In this talk, we will introduce some aspects of nonlocal (infinite derivative) field theories. First of all, we will show how and which principles of standard quantum field theory are affected when the theory is described by higher (infinite) order derivative Lagrangians. In particular, we will discuss on the issue of unitarity and how to make higher order derivative theories healthy. Subsequently, we will focus on ghost-free nonlocal theories of gravity and investigate spherically symmetric spacetime solutions. 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. Finally, we will discuss and make a comparison among different nonlocal differential operators which satisfy the ghost-free condition.
Oct 2019 - Sept 2020
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