General theory of the gauge transformation for vector meson fields

Abstract

The general theory of gauge transformations for multiplet vector fields is considered by extending the three-dimensional rotation group of the Yang-Mills type into any simple Lie group. The neutral vector theory, the Yang-Mills theory of the triplet field and the Gell-Mann theory of the octad field are obtained as special cases of our general theory. Main results concerning the latter theory are stated in the form of equivalence theorems. The theory is not renormalizable when the masses of the vector fields are not zero. General features of the theory are briefly reviewed in the last section.