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

2022/01/20 by Biagio Cassano, Cassano, Biagio, Vladimir Lotoreichik +1 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Advanced Operator Algebra Research #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2201.08192

openalex publication_date 2022/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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