Essential Self-Adjointness of Anti-Commutative Operators

TL;DR

This paper investigates the conditions under which symmetric operators satisfying anti-commutation relations are essentially self-adjoint, extending known theorems and applying results to an abstract Dirac operator.

Contribution

It proves an anti-commutative version of the Glimm-Jaffe-Nelson commutator theorem and applies it to an abstract Dirac operator.

Findings

Established essential self-adjointness under anti-commutation relations

Extended the Glimm-Jaffe-Nelson theorem to anti-commutative operators

Applied the results to an abstract Dirac operator

Abstract

In this article, the self-adjoint extensions of symmetric operators satisfying anti-commutation relations are considered. It is proven that an anti-commutative type of the Glimm-Jaffe-Nelson commutator theorem follows. Its application to an abstract Dirac operator is also considered.