Yang-Mills redux

Abstract

It is noted that a given pairing of the phase factor and gauge transformation to retain gauge symmetry is not unique. In their seminal paper, when Yang and Mills (YM) discuss the phase factor - gauge transformation relationship, they cite Pauli's review paper. It is interesting that although Pauli in that paper presents the electromagnetic field strength in terms of a commutator, for whatever reason YM did not extrapolate the commutator's use to obtain the Yang-Mills field strength -- they obtained it by trial and error. Presented is a derivation of this field strength using the commutator approach detailing how certain terms cancel each other. Finally, the Yang-Mills field transformation is derived in a slightly different way than is traditionally done.