From global symmetries to local currents: the free (scalar) case in 4 dimensions

TL;DR

This paper introduces a new algebraic quantum field theory method to construct local gauge symmetry generators from global symmetries, demonstrated on free scalar fields, recovering conserved currents via a pointlike limit.

Contribution

It presents a novel approach to derive local gauge generators from global symmetries using automorphisms in algebraic QFT, applied to free scalar fields.

Findings

Local generators of gauge symmetries can be constructed from automorphisms.

Conserved currents are recovered in the pointlike limit.

Method applies to free scalar fields in four dimensions.

Abstract

Within the framework of algebraic quantum field theory, we propose a new method of constructing local generators of (global) gauge symmetries in field theoretic models, starting from the existence of unitary operators implementing locally the flip automorphism on the doubled theory. We show, in the simple example of the internal symmetries of a multiplet of free scalar fields, that through the pointlike limit of such local generators the conserved Wightman currents associated with the symmetries are recovered.