Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2011-12-20
Physics
High Energy Physics
High Energy Physics - Theory
15 pages, 2 figures, Based on the talk presented at Quantum Theory and Symmetries 7, Prague, August 7-13, 2011, JPconf style
Scientific paper
Recent work on exotic smooth R^4's, i.e. topological R^4 with exotic differential structure, shows the connection of 4-exotics with the codimension-1 foliations of $S^{3}$, SU(2) WZW models and twisted K-theory $K_{H}(S^{3})$, $H\in H^{3}(S^{3},\mathbb{Z})$. These results made it possible to explicate some physical effects of exotic 4-smoothness. Here we present a relation between exotic smooth R^4 and operator algebras. The correspondence uses the leaf space of the codimension-1 foliation of S^3 inducing a von Neumann algebra $W(S^{3})$ as description. This algebra is a type III_1 factor lying at the heart of any observable algebra of QFT. By using the relation to factor II, we showed that the algebra $W(S^{3})$ can be interpreted as Drinfeld-Turaev deformation quantization of the space of flat SL(2,\mathbb{C}) connections (or holonomies). Thus, we obtain a natural relation to quantum field theory. Finally we discuss the appearance of concrete action functionals for fermions or gauge fields and its connection to quantum-field-theoretical models like the Tree QFT of Rivasseau.
Asselmeyer-Maluga Torsten
Mader Ruben
No associations
LandOfFree
Exotic R^4 and quantum field theory 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 Exotic R^4 and quantum field theory, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Exotic R^4 and quantum field theory will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-189170