| The standard constructions of special relativistic quantum field theory rely heavily on both Poincare symmetry and Fourier transforms. In general relativity, however, neither of these may be available. For example, in the seemingly simple trousers spacetime, Manogue, Dray and Copeland show that the plane wave modes are incapable of capturing all the degrees of freedom of the field. They suggest that the remaining degrees of freedom are of a singular nature, so that the quantization of certain singular modes, the distributional modes, would be required. It was further conjectured that a reformulation of quantum field theory based solely on the distributional modes is possible and would be more generally applicable than quantum field theory based on plane wave modes.; In this dissertation, the reformulation of flat space quantum field theory in terms of the distributional modes is provided, as is the relationship with the standard formalism. The same is accomplished for the case of Rindler spacetime. A canonical generalization of the distributional mode theory to general, globally hyperbolic spacetimes in n≥2 dimensions is made. From this canonical theory, we show how to associate a quantum field theory to a given Cauchy surface and choice of time coordinate. Also included is a result which shows that the "Unruh effect" may be derived using any one set of modes {lcub}Vk{rcub} from a one-parameter family F of sets of modes, where each Vk is related to the set of plane wave modes by a Bogolubov transformation. Each Vk in F defines a different notion of positive frequency, which implies that the source of the Unruh effect is attributed to something deeper than simply the standard notions of particle associated with Minkowski and Rindler observers. |
