The Construction of Pointlike Localized Charged Fields from Conformal Haag-Kastler Nets

TL;DR

This paper constructs pointlike localized charged fields from conformal Haag-Kastler nets, proving key theorems like Spin-Statistics and PCT, and extending previous neutral sector results to charged sectors.

Contribution

It introduces a method to build charged pointlike fields from conformal nets, generalizing prior neutral sector results to include arbitrary charges with finite statistics.

Findings

Construction of charged pointlike localized fields

Proof of Spin-Statistics and PCT theorems

Extension of results to full charged sectors

Abstract

Starting from a chiral conformal Haag-Kastler net on 2 dimensional Minkowski space we construct associated charged pointlike localized fields which intertwine between arbitrary superselection sectors with finite statistics of the theory. This amounts to a proof of the Spin-Statistics theorem, the PCT theorem and the existence of operator product expansions. This paper generalizes similar results of a recently published paper by Fredenhagen and the author \cite{FrJ} from the neutral vacuum sector to the the full theory with arbitrary charge and finite statistics.