19-14 Jussi Behrndt, Pavel Exner, Markus Holzmann, Vladimir Lotoreichik

On Dirac operators in R^3 with electrostatic and Lorentz scalar delta-shell interactions (497K, pdf) Jan 31, 19

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Abstract. In this article Dirac operators A_{\eta, au} coupled with combinations of electrostatic and Lorentz scalar \delta-shell interactions of constant strength \eta and au, respectively, supported on compact surfaces \sigma\subset 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, au} 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, au} is possible. In particular, the essential spectrum of A_{\eta, au} 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, au} is computed and it is discussed that for some special interaction strengths A_{\eta, au} is decoupled to two operators acting in the domains with the common boundary \Sigma.

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