Non-self-adjoint relativistic point interactions and their approximations by non-local potentials
Type of document
výzkumná zprávaresearch report
Author
Heriban, Lukáš
Supervisor
Tušek, Matěj
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The research project deals with the Dirac operator with non–local potential given by the projec tion on a fixed scaled function from L
2
(R)∩ L
1
(R) multiplied by complex matrix A. The norm–resolvent
limit of this not necessarily self–adjoint operator is discussed in this thesis. Furthermore, the rigorous ex pression for the norm resolvent limit is compared to the formal limit of the Dirac operator with non–local
potential. This formal limit corresponds to the norm–resolvent limit. In other words, renormalization of
the coupling constant does not occur. This property will lead to generalization of the definition of the
Dirac operator with relativistic point interaction. Moreover, the spectrum of this newly defined operator
is discussed. Remarkable spectral transitions in special cases will be presented. Finally, this spectral
transition will be explained by examining ε–pseudospectrum of the operator.
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