Quantum scalar field theory on anti-de Sitter space

This thesis considers a real massive free quantum scalar field propagating with arbitrary coupling to $n$-dimensional anti-de Sitter space. Analytical expressions are found for the field modes and Feynman Green function. The condition for the equivalence of rotational vacuum states is also established. The rotational and thermal anti-commutator functions are then derived. A method is developed for computing the Hadamard renormalised vacuum and thermal expectation values of the quadratic field fluctuations and the stress-energy tensor. Results are obtained for $n=2$ to $n=11$, satisfying Wald's axioms and exhibiting the trace anomaly.