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

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