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• W2912904777 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 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 $$Sigma $$ ." @default.
• W2912904777 created "2019-02-21" @default.
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• W2912904777 date "2019-03-02" @default.
• W2912904777 modified "2023-10-17" @default.
• W2912904777 title "On Dirac operators in $$mathbb {R}^3$$ R 3 with electrostatic and Lorentz scalar $$delta $$ δ -shell interactions" @default.
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• W2912904777 doi "https://doi.org/10.1007/s40509-019-00186-6" @default.
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