QUANTIZED MAXWELL-THEORY IN A CONFORMALLY INVARIANT GAUGE

Maxwell theory can be studied in a gauge which is invariant under conf ormal rescalings of the metric, as first proposed by Eastwood and Sing er. This paper studies the corresponding quantization in aat Euclidean four-space. The resulting ghost operator is a fourth-order elliptic o perator, while the operator P on perturbations A(mu) of the potential is a sixth-order elliptic operator. The operator P may be reduced to a second-order nonminimal operator if a gauge parameter tends to infini ty. Gauge-invariant boundary conditions are obtained by setting to zer o at the boundary the whole set of A(mu) perturbations, jointly with g host perturbations and their normal derivatives. This is made possible by the fourth-order nature of the ghost operator. An analytic represe ntation of the ghost basis functions is also obtained.