Nonperturbative study of the Gross-Neveu model based on the generalized Hartree-Fock method

Due to integrability, baryon-baryon scattering in the massless Gross-Neveu model at large $N$ features only forward elastic scattering. A bare mass term breaks integrability and is therefore expected to induce backward elastic scattering as well as inelastic reactions. We confirm these expectations by a study of baryon-baryon scattering in the massive Gross-Neveu model near the nonrelativistic limit. This restriction enables us to solve the time-dependent Hartree-Fock equations with controlled approximations, using a combination of analytical methods from an effective field theory and the numerical solution of partial differential equations.Due to integrability, baryon-baryon scattering in the massless Gross-Neveu model at large $N$ features only forward elastic scattering. A bare mass term breaks integrability and is therefore expected to induce backward elastic scattering as well as inelastic reactions. We confirm these expectations by a study of baryon-baryon scattering in the massive Gross-Neveu model near the nonrelativistic limit. This restriction enables us to solve the time-dependent Hartree-Fock equations with controlled approximations, using a combination of analytical methods from an effective field theory and the numerical solution of partial differential equations.

arXiv:1706.06382Physical review. D/Physical review. D.Oct 23, 20173 citations

Generalized Hartree-Fock theory and the Hubbard model

Volker Bach, Élliott H. Lieb, Jan Philip Solovej

arXiv:cond-mat/9312044Journal of Statistical PhysicsJul 1, 1994222 citations

Due to integrability, baryon-baryon scattering in the massless Gross-Neveu model at large

N

features only forward elastic scattering. A bare mass term breaks integrability and is therefore expected to induce backward elastic scattering as well as inelastic reactions. We confirm these expectations by a study of baryon-baryon scattering in the massive Gross-Neveu model near the nonrelativistic limit. This restriction enables us to solve the time-dependent Hartree-Fock equations with controlled approximations, using a combination of analytical methods from an effective field theory and the numerical solution of partial differential equations.