Current Algebra and Gauge Theories. I

Abstract

The methods of current algebra are applied to the problem of calculating corrections to the symmetries of the strong interactions in renormalizable gauge theories of the weak and electromagnetic interactions. The strong interactions are described by a neutral-vector-gluon model, so that their symmetries are just the symmetries of the quark mass matrix, and are determined by the vacuum expectation values of the weakly coupled scalar fields. Corrections to these symmetries are calculated to all orders in the gluon coupling, but only to second order in the gauge coupling $e$. After putting the results in a gauge-invariant form, it is found that all divergences cancel in the corrections to "natural" symmetries of the strong interactions. The weak interactions can produce corrections to strong-interaction symmetries of the same order of magnitude as the electromagnetic corrections, but such "order $\alpha$" effects occur only as corrections to the quark mass matrix, and therefore necessarily conserve parity, strangeness, charm, etc., and may produce only isovector corrections to isotopic-spin conservation. It is suggested that these weak-interaction effects of order $\alpha$ are responsible for the nonelectromagnetic corrections to isotopic-spin conservation which seem to be needed in calculations of mass differences and $\eta$ decay.