Kakutani Dichotomy on Free States

TL;DR

This paper investigates the conditions under which two quasi-free states on CAR or CCR algebras generate quasi-equivalent representations, establishing a dichotomy based on their disjointness.

Contribution

It proves a Kakutani dichotomy for free states, clarifying when they produce quasi-equivalent or disjoint representations.

Findings

Quasi-free states are quasi-equivalent unless disjoint.

Disjointness implies non-quasi-equivalence.

Provides a dichotomy criterion for free states.

Abstract

Two quasi-free states on a CAR or CCR algebra are shown to generate quasi-equivalent representations unless they are disjoint.