Includes bibliographical references. / We present a systematic development and application of Geometric Algebra, an extended vector calculus. The entire algebraic structure, which is a graded Clifford algebra, is developed. To illustrate the derived results, examples are given for two and three dimensions. Here it becomes clear, how rotations and Lorentz boosts can be formulated in the Geometric Algebra. Further we realize that the Geometric Algebra contains elements, which can be used as representations of the complex unit. Having derived the necessary tools, we turn our attention to physics. We give applications to classical mechanics, quantum mechanics, ï¬ eld theory, curved manifolds, electromagnetism, and gravity as a gauge theory.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/14639 |
| Date | January 1999 |
| Creators | Kirchner, Ulrich |
| Contributors | Ellis, GFR |
| Publisher | University of Cape Town, Faculty of Science, Department of Mathematics and Applied Mathematics |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Master Thesis, Masters, MSc |
| Format | application/pdf |
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