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, $g_0\to 0$ and $m_0\to 0$ 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 $\mathrm{SU}\left(3\right)\mathrm{}$ breaking into the theory, retaining canonical structure for electromagnetism.