Fermion Doubling in Loop Quantum Gravity
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Date
2015
Authors
Barnett, Jacob
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
For the last 20 years, it has been known how to couple matter to the theory of loop quantum gravity. However, one of the most simple questions that can be asked about this framework has not been addressed; is there a fermion doubling in loop quantum gravity? This is an exceptionally important issue if we are to connect the theory to experiments. In this thesis, we will arrive at a demonstration of fermion doubling around some graphs in the large bare ? limit. To obtain this result, we ?rst perform a Born-Oppenheimer like approximation to the Hamiltonian formulation of loop quantum gravity to work around a theory with a ?xed graph. We then make the case for identifying the energy spectrum this theory with a model of lattice gauge theory which is known to double. Appropriate reviews of fermion doubling and loop quantum gravity are provided along with an outlook of constructing a doubling-free version of LQG. Our ?ndings suggest one should interpret matter in loop quantum gravity in a much different way.
Description
The Independent Studies program closed in 2016. This thesis was one of 25 accepted by Library for long-term preservation and presentation in UWSpace.
Keywords
loop quantum gravity, fermion doubling, Born-Oppenheimer approximation, Hamiltonian formulation, energy spectrum