On quasi-free dynamics on the resolvent algebra

Abstract

The resolvent algebra is a new C*-algebra of the canonical commutation relations of a boson field given by Buchholz-Grundling. We study analytic properties of quasi-free dynamics on the resolvent algebra. Subsequently we consider a supersymmetric quasi-free dynamics on the graded C*-algebra made of a Clifford (fermion) algebra and a resolvent (boson) algebra. We establish an infinitesimal supersymmetry formula upon the GNS Hilbert space for any regular state satisfying some mild requirement which is standard in quantum field theory. We assert that the supersymmetric dynamics is given as a C*-dynamics.