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We study initial value problem of the $(1+4)$-dimensionalMaxwell-Klein-Gordon system (MKG) in the Lorenz gauge. Since (MKG) in theLorenz gauge does not possess an obvious null structure, it is not easy tohandle the nonlinearity. To overcome this obstacle, we impose an additionalangular regularity. In this paper, we prove global well-posedness andscattering of (MKG) for small data in a scale-invariant space which has extraweighted regularity in the angular variables. Our main improvement is to attainthe scaling critical regularity exponent and prove global existence ofsolutions to (MKG) in the Lorenz gauge.

Global well-posedness and scattering of the energy critical Maxwell-Klein-Gordon system in the Lorenz gauge