Excited states and a fermion confinemet in a four-fermi model

Abstract

A scalar-pseudoscalar four-Fermi quantum field model for a doublet of fermion is considered. It is shown by a partly nonperturbative analysis that excited states of collective bosons do exist and form finite approximately linear trajectories M n 2( I). For the same value of model free parameters no bound or excited fermion states do exist: this provides an example of a mechanism for a fermion confinement. However the fermion excited states do exist for selected other values of model parameters.