Renormalization-group approach to the theory of the Fermi surface

We describe an approach to the theory of the Fermi surface based on the renormalization group. A notion of quasi particle appears naturally in the theory. The beta function is finite to all orders of perturbation theory and we compute and discuss it to second order. The normality of the Fermi surface is linked to the repulsivity of the quasi particle potential: the remarkable cancellations that occur in the beta function lead to think that a normal Fermi surface can perhaps occur, but only when the interaction between the quasi particles is repulsive. The approach was first proposed in an earlier paper, [BG1], and we give here an improved version of it, referring to [BG1] only to make use of technical estimates derived there.