On the Spectral Properties of Dirac Operators with Electrostatic Δ-shell Interactions
نویسندگان
چکیده
In this paper the spectral properties of Dirac operators Aη with electrostatic δ-shell interactions of constant strength η supported on compact smooth surfaces in R3 are studied. Making use of boundary triple techniques a Krein type resolvent formula and a Birman-Schwinger principle are obtained. With the help of these tools some spectral, scattering, and asymptotic properties of Aη are investigated. In particular, it turns out that the discrete spectrum of Aη inside the gap of the essential spectrum is finite, the difference of the third powers of the resolvents of Aη and the free Dirac operator A0 is trace class, and in the nonrelativistic limit Aη converges in the norm resolvent sense to a Schrödinger operator with an electric δ-potential of strength η.
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