Self-adjointness for the MIT bag model on an unbounded cone

0581041 - ÚJF 2025 RIV DE eng J - Journal Article
Cassano, B. - Lotoreichik, Vladimir
Self-adjointness for the MIT bag model on an unbounded cone.
Mathematische Nachrichten. Roč. 297, č. 3 (2024), s. 1006-1041. ISSN 0025-584X. E-ISSN 1522-2616
R&D Projects: GA ČR(CZ) GA21-07129S
Institutional support: RVO:61389005
Keywords : Dirac operator * Hardy inequality * MIT bag model * ortogonal decomposition * self-adjointness * unbounded circular cone
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Open access
https://doi.org/10.1002/mana.202200386

We consider the massless Dirac operator with the MIT bag boundary conditions on an unbounded three-dimensional circular cone. For convex cones, we prove that this operator is self-adjoint defined on four-component H1-functions satisfying the MIT bag boundary conditions. The proof of this result relies on separation of variables and spectral estimates for one-dimensional fiber Dirac-type operators. Furthermore, we provide a numerical evidence for the self-adjointness on the same domain also for non-convex cones. Moreover, we prove a Hardy-type inequality for such a Dirac operator on convex cones, which, in particular, yields stability of self-adjointness under perturbations by a class of unbounded potentials. Further extensions of our results to Dirac operators with quantum dot boundary conditions are also discussed.
Permanent Link: https://hdl.handle.net/11104/0352190