In this thesis we consider a number of different aspects of dynamical locality, an axiom on locally covariant theories proposed by Fewster and Verch that is closely related to the question of whether a theory describes the same physics in all spacetimes.
After some introductory material, in Chapters 3 and 4 we examine dynamical locality for the nonminimally coupled scalar field and its enlarged algebra of observables. We show that dynamical locality holds at all masses, including non-zero masses, for the nonminimally coupled scalar field theory. We also demonstrate that dynamical locality holds in the massive minimally
coupled and massive conformally coupled cases for the enlarged algebra of observables, and fails to hold in the massless minimally coupled case.
In Chapter 5, we discuss a number of categorical structures that can be used in the construction of classical theories that may be quantized using canonical anticommutation relations (CAR), and their subsequent quantization. We prove a number of results pertaining to dynamical locality of classical theories and their CAR-quantized counterparts.
In Chapters 6 and 7, we give a simplified version of the locally covariant classical and quantum Dirac theories, using the machinery developed in Chapter 5. We also formulate for the first time versions of these theories
that are entirely independent of the choice of a global reference frame for the spacetime, and depend only on an equivalence class of these frames. We demonstrate that both the simplified frame-dependent theories and the frame-independent theories are dynamically local.
