Essential self-adjointness of symmetric first-order differential systems and confinement of Dirac particles on bounded domains in ${\mathbb{R}}^d$

Abstract

We prove essential self-adjointness of Dirac operators with Lorentz scalar potentials which grow sufficiently fast near the boundary $\partial \Omega$ of the spatial domain $\Omega \subset {\mathbb{R}}^d$. On the way, we first consider general symmetric first order differential systems, for which we identify a new, large class of potentials, called scalar potentials, ensuring essential self-adjointness. Furthermore, using the supersymmetric structure of the Dirac operator in the two dimensional case, we prove confinement of Dirac particles, i.e. essential self-adjointness of the operator, solely by magnetic fields $\mathcal{B}$ assumed to grow, near $\partial \Omega$, faster than $1/(2\text{dist}(x,\partial \Omega {)}^2)$.

40 pages, minor typos corrected and a new Comment 5 added to Section 7

References in corpus (1)

• Self-adjointness of Dirac operators via Hardy-Dirac inequalities