Non-Abelian Gauge Fields and Goldstone Bosons

The theory of a massless, in general non-Abelian, gauge vector field is considered and the relation between the supplementary condition for the vector field and the condition for spontaneously broken symmetry is explored. Goldstone bosons are found to exist and their equations of motion are determined; the non-Abelian nature of the gauge group leads to interaction for the Goldstone bosons. The results are applied to the problems of broken isotopic and unitary symmetries.