  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.
