Electromagnetic part of the free Yang-Mills field

Abstract

The free Yang-Mills field (not restricted toSU2) carries electric charge and therefore has an electromagnetic part. Two types of identifications of this electromagnetic part are considered: Lie-algebraic identifications and the asymptotic identification. If free Yang-Mills fields falling into parts which do not interact or which interact unilaterally are excluded, the Lie-algebraic identification usually gives a nonvanishing magnetic-charge density. Therefore, we dismiss this type of electromagnetic identification. The asymptotic identification gives an undetectably small magnetic charge and results in the proper electromagnetic long-range interaction in case the holonomy group has rank one. For higher-rank holonomy groups, it remains to be demonstrated that there is only a single electromagnetic-type long-range interaction. Decomposition of the time-space components of the free Yang-Mills field into a covariant transverse and a covariant longitudinal field shows that, under certain broad conditions, Yang-Mills particles need to have a transverse field inside, in order that they can be charged.