On the Single Layer Boundary Integral Operator for the Dirac Equation

This paper is devoted to the analysis of the single layer boundary integral operator [Formula: see text] for the Dirac equation in the two- and three-dimensional situation. The map [Formula: see text] is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator [Formula: see text] and z belongs to the resolvent set of [Formula: see text] . In the case of smooth boundaries fine mapping properties and a decomposition of [Formula: see text] in a ‘positive’ and ‘negative’ part are analyzed. The obtained results can be applied in the treatment of Dirac operators with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions that are combined in a critical way.