Miguel C. Alvarez thesis posted today (Baez student)

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Discussion Overview

The discussion revolves around the thesis of Miguel C. Alvarez, a PhD student of John Baez, which focuses on the quantization of the electromagnetic field using Wilson loops in the context of loop quantum gravity (LQG). The scope includes theoretical aspects of quantum gravity, specifically addressing challenges in reproducing results in static flat vacuum scenarios such as Minkowski spacetime.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants note that Alvarez's thesis addresses the difficulties LQG faces in reproducing results that are typically straightforward in conventional quantum field theory contexts.
  • It is mentioned that Wilson loops do not correspond to operators in Fock space, but their matrix elements can exist when they are linear combinations of regular coherent states, which span a dense subset of Fock space.
  • Some participants reference other researchers, such as Madhavan Varadarajan and Florian Conrady, who are also working on related topics in LQG, suggesting a growing interest in this area.
  • A participant expresses uncertainty about whether Alvarez cites Conrady's work in his thesis.
  • There is a mention of a potential connection between Alvarez's work and previous discussions on cylinder functions, indicating a shared strategy in the approach to quantization.
  • One participant reflects on the relevance of Alvarez's thesis to their own theories regarding electromagnetic vacuum, while acknowledging the potential for personal theories to be dismissed in forum discussions.

Areas of Agreement / Disagreement

Participants express a mix of interest and uncertainty regarding the implications of Alvarez's work and its connections to other research in the field. No consensus is reached on the significance or correctness of the approaches discussed.

Contextual Notes

Some limitations are noted regarding the definitions and assumptions underlying the discussion, particularly in relation to the treatment of Wilson loops and their role in quantization.

marcus
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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/math-ph/0412032
"Loop Quantization versus Fock Quantization of p-Form 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 vacuum---Minkowski spacetime----which 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 fencing---which 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.
 
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Here are papers by two other researchers working on getting gravitons in LQG, i.e. approximating a flat vacuum

http://arxiv.org/gr-qc/0410120
The graviton vacuum as a distributional state in kinematic Loop Quantum Gravity
Madhavan Varadarajan
44 pages
*
http://arxiv.org/gr-qc/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 C-A mentions Varadarajan, I don't know if he cites Conrady or not
 
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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!
 
marcus said:
Here are papers by two other researchers working on getting gravitons in LQG, i.e. approximating a flat vacuum

http://arxiv.org/gr-qc/0410120
The graviton vacuum as a distributional state in kinematic Loop Quantum Gravity
Madhavan Varadarajan
44 pages
*
http://arxiv.org/gr-qc/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 C-A mentions Varadarajan, I don't know if he cites Conrady or not

Marcus thanks for the link, this paper is really interesting form my and Olias's and Ranyarts perspective!

Here: https://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 Electro-Magnetic-Vacuum 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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