# $J$-self-adjoint operators with $mathcal{C}$-symmetries: extension theory approach - Mathematical Physics

$J$-self-adjoint operators with $mathcal{C}$-symmetries: extension theory approach - Mathematical Physics - Download this document for free, or read online. Document in PDF available to download.

Abstract: A well known tool in conventional von Neumann quantum mechanics is theself-adjoint extension technique for symmetric operators. It is used, e.g., forthe construction of Dirac-Hermitian Hamiltonians with point-interactionpotentials. Here we reshape this technique to allow for the construction ofpseudo-Hermitian $J$-self-adjoint Hamiltonians with complexpoint-interactions. We demonstrate that the resulting Hamiltonians arebijectively related with so called hypermaximal neutral subspaces of the defectKrein space of the symmetric operator. This symmetric operator is allowed tohave arbitrary but equal deficiency indices $

Author: ** S. Albeverio, U. Guenther, S. Kuzhel**

Source: https://arxiv.org/