Essential Self-adjointness of Symmetric First-Order Differential Systems and Confinement of Dirac Particles on Bounded Domains in $${\mathbb {R}}^d$$ R d

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 $$1/\big (2\text {dist} (x, \partial \Omega )^2\big )$$ .