Continuous renormalization for fermions and Fermi liquid theory

TL;DR

This paper develops a new continuous renormalization group equation for fermion systems, simplifying the analysis of many-fermion systems and establishing criteria for Fermi liquid behavior at positive temperatures.

Contribution

It introduces a Wick ordered continuous RG equation with improved combinatorial properties and proves regularity of the interacting Fermi surface in higher dimensions.

Findings

Determinant bound applies directly to the RG equation.

Simplified proof of regularity properties of the Fermi surface.

Defines a criterion for Fermi liquid behavior at positive temperatures.

Abstract

I derive a Wick ordered continuous renormalization group equation for fermion systems and show that a determinant bound applies directly to this equation. This removes factorials in the recursive equation for the Green functions, and thus improves the combinatorial behaviour. The form of the equation is also ideal for the investigation of many-fermion systems, where the propagator is singular on a surface. For these systems, I define a criterion for Fermi liquid behaviour which applies at positive temperatures. As a first step towards establishing such behaviour in d ge 2, I prove basic regularity properties of the interacting Fermi surface to all orders in a skeleton expansion. The proof is a considerable simplification of previous ones.