An Algebraic Jost-Schroer Theorem for Massive Theories

TL;DR

This paper proves that certain massive local quantum field theories with specific single-particle creation operators are equivalent to free fields, extending the algebraic Jost-Schroer theorem to include particles with arbitrary spin and string-like localization.

Contribution

It extends the algebraic Jost-Schroer theorem to massive theories with string-localized particles and polarization-free generators, showing their unitary equivalence to free fields.

Findings

The theory is unitarily equivalent to a free field under the given conditions.

Applicable to particles with any spin and string-like localization.

Generalizes previous results to a broader class of massive theories.

Abstract

We consider a purely massive local relativistic quantum theory specified by a family of von Neumann algebras indexed by the space-time regions. We assume that, affiliated with the algebras associated to wedge regions, there are operators which create only single particle states from the vacuum (so-called polarization-free generators) and are well-behaved under the space-time translations. Strengthening a result of Borchers, Buchholz and Schroer, we show that then the theory is unitarily equivalent to that of a free field for the corresponding particle type. We admit particles with any spin and localization of the charge in space-like cones, thereby covering the case of string-localized covariant quantum fields.