Local Solutions of RG Flow Equations from the Nash–Moser Theorem

We prove local existence of solutions of a functional renormalisation group equation for the effective action of an interacting quantum field theory, when a suitable local potential approximation is considered. To obtain this equation in a Lorentzian setting a quantum state for the theory is selected and a regulator consisting in a mass is added to the action. The flow equation for mass rescalings is then studied using the renown Nash-Moser theorem.