Decomposability of multiparameter CAR flows

TL;DR

This paper investigates the decomposability of product systems associated with multiparameter CAR flows over convex cones, establishing conditions for decomposability and revealing many CAR flows are cocycle conjugate to CCR flows.

Contribution

It provides a necessary and sufficient condition for the decomposability of CAR flows over convex cones, advancing understanding of their structure and classification.

Findings

Characterization of decomposability conditions for CAR flows

Existence of uncountably many CAR flows cocycle conjugate to CCR flows

Extension of product system theory to multiparameter settings

Abstract

Let $P$ be a closed convex cone in $\mathbb{R}^d$ which is assumed to be spanning $\mathbb{R}^d$ and contains no line. In this article, we consider a family of CAR flows over $P$ and study the decomposability of the associated product systems. We establish a necessary and sufficient condition for CAR flow to be decomposable. As a consequence we show that there are uncountable many CAR flows which are cocycle conjugate to the corresponding CCR flows.