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Miguel C. Alvarez thesis posted today (Baez student) 
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#1
Dec1204, 08:20 PM

Astronomy
Sci Advisor
PF Gold
P: 23,271

Miguel C. Alvarez is a PhD student of John Baez at UC Riverside
he posted his thesis today. congratulations! (both to the student and teacher) http://arxiv.org/abs/mathph/0412032 "Loop Quantization versus Fock Quantization of pForm Electromagnetism on Static Spacetimes" Here's the abstract: "As a warmup for studying dynamics and gravitons in loop quantum gravity, Varadarajan showed that Wilson loops give operators on the Fock space for electromagnetism in Minkowski spacetime  but only after regularizing the loops by smearing them with a Gaussian. Unregularized Wilson loops are too singular to give densely defined operators. Here we present a rigorous treatment of unsmeared Wilson loops for vacuum electromagnetism on an arbitrary globally hyperbolic static spacetime. Our Wilson loops are not operators, but "quasioperators": sesquilinear forms on the dense subspace of Fock space spanned by coherent states corresponding to smooth classical solutions..." this research can be seen as illustrating the difficulty LQG has in reproducing results in a static flat vacuumMinkowski spacetimewhich are almost taken for granted in that more conventional context. Several people are currently working on this and making gradual progress. I cannot judge the thesis itself, but by outward appearances Miguel did not pick an easy problem but, instead, chose an important gnarly issue to tackle for this thesis. Miguel has written some for Wikipedia. PF may have already been reading his encyclopedia articles with or without knowing of the author. he also does fencingwhich I think is arivero's sport as well Thanks to selfAdjoint for pointing out an error in the link as I first typed it. I have corrected it and it seems to be right now. 


#2
Dec1204, 08:30 PM

Astronomy
Sci Advisor
PF Gold
P: 23,271

Here are papers by two other researchers working on getting gravitons in LQG, i.e. approximating a flat vacuum
http://arxiv.org/grqc/0410120 The graviton vacuum as a distributional state in kinematic Loop Quantum Gravity Madhavan Varadarajan 44 pages * http://arxiv.org/grqc/0409036 Free vacuum for loop quantum gravity Florian Conrady (CPT, Marseille & Potsdam, Max Planck Inst.) 30 pages, 3 diagrams that is 3 papers in one year (in a modest size field) so maybe it is becoming something good to work on Miguel CA mentions Varadarajan, I dont know if he cites Conrady or not 


#3
Dec1204, 09:00 PM

Emeritus
PF Gold
P: 8,147

Marcus the link you give, grqc/0412044, is not CarrionAlvarez's paper. I found the paper here: http://www.arxiv.org/abs/mathph/0412032



#4
Dec1204, 09:21 PM

Emeritus
PF Gold
P: 8,147

Miguel C. Alvarez thesis posted today (Baez student)
He is trying to quantize the electromagnetic field using Wison Loops in flat Minkowski background. The point is the Wilson Loops; they do not, as is known, correspond to operators in Foch space. But their matrix elements exist when they are linear combinations of "regular coherent states", and these regular coherent states span a dense subset of Foch space.
Does this strategy sound familiar to you? Recall cylinder functions? A different algebra, but the same strategy! 


#5
Dec1304, 10:24 PM

P: 134

Here: http://www.physicsforums.com/showthread.php?t=40814 I actually used a link by Varadarajan on 'Wik' site to convey a question relative to certain aspects of Fields, dimensionally:http://en.wikipedia.org/wiki/Observable Now it seems that the Miguel C. Alvarez thesis paper has some aspects for the ElectroMagneticVacuum theory that I have been banding around on many forums for a long time, of course one can simply state,as admin often do its an unqualified personal theory and warrents a forum ban! Again thanks. 


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