The four-fermion interaction in D=2,3,4: a nonperturbative treatment

TL;DR

This paper introduces a nonperturbative method to analyze the Gross-Neveu model across dimensions 2, 3, and 4, revealing spontaneous symmetry breaking in lower dimensions and triviality in four dimensions.

Contribution

It presents a novel nonperturbative approach to study four-fermion interactions in various dimensions, providing insights into symmetry breaking and coupling behavior.

Findings

Spontaneous symmetry breaking occurs in D=2 and D=3.

The running coupling constant is calculated for these dimensions.

The four-dimensional theory appears to be trivial.

Abstract

A new nonperturbative approach is used to investigate the Gross-Neveu model of four fermion interaction in the space-time dimensions 2, 3 and 4, the number $N$ of inner degrees of freedom being a fixed integer. The spontaneous symmetry breaking is shown to exist in $D=2,3$ and the running coupling constant is calculated. The four dimensional theory seems to be trivial.