After a self contained review of the Arnowitt -Deser-Misner (ADM) formalism of canonical gravity, the Wheeler-DeWitt (WD) equations of Quantum Cosmology are introduced. In the first half of the dissertation, a semi -classical effective action for Dirac Fermion in an adiabatically expanding closed Robertson-Walker Spacetime (RWST) is calculated by a path integration over homogeneous Fermionic fluctuations. It is shown that such a Universe has a maximal radius. The form of variation of the scale factor consistent with the adiabaticity condition is then worked out. In the second half of the thesis, the canonical quantum gravity for Dirac field is set up. The WD equations with Fermionic source are then linearized around a flat geometry and a homogeneous field configuration. A wave function solution in a form of an ansatz is then constructed to leading order in the perturbation parameter.
- Pub Date:
- February 1991
- Physics: Elementary Particles and High Energy, Physics: General, Physics: Astronomy and Astrophysics