We prove the existence of a "ground state" solution for the Dirac-Maxwell system coupled with an external potential of Coulomb type.

After applying the Foldy-Wouthuysen (unitary) transformation of the Dirac operator we consider its realization as an elliptic problem in the 4-dim half space R^4_+ with a Neumann boundary condition. The result follows via critical point theory. The result is contained in a paper with Margherita Nolasco.