### Relation between AQFT and Extended Functorial QFT

#### Posted by Urs Schreiber

**Update:** the article is now on the arXiv.

This is your last chance (your first chance was here) to make it into the acknowledgements of

Urs Schreiber
*On the relation between algebraic QFT and extended functorial QFT*

arXiv:0806.1079

by complaining about which important references I missed, or complaining about how un-understandable the main argument is, or other complaints like this.

Posted at May 20, 2008 9:29 AM UTC

Abstract.There are essentially two different approaches to the axiomatization of quantum field theory (QFT): algebraic QFT, going back to Haag and Kastler, and functorial QFT, going back to Atiyah and Segal. More recently, based on ideas by Baez and Dolan, the latter is being refined to “extended” functorial QFT by Freed, Hopkins, Lurie and others. The first approach uses local nets of operator algebras which assign to each patch an algebra “of observables”, the latter uses $n$-functors which assign to each patch a “propagator of states”.Here we present an observation about how these two axiom systems are naturally related: we demonstrate under mild assumptions that every 2-dimensional extended QFT 2-functor (“parallel surface transport”) naturally yields a local net. This is obtained by postcomposing the propagation 2-functor with the formation of 2-endomorphisms. The argument has a straightforward generalization to higher dimensions.

## Re: Relation between AQFT and Extended Functorial QFT

There is now a sketch of an argument of how any equivariant structure on the QFT 2-functor induces a covariant structure on the correspondding local AQFT net. Section 6.