Hertz Potentials and Differential Geometry

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dc.contributorFulling, Stephen
dc.creatorBouas, Jeffrey David
dc.date.accessioned2011-08-08T22:48:41Z
dc.date.accessioned2011-08-09T01:30:45Z
dc.date.accessioned2017-04-07T19:58:22Z
dc.date.available2011-08-08T22:48:41Z
dc.date.available2011-08-09T01:30:45Z
dc.date.available2017-04-07T19:58:22Z
dc.date.created2011-05
dc.date.issued2011-08-08
dc.description.abstractI review the construction of Hertz potentials in vector calculus starting from Maxwell's equations. From here, I lay the minimal foundations of differential geometry to construct Hertz potentials for a general (spatially compact) Lorentzian manifold with or without boundary. In this general framework, I discuss "scalar" Hertz potentials as they apply to the vector calculus situation, and I consider their possible generalization, showing which procedures used by previous authors fail to generalize and which succeed, if any. I give specific examples, including the standard at coordinate systems and an example of a non-flat metric, specifically a spherically symmetric black hole. Additionally, I generalize the introduction of gauge terms, and I present techniques for introducing gauge terms of arbitrary order. Finally, I give a treatment of one application of Hertz potentials, namely calculating electromagnetic Casimir interactions for a couple of systems.
dc.identifier.urihttp://hdl.handle.net/1969.1/ETD-TAMU-2011-05-9409
dc.language.isoen_US
dc.subjectHertz potential
dc.subjectHertz
dc.subjectEM
dc.subjectelectromagnetism
dc.subjectelectric
dc.subjectmagnetic
dc.subjectCasimir
dc.subjectquantum field
dc.subjectquantum field theory
dc.subjectdifferential geometry
dc.titleHertz Potentials and Differential Geometry
dc.typeThesis

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