• Batalin-Vilkovisky formalism
• Nonlocal quantum field theories
• quantum gravity

Our purpose is to explore generalized approaches to the quantization of gravity. In particular, we studied nonlocal modifications of quantum gravity and gauge theories based on some ideas put forward by E.T. Tomboulis in 1997, which are able to even turn nonrenormalizable theories into super-renormalizable ones, without introducing ghosts. We started by analizing a class of nonlocal Yang-Mills theories as a toy model, using the Batalin-Vilkovisky (BV) formalism. Under some assumptions, these are superrenormalizable theories (only one-loop divergences survive). We computed the (only) counterterm that renormalizes the theory and determines the running of the coupling constant. A similar nonlocal modification of the Einstein-Hilbert action also leads to a super-renormalizable theory. We also searched for approaches to nonlocal QFT that are more general than those of Tomboulis, by attempting to formulate nonlocal theories as limits of local ones. The result of such attempts is however negative, because the beta functions we have computed do not admit a regular limit.