Strong anticommutativity of Dirac operators on boson-fermion Fock spaces and representations of a supersymmetry algebra

On the boson-fermion Fock space F(H, K) associated with two complex Hilbert spaces H and K, there exists a family {Q(S) \ S is an element of 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 Q(S) and Q(T) is established. As an application, repre sentations on F(H, K) of a supersymmetry algebra arising in a two-dimension al relativistic supersymmetric quantum field theory are discussed.