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