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

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 multibreather 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 time-dependent Hartree-Fock 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.