A space-time approach to quantum mechanics

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.

Grantor dc:publisher.institution

Department of Mathematics and Applied Mathematics

Year dc:date.issued

1999

Author dc:creator

• Kirchner, Ulrich

Advisor dc:contributor.advisor

• Ellis, GFR

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/11427/14639

OAI identifier oai:identifier

oai:open.uct.ac.za:11427/14639