On Dirac operators in R3 with electrostatic and Lorentz scalar delta-shell interactions

0561421 - ÚJF 2023 RIV US eng J - Journal Article
Behrndt, J. - Exner, Pavel - Holzmann, M. - Lotoreichik, Vladimir
On Dirac operators in R3 with electrostatic and Lorentz scalar delta-shell interactions.
Quantum Studies: Mathematics and Foundations. Roč. 6, č. 3 (2019), s. 295-314. ISSN 2196-5609. E-ISSN 2196-5617
R&D Projects: GA MŠMT 7AMB17AT022; GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : Dirac operator * Shell interaction * coupling condition * Spectral analysis * Nonrelativistic limit
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Method of publishing: Open access
https://doi.org/10.1007/s40509-019-00186-6

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.
Permanent Link: https://hdl.handle.net/11104/0334044