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Title: Supersymmetric quantum Bianchi models
Author: Cheng, A. D. Y.
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 1997
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This thesis is about the quantum cosmology of supergravity theories, in particular N = 1 supergravity. In chapter 2, the Bianchi-IX model in N = 1 supergravity with a cosmological constant is investigated. This example is also restricted to the case of the k = +1 Friedmann universe. In chapter 3, the most general solution of the Lorentz constraints is found. Using this solution, N = 1 supergravity in the diagonal Bianchi-IX model is studied. The Hamilton-Jacobi equation is derived and completely solved. The Hartie-Hawking and wormhole actions are both found among the solutions. In chapter 4, the relation between the Chern-Simons functional and the no-boundary proposal is considered. The exponential of the Chern-Simons functional is the first known exact solution of quantum general relativity with a cosmological constant, being defined in the Ashtekar variables. However, it has turned out to be possible to show that the Chern-Simons functional and the no-boundary proposal are not related to each other in general relativity and N = 1 supergravity by considering perturbations around the k = +1 Friedmann universe. In chapter 5, the canonical formulation of N = 1 supergravity coupled to supermatter is presented. The supersymmetry and gauge constraints are derived. This model is then studied in the k = +1 Friedmann universe. It is found there are solutions in the case of a scalar multiplet. However, no non-trivial solution exists for a Yang-Mills multiplet, and it is explained why there is no physical state. Chapter 6 describes a brief investigation of the quantum cosmology of N = 2 and N = 4 supergravity theories. The thesis ends with concluding remarks and an indication of directions of future development.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available