Continuous Constructive Fermionic Renormalization

TL;DR

This paper introduces a novel method for constructing the 2D Gross-Neveu model that reorganizes perturbation series into trees, enabling non-perturbative definition and explicit solution of the renormalization group equations without traditional discretization or cluster expansion.

Contribution

It presents a new approach that reorganizes perturbative series into trees, allowing non-perturbative analysis and explicit solutions of renormalization group equations for the model.

Findings

First non-perturbative definition of RG equations for the model

Explicit construction of RG solutions

Elimination of cluster expansion and phase-space discretization

Abstract

We build the two dimensional Gross-Neveu model by a new method which requires neither cluster expansion nor discretization of phase-space. It simply reorganizes the perturbative series in terms of trees. With this method we can for the first time define non perturbatively the renormalization group differential equations of the model and at the same time construct explicitly their solution.