Structure and Extensions of a Theory of Currents

Abstract

We show that Sugawara's theory of currents can be obtained as a formal limit of the massive Yang-Mills theory. In this limit, ${g}_{0}\ensuremath{\rightarrow}0$ and ${m}_{0}\ensuremath{\rightarrow}0$ in such a way that $\frac{{{m}_{0}}^{2}}{{{g}_{0}}^{2}}=C$, the constant appearing in Sugawara's theory. The limiting procedure is used to incorporate electromagnetism, the hypothesis of partially conserved axial-vector current, and $\mathrm{SU}(3)$ breaking into the theory, retaining canonical structure for electromagnetism.