As funções do grupo de renormalização no modelo com auto-interação quártica fermiônica

Abstract

Four femion interactions models have been studied to clarify their conceptual aspects and possible applications in quantum field theory. In this work we present the structure of the renormalization group in the Nambu-Jona-Lasinio model up to 1-loop order. The model is not perturbatively renormalizable in the usual power counting sense, but it is treated as an effective theory, valid in a scale of energy where p <<^, being p the external moment of the loop and ^ a massive parameter that characterizes the coupling of the non-renormalizable vertex. We clarify the tensorial structure of the interaction vertices and calculate the functions of the renormalization group. The analysis of the fixed points of the theory is also presented using Zimmermann procedure for reducing the coupling constants. We find that the origin is an infrared-stable fixed point at low energies and has also a nontrivial ultraviolet stable fixed point, indicating that the theory could be perturbatively investigated if the momentum is low enough.