Finite-energy global well-posedness of the Maxwell-Klein-Gordon system\n in Lorenz gauge

It is known that the Maxwell-Klein-Gordon system (M-K-G), when written\nrelative to the Coulomb gauge, is globally well-posed for finite-energy initial\ndata. This result, due to Klainerman and Machedon, relies crucially on the null\nstructure of the main bilinear terms of M-K-G in Coulomb gauge. It appears to\nhave been believed that such a structure is not present in Lorenz gauge, but we\nprove here that it is, and we use this fact to prove finite-energy global\nwell-posedness in Lorenz gauge. The latter has the advantage, compared to\nCoulomb gauge, of being Lorentz invariant, hence M-K-G in Lorenz gauge is a\nsystem of nonlinear wave equations, whereas in Coulomb gauge the system has a\nless symmetric form, as it contains also a nonlinear elliptic equation.\n