We show that within the framework of stochastic mechanics, the quantization of a free electromagentic or Yang-Mills field in the temporal gauge can be consistently carried out. The resulting longitudinal component of the photon or gluon propagator is time-translation noninvariant. The exact form of the propagator depends on the additional boundary condition which fully fixes the temporal gauge. This stochastic formalism not only provides a simple and unified derivation of the various forms of the gauge field propagator in the temporal gauge, it also shows that the time-translation noninvariance is an inherent property of the propagator.

• Received 18 November 1992

DOI:https://doi.org/10.1103/PhysRevD.48.2957