Maxwell–Dirac Equations in Four-Dimensional Minkowski Space

I derive the global existence and asymptotic behavior of small amplitude solutions to the system of massive coupled classical Maxwell–Dirac equations in the four-dimensional Minkowski space. Because the physically defined energy of the system is not positive definite, I transform it into an equivalent system of Maxwell–Klein–Gordon equations, which I study with a method based on gauge invariant energy estimates and geometric properties of the equations.