Any compact group is a gauge group

TL;DR

This paper proves that any compact metrizable gauge group with a central involution can be realized in a quantum field theory model, showing the universality of such gauge groups in local quantum physics.

Contribution

It demonstrates that any pair of a compact metrizable group and a central involution can serve as a gauge group in a quantum field theory model, extending the understanding of gauge symmetries.

Findings

Any such pair {G,k} can be realized as a gauge group in a constructed model.

The models can satisfy the split property, ensuring a well-behaved local structure.

The construction involves subnets of local algebras from free field theories.

Abstract

The assignment of local observables in the vacuum sector, fulfilling the standard axioms of local quantum theory, is known to determine uniquely a compact group G of gauge transformations of the first kind together with a central involutive element k of G, and a complete normal algebra of fields carrying the localizable charges, on which k defines the Bose/Fermi grading. We show here that any such pair {G,k}, where G is compact metrizable, does actually appear. The corresponding model can be chosen to fulfill also the split property. This is not a dynamical phenomenon: a given {G,k} arises as the gauge group of a model where the local algebras of observables are a suitable subnet of local algebras of a possibly infinite product of free field theories.