Aspects of Dynamical Symmetry Breaking on a Lattice

TL;DR

This paper investigates how dynamical symmetry breaking manifests on a lattice using Wilson fermions, revealing modifications to the critical line and the absence of new Goldstone bosons, with massive solutions possible at low gauge coupling.

Contribution

It provides new insights into the lattice formulation of dynamical symmetry breaking, specifically modifying the critical line and analyzing the spectrum of particles.

Findings

The critical line is modified from previous models.

No additional Goldstone bosons are found in the spectrum.

Massive solutions exist at small gauge coupling.

Abstract

In the context of four-fermion and gauge interactions, the Schwinger-Dyson equation for the fermion self-energy function is studied with the Wilson fermion on a lattice. We find that the critical line obtained by Bardeen, Leung and Love is modified. No additional Goldstone bosons appear in the spectrum of fundamental particles. Massive solutions to the Schwinger-Dyson equation turn out to be possible for a small gauge coupling.