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abstract: 'In this article Dirac operators $A_{\eta, \tau}$ coupled with combinations of electrostatic and Lorentz scalar $\delta$-shell interactions of constant strength $\eta$ and $\tau$, respectively, supported on compact surfaces $\Sigma \subset \mathbb{R}^3$ are studied. In the rigorous definition of these operators the $\delta$-potentials are modelled by coupling conditions at $\Sigma$. In the proof of the self-adjointness of $A_{\eta, \tau}$ a Krein-type resolvent formula and a Birman-Schwinger principle are obtained. With their help a detailed study of the qualitative spectral properties of $A_{\eta, \tau}$ is possible. In particular, the essential spectrum of $A_{\eta, \tau}$ is determined, it is shown that at most finitely many discrete eigenvalues can appear, and several symmetry relations in the point spectrum are obtained. Moreover, the nonrelativistic limit of $A_{\eta, \tau}$ is computed and it is discussed that for some special interaction strengths $A_{\eta, \tau}$ is decoupled to two operators acting in the domains with the common boundary $\Sigma$.'
address:
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    Institut für Angewandte Mathematik\
    Technische Universität Graz\
    Steyrergasse 30, 8010 Graz, Austria\
    E-mail: [behrndt@tugraz.at]{}
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    Doppler Institute for Mathematical Physics and Applied Mathematics\
    Czech Technical University in Prague\
    Břehová 7, 11519 Prague, Czech Republic, [and]{} Department of Theoretical Physics\
    Nuclear Physics Institute, Czech 