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

  title={Essential Self-adjointness of Symmetric First-Order Differential Systems and Confinement of Dirac Particles on Bounded Domains in \$\$\{\mathbb \{R\}\}^d\$\$},
  author={Gheorghe Nenciu and Irina Nenciu and Ryan Obermeyer},
  journal={Communications in Mathematical Physics},
We prove essential self-adjointness of Dirac operators with Lorentz scalar potentials which grow sufficiently fast near $\partial\Omega$, for a bounded 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… 


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