Hertz Potentials and Differential Geometry
dc.contributor.advisor | Fulling, Stephen | |
dc.creator | Bouas, Jeffrey David | |
dc.date.accessioned | 2011-08-08T22:48:41Z | |
dc.date.accessioned | 2011-08-09T01:30:45Z | |
dc.date.available | 2011-08-08T22:48:41Z | |
dc.date.available | 2011-08-09T01:30:45Z | |
dc.date.created | 2011-05 | |
dc.date.issued | 2011-08-08 | |
dc.date.submitted | May 2011 | |
dc.identifier.uri | https://hdl.handle.net/1969.1/ETD-TAMU-2011-05-9409 | |
dc.description.abstract | I 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. | en |
dc.format.mimetype | application/pdf | |
dc.language.iso | en_US | |
dc.subject | Hertz potential | en |
dc.subject | Hertz | en |
dc.subject | EM | en |
dc.subject | electromagnetism | en |
dc.subject | electric | en |
dc.subject | magnetic | en |
dc.subject | Casimir | en |
dc.subject | quantum field | en |
dc.subject | quantum field theory | en |
dc.subject | differential geometry | en |
dc.title | Hertz Potentials and Differential Geometry | en |
dc.type | Thesis | en |
thesis.degree.department | Mathematics | en |
thesis.degree.discipline | Mathematics | en |
thesis.degree.grantor | Texas A&M University | en |
thesis.degree.name | Master of Science | en |
thesis.degree.level | Masters | en |
dc.contributor.committeeMember | Robles, Colleen | |
dc.contributor.committeeMember | Saslow, Wayne | |
dc.type.genre | thesis | en |
dc.type.material | text | en |
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