Green Functions for Classical Euclidean Maxwell Theory

Recent work on the quantization of Maxwell theory has used a non-covariant class of gauge-averaging functionals which include explicitly the effects of the extrinsic-curvature tensor of the boundary, or covariant gauges which, unlike the Lorentz case, are invariant under conformal rescalings of the background 4-metric. This paper studies in detail the admissibility of such gauges at the classical level. It is proved that Euclidean Green functions of a second-or fourth-order operator exist which ensure the fulfillment of such gauges at the classical level, i.e. on a portion of flat Euclidean 4-space bounded by 3-dimensional surfaces. The admissibility of the axial and Coulomb gauges is also proved.