Abstract
This paper is devoted to the analysis of the single layer boundary integral operator mathcal {C}_z for the Dirac equation in the two- and three-dimensional situation. The map mathcal {C}_z is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator A_0 and z belongs to the resolvent set of A_0. In the case of smooth boundaries fine mapping properties and a decomposition of mathcal {C}_z 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.
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