A sampler of (algebraic) quantum field theory
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Mon, 24/01/2011 15:45 |
Andre Henriques (Universiteit Utrecht) |
Topology Seminar  |
L3 |
| Roughly speaking, a quantum field theory is a gadget that assigns algebraic data to manifolds. The kind of algebraic data depends on the dimension of the manifold.Conformal nets are an example of this kind of structure. Given a conformal net, one can assigns a von Neumann algebra to any 1-dimensional manifold, and (at least conjecturally) a Hilbert space to any 2-dimensional Riemann surfaces.I will start by explaining what conformal nets are. I will then give some examples of conformal net: the ones associated to loop groups of compact Lie groups. Finally, I will present a new proof of a celebrated result of Kawahigashi, Longo, andMueger:The representation category of a conformal net (subject to appropriate finiteness conditions) is a modular tensor category.All this is related to my ongoing research projects with Chris Douglas and Arthur Bartels, in which we investigate conformal nets from a categorytheoretical perspective. | |||