Fermion Doubling in Loop Quantum Gravity

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.