Is the Fermi Theory of Weak Interactions a Yang-Mills Theory in Disguise?

Abstract

We outline the proof of a consistent renormalization scheme for the Fermi theory ${\left(\overline{\psi }{\gamma }_{\mu }\frac{1}{2}\tau \psi \right)}^2$ in the context of a mean-field expansion in the collective excitation ${A_i}^{\mu }\equiv \overline{\psi }{\gamma }_{\mu }\frac{1}{2}{{\tau }_i}^{\prime }\psi$. Ward's identities show that there is only one mass and coupling and that the induced vertices are identical to those of Yang-Mills theory with elementary gauge fields at low energy. The Green's-functions equations are displayed and used to derive an eigenvalue restriction on the coupling.