AG Mathematische Physik, Edoardo D'Angelo (Genua): Functional Renormalization and the Nash-Moser theorem

Edoardo D’Angelo (Genua)

Functional Renormalization and the Nash-Moser theorem

Abstract: The Renormalization Group (RG) Equation determines the flow of the effective action under changes in an artificial energy scale, which roughly corresponds to the scale of the system under consideration. I report on a rigorous construction of a non-perturbative RG flow for the effective action in Lorentzian manifolds. I give the main ideas of a proof of local existence of solutions for the RG equation, when a suitable Local Potential Approximation is considered. The proof is based on an application of the renown Nash-Moser theorem. Time permitting, I also discuss an application of the RG equation to the non-perturbative renormalizability of quantum gravity.