Ground State for the Relativistic One Electron Atom in a Self-Generated Electromagnetic Field

Abstract

We study the Dirac--Maxwell system coupled with an external potential of Coulomb type. We prove the existence of a “ground state" solution using the Foldy--Wouthuysen (unitary) transformation of the Dirac operator and its realization as an elliptic problem in the 4-dim half space $\mathbb{R}^4_{+}$ with a Neumann boundary condition.