Effects of Non-locality in Gravity and Quantum Theory

Spacetime---the union of space and time---is both the actor and the stage during physical processes in our fascinating Universe. In Lorentz invariant local theories, the existence of a maximum signalling speed (the "speed of light") determines a notion of causality in spacetime, distinguishing the past from the future, and the cause from the effect. This thesis is dedicated to the study of \emph{deviations} from locality. Focussing on a particular class of \emph{non-local} theories that is both Lorentz invariant and free of ghosts, we aim to understand the effects of such non-local physics in both gravity and quantum theory. Non-local ghost-free theories are accompanied by a parameter $\ell$ of dimension length that parametrizes the scale of non-locality, and for that reason we strive to express all effects of non-locality in terms of this symbol. In the limiting case of $\ell=0$ one recovers the local theory, and the effects of non-locality vanish. In order to address these questions we develop the notion of non-local Green functions [...]. The results presented in this thesis establish several effects of a Lorentz invariant, ghost-free non-locality in the areas of both gravitational and quantum physics. (Full abstract in document.)