Faithful realizations and semi-classical physics
Open Access
- Author:
- Crowe, Sean Thomas
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- June 03, 2019
- Committee Members:
- Martin Bojowald, Dissertation Advisor/Co-Advisor
Martin Bojowald, Committee Chair/Co-Chair
Eugenio Bianchi, Committee Member
Kenneth O'Hara, Committee Member
Ping Xu, Outside Member - Keywords:
- semi-classical physics
quantum tunneling
quantum cosmology
poisson algebras
Casimirs
Darboux coordinates - Abstract:
- The method of faithful realizations is defined and explored within the context of several physical problems. We constructed a general procedure for deriving faithful realizations from arbitrary semi-classical truncations, as well as applying this procedure to several explicit examples. This method is useful in systems which have a strong time dependence or which lack a ground state, because in these situations one cannot use the standard tools, such as the effective action. Using the faithful canonical realizations we developed, as well as an all orders closure, we studied the problem of tunneling times, which has been recently debated in the literature. Our definition of tunneling times, based on the canonical realizations, always gives a time delay. The usage of a canonical coordinate system also allowed us to use the moments as a tool to study the purity of a quantum state. That is, given a set of moments, a faithful canonical realization will have some parameters that correspond to the purity of the state. Moreover, canonical realizations facilitate the usages of methods from statistical mechanics in the realm of canonical effective methods, allowing one to consider ensemble averages of semi-classical quantities. They also facilitate the usage of the powerful techniques of canonical transformations in semi-classical physics. Using the framework of realization equivalence, we were also able to explore a link between the model of loop quantum cosmology as well as a model of group field cosmology. This link has led to several implications on the group field side of the equivalence, with regards to the formations of singularities and of quantization ambiguities.