Quasi-free isomorphisms of second quantisation algebras and modular theory

TL;DR

This paper establishes an abstract criterion for isomorphisms between second quantization algebras using modular theory, with potential applications to quantum field theory vacua.

Contribution

It provides a new criterion for isomorphisms of second quantization algebras based on modular operators, extending previous quasi-equivalence results.

Findings

Criterion for isomorphisms via modular operators

Application to Klein-Gordon field vacua

Connection to quasi-free representations

Abstract

Using Araki-Yamagami's characterization of quasi-equivalence for quasi-free representations of the CCRs, we provide an abstract criterion for the existence of isomorphisms of second quantization local von Neumann algebras induced by Bogolubov transformations in terms of the respective one particle modular operators. We discuss possible applications to the problem of local normality of vacua of Klein-Gordon fields with different masses.