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Title: Applications of geometric algebra in physics and cosmology
Author: Challinor, A.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 1999
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Geometric algebra - a unified language for mathematics and physics which takes Clifford algebra as its grammar - is slowly gaining the recognition it deserves in the physics community. The advantages of geometric algebra over existing techniques are being demonstrated continually through its application to a wide variety of topics in modern physics. This thesis adds to the growing body of applications of geometric algebra by considering problems in cosmology and relativistic quantum theory. The aim is to bring fresh insight and novel resolutions to the problems considered by exploiting the conceptual and computational advantages afforded by formulating the underlying theory in the language of geometric algebra. The applications to relativistic quantum theory include a reconsideration of the tunnelling time problem, where a resolution is offered which has significant implications for fields such as quantum measurement theory and solid state device physics. Also included is the developed of models of the early universe based on spin - ½ fields coupled to gravity through their inertia and quantum spin, where new, exact solutions to the Einstein-Cartan-Dirac equations are given. The treatment here employs a gauge-theoretic approach to gravity, developed recently in Cambridge by Lasenby, Doran, & Gull, which has a very elegant formulation in geometric algebra, and simplifies the treatment of many problems in general relativity and its spin-torsion extension. As a prelude to the discussion of spin-1/2 fields in the early universe, the torsion sector of the gauge theory of Lasenby et al. is explored thoroughly, and a number of new results are obtained. The applications to cosmology focus on the development of covariant methods for the description of inhomogeneity and anisotropy in the universe. A reformulation of the covariant approach to cosmology of Ehlers and Ellis, and the perturbation theory of Ellis & Bruni derived from it, is given using the gauge theory of gravity, resulting in a powerful set of tools for later application.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available