DSF preprint 96/42 QUANTIZED MAXWELL THEORY IN A CONFORMALLY INVARIANT GAUGE

Maxwell theory can be studied in a gauge which is invariant under conformal rescalings of the metric, and first proposed by Eastwood and Singer. This paper studies the corresponding quantization in flat Euclidean 4-space. The resulting ghost operator is a fourth-order elliptic operator, while the operator P on perturbations Aμ of the potential is a sixth-order elliptic operator. The operator P may be reduced to a second-order nonminimal operator if a dimensionless gauge parameter tends to infinity. In the presence of boundaries, one obtains gauge-invariant boundary conditions by setting to zero the whole set of Aμ perturbations, jointly with ghost perturbations and their normal derivative. This is made possible by the fourth-order nature of the ghost operator. An analytic representation of the ghost basis functions is obtained.