On the Single Layer Boundary Integral Operator for the Dirac Equation

Markus Holzmann

doi:10.1007/s11785-023-01434-9

On the Single Layer Boundary Integral Operator for the Dirac Equation

Markus Holzmann^*

^*Corresponding author for this work

Institute of Applied Mathematics (5040)

Research output: Contribution to journal › Article › peer-review

Abstract

This paper is devoted to the analysis of the single layer boundary integral operator C_z for the Dirac equation in the two- and three-dimensional situation. The map C_z is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator A and z belongs to the resolvent set of A . In the case of smooth boundaries fine mapping properties and a decomposition of C_z in a ‘positive’ and ‘negative’ part are analyzed. The obtained results can be applied in the treatment of Dirac operators with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions that are combined in a critical way.

Original language	English
Article number	135
Journal	Complex Analysis and Operator Theory
Volume	17
Issue number	8
DOIs	https://doi.org/10.1007/s11785-023-01434-9
Publication status	Published - Nov 2023

ASJC Scopus subject areas

Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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abstract = "This paper is devoted to the analysis of the single layer boundary integral operator Cz for the Dirac equation in the two- and three-dimensional situation. The map Cz is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator A and z belongs to the resolvent set of A . In the case of smooth boundaries fine mapping properties and a decomposition of Cz in a {\textquoteleft}positive{\textquoteright} and {\textquoteleft}negative{\textquoteright} part are analyzed. The obtained results can be applied in the treatment of Dirac operators with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions that are combined in a critical way.",

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AB - This paper is devoted to the analysis of the single layer boundary integral operator Cz for the Dirac equation in the two- and three-dimensional situation. The map Cz is the strongly singular integral operator having the integral kernel of the resolvent of the free Dirac operator A and z belongs to the resolvent set of A . In the case of smooth boundaries fine mapping properties and a decomposition of Cz in a ‘positive’ and ‘negative’ part are analyzed. The obtained results can be applied in the treatment of Dirac operators with singular electrostatic, Lorentz scalar, and anomalous magnetic interactions that are combined in a critical way.

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On the Single Layer Boundary Integral Operator for the Dirac Equation

Abstract

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