CCR flows associated to closed convex cones

Abstract

Let $P$ be a closed convex cone in ${\mathbb{R}}^d$ which we assume to be spanning and pointed i.e. $P-P={\mathbb{R}}^d$ and $P\cap -P=\{0\}$. In this article, we consider CCR flows over $P$ associated to isometric representations that arises out of $P$-invariant closed subsets, also called as $P$-modules, of ${\mathbb{R}}^d$. We show that for two $P$-modules the associated CCR flows are cocycle conjugate if and only if the modules are translates of each other.

Revised version