English

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 δ\delta-shell interactions. We approximate this operator with general local interactions VV. Without any hypotheses of smallness on the potential VV, converges in the strong resolvent sense to the Dirac Hamiltonian coupled with a δ\delta-shell potential supported on §\S, a bounded smooth surface. However, the coupling constant depends nonlinearly on the potential V.V.

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}
}
R2 v1 2026-06-28T12:29:31.889Z