Perturbative renormalization of PDEs describing classical fields coupled to pointlike bodies

Point-like sources are commonly used in physics. They usually represent compact bodies whose inner structure is not physically significant. This idealization simplifies the description of the motion of the bodies. However, because of the distributional character of the sources the equations of motion governing the evolution of the system typically contain ill-defined products of distributions. In the talk, I will present a method which allows to consistently renormalize PDEs describing classical fields coupled to pointlike bodies in the approximation in which the non-linear terms are treated as a perturbation of the linear equation. The motivation behind the ongoing project is the description of the motion of two compact bodies interacting gravitationally. The problem is of great importance especially because of the need to construct accurate template waveforms which are necessary to detect and interpret gravitational waves emitted by coalescing binary systems.