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

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 H 1 -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 Hardytype 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.

Dirac-Coulomb Operators with Infinite Mass Boundary Conditions in Sectors

“…Moreover, we report to [11] for the analysis of the self-adjointness in the case of discontinuous infinite mass boundary conditions. Finally, the analogous problem in the three dimensional setting, namely the self-adjointness of the Dirac operator on a three dimensional cone with MIT bag boundary conditions, can be found in [12].…”