QED Representation for the Net of Causal Loops

TL;DR

This paper develops a framework using the net of causal loops in AQFT to represent QED, connecting gauge symmetries with algebraic structures in a covariant, spacetime-independent manner.

Contribution

It introduces a novel representation of QED within the net of causal loops framework, linking gauge transformations to connection systems in AQFT.

Findings

Realizes QED as a representation of the net of causal loops in Minkowski spacetime.

Maps the electromagnetic field into the algebraic framework, capturing gauge transformations.

Establishes a structural connection between gauge symmetries and algebraic quantum field theory.

Abstract

The present work tackles the existence of local gauge symmetries in the setting of Algebraic Quantum Field Theory (AQFT). The net of causal loops, previously introduced by the authors, is a model independent construction of a covariant net of local C*-algebras on any 4-dimensional globally hyperbolic spacetime, aimed to capture some structural properties of any reasonable quantum gauge theory. In fact, representations of this net can be described by causal and covariant connection systems, and the local gauge transformations arise as maps between equivalent connection systems. The present paper completes these abstract results, realizing QED as a representation of the net of causal loops in Minkowski spacetime. More precisely, we map the quantum electromagnetic field F{\mu}{\nu}, not free in general, into a representation of the net of causal loops and show that the corresponding connection system and local gauge transformations find a counterpart in terms of F{\mu}{\nu}.