Aspects of (quantum) field theory on curved spacetimes, particularly in the presence of boundaries

This thesis has two main themes: on the one hand, in Chapters 3 and 5 we study some effects of the presence of timelike boundaries on linear classical and quantum field theories; the second theme is the analysis of technical issues with the paper B.S. Kay and R.M. Wald, Phys. Rep. 207, 49-136 (1991), which is carried out in parts of Chapter 2 and in Chapter 4. Chapter 2 contains a novel result on the characteristic initial value problem on globally hyperbolic spacetimes. In Chapter 3, we conjecture that (when the notion of a Hadamard state is suitably adapted to spacetimes with timelike boundaries) there is no isometry-invariant Hadamard state for the Klein-Gordon equation defined on the region of the Kruskal spacetime 'to the left of' a surface of constant Schwarzschild radius in the right Schwarzschild wedge, if Dirichlet boundary conditions are imposed there. We also prove that, under a suitable notion for 'boost-invariant Hadamard state' which also takes into account the special infra-red pathology of massless fields in 1+1 dimensions, there is no such state for the massless 1+1 wave equation on the region of Minkowski space to the left of an eternally uniformly accelerating mirror – with Dirichlet boundary conditions at the mirror. Chapter 5 collects and extends results of Solis about the causal structure of spacetimes with timelike boundaries, and deals with algebraic aspects of the interplay between Green hyperbolicity and boundary conditions in classical field theory. It also outlines a plan for generalizing the established work on wave-like equations from globally hyperbolic spacetimes to 'globally hyperbolic spacetimes-with-timelike-boundaries'. Appendix B contains a non-existence result for boost-invariant Hadamard states of a massless scalar field in (1+1)-dimensional Minkowski spacetime.