Non-self-adjoint relativistic point interaction in one dimension

• URL: http://arxiv.org/abs/2205.05005v1
• Date: Tue, 10 May 2022 16:20:21 GMT
• Title: Non-self-adjoint relativistic point interaction in one dimension
• Authors: Luk\'a\v{s} Heriban, Mat\v{e}j Tu\v{s}ek
• Abstract summary: The one-dimensional Dirac operator with a singular interaction term is introduced as a closed not necessarily self-adjoint operator. We study its spectral properties, find its non-relativistic limit and also address the question of regular approximations. In particular, we show that, contrary to the case of local approximations, for non-local approximating potentials, coupling constants are not renormalized in the limit.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The one-dimensional Dirac operator with a singular interaction term which is formally given by $A\otimes|\delta_0\rangle\langle\delta_0|$, where $A$ is an arbitrary $2\times 2$ matrix and $\delta_0$ stands for the Dirac distribution, is introduced as a closed not necessarily self-adjoint operator. We study its spectral properties, find its non-relativistic limit and also address the question of regular approximations. In particular, we show that, contrary to the case of local approximations, for non-local approximating potentials, coupling constants are not renormalized in the limit.

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