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arXiv · 1309.2443

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

Gerald V. Dunne·Michael Thies
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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.

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Gerald V. Dunne, Michael Thies. 2013-09-13. Full time-dependent Hartree-Fock solution of large N Gross-Neveu models. https://doi.org/10.1103/physrevd.89.025008

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