Path Integral formulation of Loop Cosmology (a first)

[marcus]

Today (17 March) we got our first news of a Path Integral formulation of LQC.
Adam Henderson is a PhD student in Ashtekar's group at Penn State.
He gave an internationally distributed seminar talk on his research.
http://relativity.phys.lsu.edu/ilqgs/henderson031709.pdf
http://relativity.phys.lsu.edu/ilqgs/henderson031709.wav

Up till now LQC has always followed the canonical approach.

By contrast the full LQG theory has developed both a canonical and a covariant (spin foam) formulation. So Henderson's work can be seen as an attempt to extend the program in the applied area of cosmology, following the general theory's lead.

So far Loop Cosmology has not been mathematically derived from LQG. It has been constructed by carrying over and using ideas from LQG, but they remain two parallel fields. Bridging and merging LQC with LQG is high on the research agenda now. Henderson's talk reveals similarities or points of contact with the spin foam path integral version of the full theory, so it fits into this effort.

 

[Coin]

So far Loop Cosmology has not been mathematically derived from LQG... Henderson's talk reveals points of contact with the spin foam path integral version of the full theory, so it fits into this effort.

This part is exciting.

 

[marcus]

This part is exciting.

Yes, see for example the slides around equation 40, about 55% of the way through the audio. Sorry I wish I could give an exact minute to help find the discussion.
If you drag the pointer almost exactly halfway thru the visual time-bar of the audio, you come up to some questions and arguments* from the audience especially referring to equation 38. When that is through (at around 55%) then Henderson resumes again, with the equation 40 slide discussing similarity with spinfoam.

*Laurent Freidel, Abhay Ashtekar, at a couple of places Kirill Krasnov. It was clear from the interruptions and the questions afterwards that the talk evoked considerable interest. Also the audio quality was better than some previous ILQS sessions I've listened to.