Abstract:
Using the method of a continuous renormalization group around the Fermi surface, we prove that a two-dimensional interacting system of Fermions at low temperature T is a Fermi liquid in the domain , where K is some numerical constant. According to [S1], this means that it is analytic in the coupling constant λ, and that the first and second derivatives of the self energy obey uniform bounds in that range. This is also a step in the program of rigorous (non-perturbative) study of the BCS phase transition for many Fermion systems; it proves in particular that in dimension two the transition temperature (if any) must be non-perturbative in the coupling constant. The proof is organized into two parts: the present paper deals with the convergent contributions, and a companion paper (Part II) deals with the renormalization of dangerous two point subgraphs and achieves the proof.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 27 July 1999 / Accepted: 31 May 2000
Rights and permissions
About this article
Cite this article
Disertori, M., Rivasseau, V. Interacting Fermi Liquid in Two Dimensions¶at Finite Temperature.¶Part I: Convergent Attributions. Commun. Math. Phys. 215, 251–290 (2000). https://doi.org/10.1007/s002200000300
Issue Date:
DOI: https://doi.org/10.1007/s002200000300