Physics – Mathematical Physics
Scientific paper
2011-02-24
Physics
Mathematical Physics
48 pages, 6 figures
Scientific paper
We review the rigorous work on many Fermions models which lead to the first constructions of interacting Fermi liquids in two dimensions, and allowed to prove that there are different scaling regimes in two dimensions, depending on the shape of the Fermi surface. We also review progress on the three dimensional case. We start with a pedagogical introduction on quantum field theory and perturbative renormalization. Emphasis is then put on using renormalization around the Fermi surface in a constructive way, in which all orders of perturbation theory are summed rigorously.
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