AQFT from n-functorial QFT

Details AQFT from n-functorial QFT AQFT from n-functorial QFT

2008-06-06

arxiv.org/abs/0806.1079v2

Commun.Math.Phys.291:357-401,2009

Mathematics

Category Theory

39 pages; further examples added: Hopf spin chains and asymptotic inclusion of subfactors; references added

Scientific paper

10.1007/s00220-009-0840-2

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". In this note we present an observation about how these two axiom systems are naturally related: we demonstrate under mild assumptions that every 2-dimensional extended Minkowskian QFT 2-functor ("parallel surface transport") naturally yields a local net. This is obtained by postcomposing the propagation 2-functor with an operation that mimics the passage from the Schroedinger picture to the Heisenberg picture in quantum mechanics. The argument has a straightforward generalization to general pseudo-Riemannian structure and higher dimensions.

Affiliated with

Also associated with

No associations

Rating

AQFT from n-functorial QFT does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with AQFT from n-functorial QFT, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and AQFT from n-functorial QFT will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-172108