Superselection Theory for Subsystems

TL;DR

This paper explores the structure of observable and field nets in quantum field theory, showing how intermediate Bose nets relate to gauge groups under certain conditions, thus advancing the understanding of superselection sectors.

Contribution

It establishes a characterization of intermediate Bose nets as fixed-point nets under compact gauge groups, extending superselection theory for observable nets.

Findings

Intermediate Bose nets are fixed-point nets of the field net under a compact group.

The canonical gauge group is identified when sectors with infinite statistics are absent.

The results apply to observable nets with separable vacuum Hilbert spaces.

Abstract

An inclusion of observable nets satisfying duality induces an inclusion of canonical field nets. Any Bose net intermediate between the observable net and the field net and satisfying duality is the fixed-point net of the field net under a compact group. This compact group is its canonical gauge group if the occurrence of sectors with infinite statistics can be ruled out for the observable net and its vacuum Hilbert space is separable.