Full time-dependent Hartree-Fock solution of large N Gross-Neveu models

TL;DR

This paper provides a comprehensive time-dependent Hartree-Fock solution for large N Gross-Neveu models, revealing new multi-breather solutions and elucidating the structure of baryons and breathers in these models.

Contribution

It introduces the first general TDHF solutions for both GN_2 and NJL_2 models, including new breather configurations and a detailed analysis of their constituent structures.

Findings

New multi-breather solutions for GN_2 and NJL_2 models.

All baryons and breathers are composed of twisted kinks.

Solutions satisfy full TDHF conditions, reducing to Sinh-Gordon in special cases.

Abstract

We find the general solution to the time-dependent Hartree-Fock problem for scattering solutions of the Gross-Neveu models, with both discrete (GN_2) and continuous (NJL_2) chiral symmetry. We find new multi-breather solutions both for the GN_2 model, generalizing the Dashen-Hasslacher-Neveu breather solution, and also new twisted breathers for the NJL_2 model. These solutions satisfy the full TDHF consistency conditions, and only in the special cases of GN_2 kink scattering do these conditions reduce to the integrable Sinh-Gordon equation. We also show that all baryons and breathers are composed of constituent twisted kinks of the NJL_2 model. Our solution depends crucially on a general class of transparent, time dependent Dirac potentials found recently by algebraic methods.