Quantized Maxwell Theory in a Conformally Invariant Gauge

TL;DR

This paper explores the quantization of Maxwell theory in a conformally invariant gauge within flat Euclidean space, analyzing the properties of associated elliptic operators and boundary conditions.

Contribution

It introduces a conformally invariant gauge quantization framework for Maxwell theory, detailing the structure of ghost and potential operators and boundary conditions.

Findings

Ghost operator is a fourth-order elliptic operator.

Operator P on potential perturbations is sixth-order, reducible to second-order.

Boundary conditions set potential and ghost perturbations to zero at the boundary.

Abstract

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 of the potential is a sixth-order elliptic operator. The operator P may be reduced to a second-order non-minimal operator if a dimensionless gauge parameter tends to infinity. Gauge-invariant boundary conditions are obtained by setting to zero at the boundary the whole set of perturbations of the potential, 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 also obtained.