Regular Representation of Affine Kac-Moody Algebras

Abstract

The question about commutative properties of the singularly perturbed self-adjoint operators arises in connection with the development of the quantum field theory. It is often necessary to know when a pair of unbounded closed self-adjoint commutative operators commute also if one of them or both were replaced by singularly perturbed operators i.e. by operators coinciding with the given operators on a dense subspace. The necessary and sufficient conditions under which the singularly perturbed self-adjoint operators commute are investigated in this note. This research may be applied to the theory of the singularly perturbed normal operators.