Note on Schwinger mechanism and a non-Abelian instability in a non-Abelian plasma

We point out that there is a non-Abelian instability for a non-Abelian plasma which does not allow both for a net nonzero color charge and the existence of field configurations which are coherent over a volume v whose size is determined by the chemical potential. The basic process which leads to this result is the Schwinger decay of chromoelectric fields, for the case where the field arises from commutators of constant potentials, rather than as the curl of spacetime dependent potentials. The case where instability is obtained can be expressed in terms of fields (with constant potentials) as FaμνFμνa<0, AaμAμa<0.