Symmetry Restorations in the Singlet Scalar Yukawa Model Within the Auxiliary Field Method

The aim of this work is to investigate the connection between thermal gap-coupled equations and the concept of symmetry restoration. For that, we consider the Yukawa model, a standard model for interactions between massless fermions mediated by a real self-interacting scalar field. To explore possible symmetry restoration, we study the thermal gap-coupled equations using the auxiliary field method (Hubbard–Stratonovich), and then we derive the effective action with thermal contributions through the background external fields method. With the thermal contributions for the effective action, we investigate the phase transitions and critical phenomena in an environment featuring mixing angles arising from the quantum description of composite states. Finally, we present the Dolan–Jackiw equations to determine the critical temperatures.