There is a natural way to formulate Loop quantum geometry as the dynamics of line defects in a flat vacuum. Just under 2 months ago, I attended a 90 minute seminar talk on this at the UC Berkeley physics department. Unfortunately that talk is not online, but we do have an earlier talk given last year at Perimeter Institute:(adsbygoogle = window.adsbygoogle || []).push({});

http://pirsa.org/11090125/

Loop Gravity as the Dynamics of Topological Defects

Speaker(s): Eugenio Bianchi

Abstract: A charged particle can detect the presence of a magnetic field confined into a solenoid. The strength of the effect depends only on the phase shift experienced by the particle's wave function, as dictated by the Wilson loop of the Maxwell connection around the solenoid. In this seminar I'll show that Loop Gravity has a structure analogous to the one relevant in the Aharonov-Bohm effect described above: it is a quantum theory of connections with curvature vanishing everywhere, except on a 1d network of topological defects. Loop states measure the flux of the gravitational magnetic field through a defect line. A feature of this reformulation is that the space of states of Loop Gravity can be derived from an ordinary QFT quantization of a classical diffeomorphism-invariant theory defined on a manifold. I'll discuss the role quantum geometry operators play in this picture, and the perspective of formulating the Spin Foam dynamics as the local interaction of topological defects.

Date: 21/09/2011 - 4:00 pm

It's an exciting development. I would say there is a key step that you see right around minute 14-19 and slides #10 and #11*. I already mentioned this new formulation of Loop in an earlier thread, back in February.

https://www.physicsforums.com/showthread.php?p=3782389#post3782389

The dynamics is worked out in terms ofsurface defects in flat 4D spacetimeor you could say spinfoam.

To me it seems significant that EB chose to talk about the dynamics of defects treatment of Loop when he was out here, because he has more than one idea that he's working on--including (I hear) a possibly deeper way to understand black hole entropy and count the geometric states of the horizon.

There is a technical problem with the PIRSA video which is slightly awkward but which one can work around: the audio was recorded at a low level. You may need some additional amplification (if your computer is like mine) in order to hear clearly.

*pages 17/48 and 20/48 of the PDF, if you happen to have downloaded it.

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# Loop Gravity as the Dynamics of Topological Defects

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