This thesis is about the quantum cosmology of supergravity theories, in particular <I>N</I> = 1 supergravity. In chapter 2, the Bianchi-IX model in <I>N</I> = 1 supergravity with a cosmological constant is investigated. This example is also restricted to the case of the <I>k</I> = +1 Friedmann universe. In chapter 3, the most general solution of the Lorentz constraints is found. Using this solution, <I>N </I>= 1 supergravity in the diagonal Bianchi-IX model is studied. The Hamilton-Jacobi<I> </I>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 <I>N</I> = 1 supergravity by considering perturbations around the <I>k</I> = +1 Friedmann universe. In chapter 5, the canonical formulation of <I>N</I> = 1 supergravity coupled to supermatter is presented. The supersymmetry and gauge constraints are derived. This model is then studied in the <I>k</I> = +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 <I>N</I> = 2 and <I>N</I> = 4 supergravity theories. The thesis ends with concluding remarks and an indication of directions of future development.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:597576 |
| Date | January 1997 |
| Creators | Cheng, A. D. Y. |
| Publisher | University of Cambridge |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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