2011/02/24 by Vincent Rivasseau, Rivasseau, Vincent
Physics and Astronomy · #Advanced Chemical Physics Studies #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Physics of Superconductivity and Magnetism #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.1102.5117
openalex publication_date 2011/02/24 · openalex created_date 2022/09/29 · openalex updated_date 2026/07/28
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.