Exact solution of N baryon problem in the Gross-Neveu model

TL;DR

This paper analytically solves the complex scattering problem of multiple kinks and antikinks in the large N Gross-Neveu model by extending known soliton solutions of the sinh-Gordon equation, linking it to inverse scattering theory.

Contribution

It generalizes the n kink-antikink scattering solution in the Gross-Neveu model using inverse scattering theory and known sinh-Gordon soliton solutions.

Findings

Analytical n kink-antikink scattering solution obtained.

Mapping of Hartree-Fock approach to inverse scattering theory.

Extension of previous two-soliton results to n-soliton case.

Abstract

Recently it was shown that kink baryons and kink-antikink scattering in the massless Gross-Neveu model are closely related to one- and two-soliton solutions of the sinh-Gordon equation. Here we generalize these findings to the case of n kinks and antikinks. Using the known n soliton solution of the sinh-Gordon equation, we solve the general n kink-antikink scattering problem in the large N Gross-Neveu model analytically, mapping the time-dependent Hartree-Fock approach onto inverse scattering theory.