Electromagnetism, metric deformations, ellipticity and gauge operators on conformal 4-manifolds

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dc.creatorBranson, Thomas
dc.creatorGover, A. Rod
dc.date2001-10-31
dc.date.accessioned2026-07-07T04:12:36Z
dc.date.available2026-07-07T04:12:36Z
dc.descriptionOn Riemannian signature conformal 4-manifolds we give a conformally invariant extension of the Maxwell operator on 1-forms. We show the extension is in an appropriate sense injectively elliptic, and recovers the invariant gauge operator of Eastwood and Singer. The extension has a natural compatibility with the de Rham complex and we prove that, given a certain restriction, its conformally invariant null space is isomorphic to the first de Rham cohomology. General machinery for extending this construction is developed and as a second application we describe an elliptic extension of a natural operator on perturbations of conformal structure. This operator is closely linked to a natural sequence of invariant operators that we construct explictly. In the conformally flat setting this yields a complex known as the conformal deformation complex and for this we describe a conformally invariant Hodge theory which parallels the de Rham result.
dc.description30 pages, LaTeX
dc.identifierhttps://arxiv.org/abs/hep-th/0111003
dc.identifierhttp://arxiv.org/abs/hep-th/0111003
dc.identifierDiffer.Geom.Appl. 17 (2001) 229-249
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/50957
dc.subjectHigh Energy Physics - Theory
dc.titleElectromagnetism, metric deformations, ellipticity and gauge operators on conformal 4-manifolds
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