Examples of Multiparameter CCR flows with non-trivial index

TL;DR

This paper constructs numerous examples of multiparameter CCR flows with index one that are not derived from one-parameter flows, and demonstrates their type I classification based on their product systems.

Contribution

It introduces uncountably many new multiparameter CCR flows with index one that are not pullbacks of one-parameter flows, expanding the understanding of their structure.

Findings

Constructed uncountably many multiparameter CCR flows with index one.

Showed these flows are not pullbacks of 1-parameter CCR flows.

Proved these flows are type I with specific product system properties.

Abstract

In this paper, we construct uncountably many examples of multiparameter CCR flows, which are not pullbacks of $1$-parameter CCR flows, with index one. Moreover, the constructed CCR flows are type I in the sense that the associated product system is the smallest subsystem containing its units.