Posted: Aug 12, 2010 2:10 pm
twistor59 wrote:...
Nope, it's not strictly a holonomy as mathematicians use the term, but it seems to have crept into the papers on LQG. And no, it's not describing a loop.
k
The quantization (which hopefully I'll get to when I come back from my holidays Wheeeeeee!) is based on spin networks, which are graphs of curves, each of which has holonomy information. These graphs, of course, contain lots of closed loops.
Do I need to get to grips with Hopf & other fibrations, first?
[youtube]http://www.youtube.com/watch?v=1yJ5EvV0K70[/youtube]
The very first attempts at doing this stuff I believe used a "loop transform" to convert from the connection representation to the loop representation (like Wilson loops in gauge theories), but in the modern approach, it's all built up from spin networks. (Unfortunately the original papers aren't on the arxiv and I don't have copies).
I think you are doing a good thing off your own bat.
c u on t'uther side... 
