Feynman-Kac perturbation of $C^*$ quantum stochastic flows

TL;DR

This paper extends the Feynman-Kac perturbation method for quantum stochastic processes from von Neumann algebras to $C^*$-algebras using operator space theory, broadening its applicability.

Contribution

It introduces a new framework leveraging operator spaces to analyze Feynman-Kac perturbations on $C^*$-algebra flows, simplifying verification in practical cases.

Findings

Broadened the scope of Feynman-Kac perturbation theory to $C^*$-algebras.

Provided auxiliary results to simplify hypotheses verification.

Included diverse examples illustrating the theory.

Abstract

The method of Feynman-Kac perturbation of quantum stochastic processes has a long pedigree, with the theory usually developed within the framework of processes on von Neumann algebras. In this work, the theory of operator spaces is exploited to enable a broadening of the scope to flows on $C^*$ algebras. Although the hypotheses that need to be verified in the general setting may seem numerous, we provide auxiliary results that enable this to be simplified in many of the cases which arise in practice. A wide variety of examples is provided by way of illustration.