Long range scattering for the Maxwell–Schrödinger system in the Lorenz gauge without any restriction on the size of data

This paper concerns the scattering theory for the Maxwell–Schrödinger (MS) system in the Lorenz gauge, or more precisely, the existence of the modified wave operators for this system in R3+1 space-time. We construct solutions to the MS system which behave as free Maxwell and Schrödinger waves with prescribed asymptotic states when t → ∞, without any restriction on the size thereof. Since this system belongs to the borderline between the short range case and the long range case, we need modification of phase for the Schrödinger function.