Aspects of ghost-free nonlocal field theories

In this talk I introduce nonlocal (infinite derivative) field theories. First of all, I discuss how and which principles of quantum field theory are affected when higher-order derivative operators are taken into account in a Lagrangian. In particular, I focus on the issue of unitarity and on how to make higher-derivative theories healthy by means of non-polynomial differential operators. I extend the treatment to the gravity sector and consider nonlocal theories whose graviton propagators are ghost-free, and explore the possibility of regularizing singularities. Next, I discuss some recent progress in proving perturbative unitarity for a very general class of nonlocal field theories. Finally, I will make some remarks on nonlocality and quantum gravity.