn about Luttinger's sum rule, but I haven't taken QM yet, and the papers on the topic are very difficult to understand without it. However it seems qualitatively like the Luttinger surface is equivalent to the Fermi surface. If this is not the case, what's the difference? Does anyone know of a source of information on the topic that can be understood without QM?

 

[sam_bell]

What I gather from Wikipedia: Luttinger's Theorem says the concept of a Fermi Surface can be applied to interacting electrons. Electrons, as you know interact via a 1/(r-r') Coulomb interaction. That makes the quantum problem extremely difficult to solve. Nevertheless, due to screening and other reasons it is often assumed the electrons are not interacting with each other. This leads to the picture of states in k-space that get filled up to form the Fermi surface. It's not a priori clear you can adapt such a picture for interacting electrons. Luttinger showed, that with properly defined quantities, you can still talk about k-space and a Fermi surface and that the same filling law applies.