Spacetime as a Hamiltonian Orbit and Geroch's Theorem on the Existence of Fermions
Viktor Bergstedt
Abstract
Over a century since its inception, general relativity continues to lie at the heart of some of the most researched topics in theoretical physics. It seems likely that the coveted solutions to problems like quantum gravity are to be found in an extension of general relativity, one which may only be visible in an alternate formulation of the theory. In this thesis we consider the possibility of casting general relativity in the form of an initial value problem where spacetime is seen as the evolution of space. This evolution is shown to be constrained and of Hamiltonian type. Not all spacetimes are physically acceptable. To be compatible with particle physics, one would like spacetime to accommodate fermions. Here we can take comfort in Geroch’s theorem, which implies that any spacetime that admits a Hamiltonian formulation automatically supports the existence of fermions. We review the elements that go into the proof of this theorem.