On Dirac operators in <mml:msup>R3</mml:msup> with electrostatic and Lorentz scalar δ-shell interactions

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 of R3 are studied. In the rigorous definition of these operators, the delta -potentials are modeled 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.