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