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marcus
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Jerzy Lewandowski has essentially codified Loop Foam gravity for us.
This had to happen, and there had to be a definitive 2009 exposition of the basics.
So far the best I know of is Jerzy's
http://arxiv.org/abs/0909.0939
Spin-Foams for All Loop Quantum Gravity
and the audio+slides version is at ILQGS
http://relativity.phys.lsu.edu/ilqgs/lewandowski102009.pdf
http://relativity.phys.lsu.edu/ilqgs/lewandowski102009.wav
http://relativity.phys.lsu.edu/ilqgs/
Something that impressed me, that may seem irrelevant, is how strongly Jerzy stressed the seminal importance of work by Michael Reisenberger done around 1994-1998. Here is a 1990 photo of MR at the Vatican Observatory
http://www34.homepage.villanova.edu...9/halpern/photos/reisenberger-leopold1990.jpg
Now Reisenberger is senior faculty at the Montevideo Instituto de Fisica. He and Rodolfo Gambini are the two top QG people at University of Montevideo.
Reisberger's 1994 paper was called Worldsheet formulations of gauge theories and gravity http://arxiv.org/abs/gr-qc/9412035 It was written while he was still at Utrecht, at Gerard 't Hooft's ITP.
His 1997 paper with Carlo Rovelli was called "Sum over Surfaces'' form of Loop Quantum Gravity http://arxiv.org/abs/gr-qc/9612035 This was written while he was at the Schrödinger Institute in Vienna, and also at Montevideo.
A 1998 paper that Jerzy says should still be studied more (still has germinal undeveloped ideas) is called On relativistic spin network vertices http://arxiv.org/abs/gr-qc/9809067
Jerzy points to these as the founding papers of the spinfoam approach, the genesis of the idea. He also acknowledges learning a lot from John Baez clear 2000 exposition, and the review paper by Perez.
Jerzy presents a development of the spinfoam concept that appears in a certain sense natural. He defines the vertex formula for the foam using an enclosing spinnetwork---without invoking terms like "10j symbol" or "15j symbol". If you accept the idea of cylinder function (basic to the uniqueness theorem of "L.O.S. & T.") then the spinnetwork idea is not ad hoc---it flows naturally from the cylinderfunctions on the space of connections. And then the spinfoam idea flows naturally from the spinnetwork idea. He avoids all disconnects between the ideas.
And he seems to be saying that he was helped to re-understand the spinfoam concept by going back to Reisenberger's initial vision of it, or his preliminary glimpse. After he has finished the development, he can derive the current spinfoam vertex formulas, such as the Engle-Livine- Pereira-Rovelli, and see how the technical numbers like the angular momentum "j" symbols arise.
Lewandowski has been a major force in making Loop-and-related physics mathematically rigorous. His long collaboration with Ashtekar, spanning many years and many papers, had this main thrust.
If the organizers of the September 2009 Corfu School eventually succeed in putting online the 5-hour series of lectures by Carlo Rovelli, this would be what I'd say was the current definitive version of Loop Foam gravity. But we don't have those lectures as online media yet. At least for time being, Jerzy's paper and talk will fill the bill.
Here's a current photo of Reisenberger, one of 9 snapshots of Theiss scientists.
http://www.theissresearch.org/scientists/
It's alphabetical so scroll down.
If anyone wants to google more information about the University of Montevideo, the official name is UDELAR universita de la republica. Montevideo is capital of Uruguay, which is a Republic, so the main Uni is the University of the Republic. Here is the Montevideo Institute of Physics page:
http://www.fisica.edu.uy/
and here's the faculty list:
http://www.fisica.edu.uy/integrantes.html
This had to happen, and there had to be a definitive 2009 exposition of the basics.
So far the best I know of is Jerzy's
http://arxiv.org/abs/0909.0939
Spin-Foams for All Loop Quantum Gravity
and the audio+slides version is at ILQGS
http://relativity.phys.lsu.edu/ilqgs/lewandowski102009.pdf
http://relativity.phys.lsu.edu/ilqgs/lewandowski102009.wav
http://relativity.phys.lsu.edu/ilqgs/
Something that impressed me, that may seem irrelevant, is how strongly Jerzy stressed the seminal importance of work by Michael Reisenberger done around 1994-1998. Here is a 1990 photo of MR at the Vatican Observatory
http://www34.homepage.villanova.edu...9/halpern/photos/reisenberger-leopold1990.jpg
Now Reisenberger is senior faculty at the Montevideo Instituto de Fisica. He and Rodolfo Gambini are the two top QG people at University of Montevideo.
Reisberger's 1994 paper was called Worldsheet formulations of gauge theories and gravity http://arxiv.org/abs/gr-qc/9412035 It was written while he was still at Utrecht, at Gerard 't Hooft's ITP.
His 1997 paper with Carlo Rovelli was called "Sum over Surfaces'' form of Loop Quantum Gravity http://arxiv.org/abs/gr-qc/9612035 This was written while he was at the Schrödinger Institute in Vienna, and also at Montevideo.
A 1998 paper that Jerzy says should still be studied more (still has germinal undeveloped ideas) is called On relativistic spin network vertices http://arxiv.org/abs/gr-qc/9809067
Jerzy points to these as the founding papers of the spinfoam approach, the genesis of the idea. He also acknowledges learning a lot from John Baez clear 2000 exposition, and the review paper by Perez.
Jerzy presents a development of the spinfoam concept that appears in a certain sense natural. He defines the vertex formula for the foam using an enclosing spinnetwork---without invoking terms like "10j symbol" or "15j symbol". If you accept the idea of cylinder function (basic to the uniqueness theorem of "L.O.S. & T.") then the spinnetwork idea is not ad hoc---it flows naturally from the cylinderfunctions on the space of connections. And then the spinfoam idea flows naturally from the spinnetwork idea. He avoids all disconnects between the ideas.
And he seems to be saying that he was helped to re-understand the spinfoam concept by going back to Reisenberger's initial vision of it, or his preliminary glimpse. After he has finished the development, he can derive the current spinfoam vertex formulas, such as the Engle-Livine- Pereira-Rovelli, and see how the technical numbers like the angular momentum "j" symbols arise.
Lewandowski has been a major force in making Loop-and-related physics mathematically rigorous. His long collaboration with Ashtekar, spanning many years and many papers, had this main thrust.
If the organizers of the September 2009 Corfu School eventually succeed in putting online the 5-hour series of lectures by Carlo Rovelli, this would be what I'd say was the current definitive version of Loop Foam gravity. But we don't have those lectures as online media yet. At least for time being, Jerzy's paper and talk will fill the bill.
Here's a current photo of Reisenberger, one of 9 snapshots of Theiss scientists.
http://www.theissresearch.org/scientists/
It's alphabetical so scroll down.
If anyone wants to google more information about the University of Montevideo, the official name is UDELAR universita de la republica. Montevideo is capital of Uruguay, which is a Republic, so the main Uni is the University of the Republic. Here is the Montevideo Institute of Physics page:
http://www.fisica.edu.uy/
and here's the faculty list:
http://www.fisica.edu.uy/integrantes.html
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for me) - I am quite suspicious of Rovelli unless Freidel or Reisenberger are coauthors.
