Quantized Maxwell Theory in a Conformally Invariant Gauge

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.

8 pages, plain Tex. In this revised version, the calculation of ghost basis functions has been amended, and the presentation has been improved

References in corpus (8)

• Virtual Black Holes
• Vector Fields on a Disk with Mixed Boundary Conditions
• QED on Curved Background and on Manifolds with Boundaries: Unitarity versus Covariance
• Euclidean Maxwell Theory in the Presence of Boundaries. II
• Relativistic Gauge Conditions in Quantum Cosmology
• Gauge-Averaging Functionals for Euclidean Maxwell Theory in the Presence of Boundaries
• Coulomb Gauge in One-Loop Quantum Cosmology
• Quantized Maxwell Theory in a Conformally Invariant Gauge

Cited by in corpus (8)

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• New Kernels in Quantum Gravity
• Quantized Maxwell Theory in a Conformally Invariant Gauge
• Dirac Operator and Spectral Geometry
• Fourth-Order Operators on Manifolds with Boundary
• The Eastwood-Singer gauge in Einstein spaces