The Quantization of Maxwell Theory in the Cauchy Radiation Gauge: Hodge Decomposition and Hadamard States
arXiv:2401.08403 · doi:10.1112/jlms.70020
Abstract
The aim of this paper is to prove the existence of Hadamard states for the Maxwell equations on any globally hyperbolic spacetime. This will be achieved by introducing a new gauge fixing condition, the Cauchy radiation gauge, that will allow to suppress all the unphysical degrees of freedom. The key ingredient for achieving this gauge is a new Hodge decomposition for differential k-forms in Sobolev spaces on complete (possibly non-compact) Riemannian manifolds.
38 pages -- to appear in J. Lond. Math. Soc
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