Nonlocal Field theories: Theoretical and Phenomenological Aspects

In this Thesis, we investigate some fundamental aspect of nonlocal field theories, like causality, unitarity and renormalizability. We show how to define and compute scattering amplitudes for a nonlocal scalar quantum field theory, and how they behave for a large number of interacting particles. We discuss the possibility to enlarge the class of symmetries under which a local Lagrangian is invariant by means the introduction of non-polynomial differential operators.
Subsequently, we move to the gravity sector. After showing how to construct a ghost-free higher derivative theory of gravity, we will find a linearized metric solution for a (neutral and charged) point-like source, and show that it is nonsingular. By analysing all the curvature tensors one can capture and understand the physical implications due to the nonlocal nature of the gravitational interaction. In particular, the Kretschmann invariant turns out to be non-singular, while all the Weyl tensor components vanish at the origin. Similar features can be also found in the case of a Delta Dirac distribution on a ring for which no Kerr-like singularity appears. Therefore, nonlocality can regularize singularities by smearing out point-like objects. At the full non-linear level, we show that the Schwarzschild metric cannot be a full metric solution valid in the entire spacetime, but it can be true only in some subregion, for instance in the large distance regime where there is vacuum.
Finally, we discuss phenomenological implications in the context of ultra-compact objects (UCOs), in which ghost-free gravity theories can be put on test and constrained.