Two homomorphic versions of the non-Abelian equations of electrodynamics ar
e developed and their advantages discussed over the received Maxwell-Heavis
ide equations. The internal gauge field symmetry in these equations is resp
ectively SU(2) and O(3), signifying, on the quantized levels, three electro
magnetic bosons, and on the classical level, three components of the electr
omagnetic field, right and left circularly polarized ((1) and (2)) and long
itudinally polarized (3). The reduction of these equations to the Maxwell-H
eaviside equations is discussed in terms of the coupling constant of the no
n-Abelian covariant derivatives. The development of these equations follows
the original intent and logic of Yang and Mills in 1955 to generalize pure
classical electrodynamics.