Strong anticommutativity of dirac operators on boson—fermion fock spaces and representations of a supersymmetry algebra

Abstract

AbstractOn the boson—fermion Fock space F(H, K) associated with two complex Hilbert spaces H and K, there exists a family {Qs | S ∈ C(H, K)} of Dirac type operators, where C(H, K) is the set of densely defined closed linear operators from H to K. A theorem on the strong anticommutativity of two Dirac operators QS and QT is established. As an application, representations on F(H, K) of a supersymmetry algebra arising in a two—dimensional relativistic supersymmetric quantum field theory are discussed.