An inversion theorem in Fermi surface theory

TL;DR

This paper proves a perturbative inversion theorem relating the interacting and noninteracting Fermi surfaces in certain fermion systems, clarifying the role of the counterterm in Fermi surface deformation.

Contribution

It introduces a new inversion theorem that connects the self-energy to Fermi surface deformation in models with convex Fermi surfaces and short-range interactions.

Findings

Establishes a mathematical link between self-energy and Fermi surface deformation.

Provides a physical interpretation of the counterterm function in renormalization.

Validates the theorem for a class of many fermion systems with convex Fermi surfaces.

Abstract

We prove a perturbative inversion theorem for the map between the interacting and the noninteracting Fermi surface for a class of many fermion systems with strictly convex Fermi surfaces and short-range interactions between the fermions. This theorem gives a physical meaning to the counterterm function K that we use in the renormalization of these models: K can be identified as that part of the self--energy that causes the deformation of the Fermi surface when the interaction is turned on.