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

الأصل · EN

We find the general solution to the time-dependent Hartree-Fock problem for scattering solutions of the Gross-Neveu models, with both discrete (GN₂) and continuous (NJL₂) chiral symmetry. We find new multi-breather solutions both for the GN₂ model, generalizing the Dashen-Hasslacher-Neveu breather solution, and also new twisted breathers for the NJL₂ model. These solutions satisfy the full TDHF consistency conditions, and only in the special cases of GN₂ 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 NJL₂ model. Our solution depends crucially on a general class of transparent, time dependent Dirac potentials found recently by algebraic methods.