Ground state for the relativistic one electron atom

Abstract

We study the Dirac-Maxwell system coupled with an external potential of Coulomb type. We use 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 Neumann boundary condition. Using this approach we study the existence of a "ground state" solution.

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