A space-time approach to quantum mechanics

Master Thesis

1999

Permanent link to this Item
http://hdl.handle.net/11427/14639
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thesis_sci_1999_kirchner_ulrich.pdf (6.76 MB)
Authors
Kirchner, Ulrich
Supervisors
Ellis, GFR
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University of Cape Town

Department
Department of Mathematics and Applied Mathematics
Faculty
Faculty of Science
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Abstract
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.
Description

Includes bibliographical references.

Keywords
Applied Mathematics

Reference:

Kirchner, U. 1999. A space-time approach to quantum mechanics. University of Cape Town.

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