Consequences of gauge-fixing ambiguities in non-Abelian gauge theories in axial and Coulomb gauges

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Abstract
We consider a pure SU(2) non-Abelian gauge theory in a first-order canonical quantization scheme, and show how the proper treatment of zero modes in solving the constraint equations for the dependent variables leads to certain conditions on the physical states. In the axial gauge this leads to a result of Schwinger's. In the Coulomb gauge this leads to previously unknown conditions on the physical states, and to the conclusion that the theory does not describe a free radiation field under circumstances for which Gribov has shown that the vector potential becomes non-unique.

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