Martin Bojowald, Dissertation Advisor/Co-Advisor Sarah Elizabeth Shandera, Committee Member Murat Gunaydin, Committee Member Nigel David Higson, Committee Member
Whenever a full theory is unavailable, effective frameworks serve as powerful tools for examining physical phenomena below some energy scale. However, standard quantum field theory techniques are not always applicable in various exotic, yet physically relevant, systems.
This thesis presents a new effective method for quantum theories, which is particularly tailored towards background independent theories such as gravity. Our main motivation is to utilize these techniques to extract the semi-classical dynamics from canonical quantum gravity theories. Application to field theoretic toy models of loop quantum gravity and non-associative quantum mechanics is elaborated in detail. We also extend this framework to fully constrained systems, as is required for gravity, and discuss several consequences for quantum gravity.
