  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.
