Renormalizeability of massive non-Abelian gauge fields: A functional integral approach

Abstract

The renormalizeability of massive non-Abelian vector gauge fields is discussed using a functional integral technique. The ideas are first developed for the case of a neutral vector meson coupled to a conserved current, where the renormalizeability holds. The non-Abelian vector field is written as the gauge transform of a four-dimensionally transverse field, and the transverse and gauge variables are then treated separately. It is shown that the renormalizeability depends solely on that of the gauge variables, which are found to be non-renormalizeable; hence, neither is the field theory. The gauge variables alone provide a representation of the σ-model and of Sugawara's theory of currents, which are thus shown to be non renormalizeable theories.