On the approximation of the $\delta$-shell interaction for the 3-D Dirac operator
Spectral Theory
2023-09-25 v1 Mathematical Physics
math.MP
Abstract
We consider the three-dimensional Dirac operator coupled with a combination of electrostatic and Lorentz scalar -shell interactions. We approximate this operator with general local interactions . Without any hypotheses of smallness on the potential , converges in the strong resolvent sense to the Dirac Hamiltonian coupled with a -shell potential supported on , a bounded smooth surface. However, the coupling constant depends nonlinearly on the potential
Keywords
Cite
@article{arxiv.2309.12911,
title = {On the approximation of the $\delta$-shell interaction for the 3-D Dirac operator},
author = {Mahdi Zreik},
journal= {arXiv preprint arXiv:2309.12911},
year = {2023}
}