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, as first proposed by Eastwood and Singer. This paper studies the corresponding quantization in flat Euclidean four-space. The resulting ghost operator is a fourth-order elliptic operator, while the operator $\mathcal{P}$ on perturbations $A_{\mu }$ of the potential is a sixth-order elliptic operator. The operator $\mathcal{P}$ may be reduced to a second-order nonminimal operator if a gauge parameter tends to infinity. Gauge-invariant boundary conditions are obtained by setting to zero at the boundary the whole set of $A_{\mu }$ perturbations, jointly with ghost perturbations and their normal derivatives. This is made possible by the fourth-order nature of the ghost operator. An analytic representation of the ghost basis functions is also obtained.