Current Algebra and Gauge Theories. II. Non-Abelian Gluons

Abstract

The considerations of the first paper in this series are extended to non-Abelian gauge models of the strong, weak, and electromagnetic interactions. It is shown that for a large class of such theories, the strong interactions naturally conserve parity and strangeness, and possibly isospin and other quantum numbers as well. The corrections of second order in gauge couplings to such natural symmetries are convergent. In addition to the ordinary photon-exchange term, these corrections include other terms of order $\ensuremath{\alpha}$, which take the form of shifts in the effective quark mass matrix, and which automatically conserve parity and strangeness. In theories with free-field asymptotic behavior, these order-$\ensuremath{\alpha}$ mass shifts may be correctly calculated ignoring all effects of the strong interactions. It is suggested that in such theories, the strong gauge group is not broken, and that the infrared divergences associated with the massless vector gluons prevent the production of quarks or gluons in collisions of ordinary hadrons.