Essential self-adjointness of semi-bounded operators

A semi-bounded operator that is bounded below by one is essentially self-adjoint if the kernel of the adjoint is trivial. This is the case if the kernel of the adjoint belongs to the form domain of the Friedrichs extension. We describe a local version of this criterion, where locality is defined in terms of bounded operators approaching the identity. The result is an abstract operator theoretic framework that generalizes the method by Wienholtz and Simader developed in the context of semi-bounded elliptic partial differential operators. As applications, we obtain competitive results on essential self-adjointness of many-particle Schr\"odinger operators, pseudo-relativistic Hamiltonians, and the standard model of non-relativistic quantum electrodynamics.