Breathers and their interaction in the massless Gross-Neveu model

TL;DR

This paper analyzes the properties and interactions of breather states in the massless Gross-Neveu model, providing exact solutions for their scattering behavior and confirming their consistency with relativistic Hartree-Fock equations.

Contribution

It presents the first exact analytical solutions for breather-breather scattering in the massless Gross-Neveu model, extending previous ansatz-based approaches.

Findings

Breathers are confirmed as solutions to the relativistic time-dependent Hartree-Fock equations.

Exact scattering solutions for two breathers with arbitrary parameters are derived.

The solutions are illustrated with specific examples.

Abstract

The breather is a vibrating multifermion bound state of the massless Gross-Neveu model, originally found by Dashen, Hasslacher and Neveu in the large N limit. We exhibit the salient features of this state and confirm that it solves the relativistic time-dependent Hartree-Fock equations. We then solve the scattering problem of two breathers with arbitrary internal parameters and velocities, generalizing an ansatz recently developed for the baryon-baryon scattering problem in the same model. The exact analytical solution is given and illustrated with a few examples.