Renormalization group for fermions. A review on mathematical results

The study of one-dimensional nonrelativistic interacting Fermi systems has attracted a vast interest over the years, among physicists andmathematicians. The mathematical interest is motivated by the possibility, due to the low dimensionality, of obtaining some rigorous nontrivial results about such systems (conversely, up to now, this is almost impossible in higher dimensions). The physical motivations arise from the fact that such systems can modelize some real materials, like organic anisotropic compounds. A new wind of interest among physicists was generatedin 1990 by the Anderson theory of high Tc superconductivity [1], which relies on the assumption that the physics of two-dimensional interacting Fermi systems is somehow similar to the physics of one-dimensional ones.