Cálculo de funciones Beta en teorías Gauge no Abelianas con grupo SU(N)

Abstract

In Quantum Field Theory with interactions divergent quantities always appear when calculating physical amplitudes. These quantities must be expressed by measurable quantities, and for this purpose, a renormalization mechanism is needed to eliminate these divergences. A consequence of renormalization is that renormalized coupling constants depend on the energy scale. This dependence can be characterized by beta functions. The understanding of its structure allows us to know the infrared and ultraviolet behavior of the theory, as well as to indicate its perturbative regime. In this paper, we present the computation of the beta function in order of 1-loop of the Quantum Electrodynamics (QED) and in Gauge Theories not Abelianas with group SU (N), the special case of SU (3) is discussed. Perturbative renormalization is used to isolate divergences in counterterms and to renormalize parameters of the theory. The method of dimensional regularization is used to regularize infinite integrals and guarantee their convergence. It is found that, in the case of QED, the beta function is positive, being safe in infrared regimes. In non-Abelian Gauge theories, the beta function is negative for nF <16, and presents the phenomenon of asymptotic freedom.