Are gauge symmetry and phase invariance identical?

Summary

We discuss the difference between Yang-Mills gauge symmetry and phase invariance in a class of gauge groupSL _N,c. In order to quantize theSL _N,c fields b ^A_μ , one must insist on the principle of phase invariance rather than the usual gauge symmetry. As a result, the independent components of b ^A_μ are reduced by half. The physics of such a theory turns out to be identical with that of theSU _N Yang-Mills theory.