Spectral Analysis of Transmission and Boundary Value Problems for Dirac Operators
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Beschreibung
This doctoral thesis is devoted to the study of Dirac operators with singular delta-type interactions and of Dirac operators on domains. In particular, the self-adjointness and the spectral properties of these operators are investigated.
The present thesis is devoted to the spectral analysis of transmission and boundary value problems for Dirac operators. Dirac operators are one of the main mathematical tools in relativistic quantum mechanics to describe the propagation of spin 1/2 particles taking relativistic effects into account. In the first part of the thesis Dirac operators with singular delta-shell interactions which are combinations of electrostatic and Lorentz scalar potentials are studied. Such operators are associated to transmission problems for the Dirac equation. The second part of the thesis is then devoted to self-adjoint Dirac operators in domains. With the aid of boundary triples the self-adjointness of the corresponding operators is shown and some of the spectral data are computed. An interesting property is the existence of critical interaction strengths and boundary values, respectively, for which the associated operators have significantly different spectral properties. Eventually, for Dirac operators with singular interactions also the nonrelativistic limit is computed.
Autor*in
Markus Holzmann
Themen in »Spectral Analysis of Transmission and Boundary Value Problems for Dirac Operators«
Dirac-Operator singuläre Interaction Randwertproblem key words: Dirac operator shell interaction boundary value problem