On quasi-free dynamics on the resolvent algebra

TL;DR

This paper investigates the properties of quasi-free dynamics on the resolvent algebra, a C*-algebra for boson fields, and extends the analysis to supersymmetric dynamics involving fermion and boson algebras.

Contribution

It introduces a detailed analysis of quasi-free dynamics on the resolvent algebra and establishes a supersymmetric framework combining fermion and boson algebras with a C*-dynamics.

Findings

Analytic properties of quasi-free dynamics are characterized.

Supersymmetric quasi-free dynamics are formulated on a graded C*-algebra.

An infinitesimal supersymmetry formula is established on the GNS Hilbert space.

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.