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.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2011-05-9409 |
| Date | 2011 May 1900 |
| Creators | Bouas, Jeffrey David |
| Contributors | Fulling, Stephen |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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