Geometry with non-compact groups, e.g. Freidel/Livine

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marcus

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connections and Lie groups are geometry objects, and bundles and such, and come up in any gauge theory (presumably all over the place in field theory) but the group is often compact

the Freidel/Livine paper is about these things, generalizing to a non-compact group.

From the abstract:

"Spin networks are a natural generalization of Wilson loop functionals.....
We finally construct the full hilbert space containing all spin network states. Having in mind applications to gravity, we illustrate our results for the groups SL(2,R) and SL(2,C)."

they use algebraic geometry concepts, a little, and also something out of algebraic topology called the genus (number of handles). It is a remarkable paper---as more than one person at PF has noted. At heart it is differential geometry but reasoning is drawn in from other branches of mathematics.

I would like to understand this paper better.

Freidel/Livine "Spin Networks for Non-Compact Groups"
http://arxiv.org/hep-th/0205268 [Broken]

it also connects to Livine's thesis---Boucles et Mousses de Spin...
 
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