  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.

Spectral Theory