Spontaneous symmetry breakings in the singlet scalar Yukawa model within the auxiliary field method

The aim of this work is to investigate the occurrence two different spontaneous symmetry breakings at levels description fermion-scalar field model, by means a set gap equations and with background effective action. For that, we consider Yukawa as toy model for interactions between nonmassive fermions intermediated self-interacting real scalar field. This has stake symmetries classical level know, might be spontaneously or dynamically broken mass generation particles. auxiliary method considered it produces coupled renormalized equations. action then written quantum contributions external method. We brought light how renormalization procedure affects physical gaps, its properties, discuss connection fields not only define composite states but also compute