Self-adjointness Criteria: Rellich, Kato and Friedrichs

We first present a result of Rellich and Kato, that provides the self-adjointness of operators in the form \(A+B\) on the same domain as that of A, under simple assumptions on the perturbation B. This is followed by a discussion of Friedrich’s theory of quadratic forms, that allows one to construct self-adjoint extensions that are natural from a physical point of view.