mass gap in Yang-Mills theories


by humanino
Tags: mass, theories, yangmills
selfAdjoint
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#55
Nov18-04, 04:25 PM
Emeritus
PF Gold
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Kea, the trouble with all your references is that nobody who doesn't have a graduate university library can see them. Isam's stuff is online at the arxive; is any of the rest of it. Anything at the level of Joyce?
Kea
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#56
Nov18-04, 05:12 PM
P: 859
Unfortunately, no.

On-line books on topos theory include Barr and Wells
and Goldblatt. John Baez's website is a good source
of references.

Sorry everybody.
Kea
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#57
Nov18-04, 05:21 PM
P: 859
Here

http://www.cwru.edu/artsci/math/wells/pub/ttt.html
marcus
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#58
Nov18-04, 06:34 PM
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Quote Quote by Kea
I believe the best explanation now for confinement begins with
W. P. Joyce "Quark state confinement as a consequence of the
extension of the Bose-Fermi recoupling to SU(3) colour"
J. Phys. A: Math. Gen. 36 (2003) 12329 - 12341

This work can now be fit into a much more general framework,
either via Joyce's so-called omega algebras (recent work)
or equivalently from the perspective of higher categories
where these algebraic structures appear naturally.

Moreover the mathematics has a close tie to LQG (this
is mostly unpublished) ...
Hello everybody, selfAdjoint asked for arxiv references for Joyce work because they are accessible to those of us who dont have a university library close by. Here are some:

http://arxiv.org/find/hep-th/1/au:+J.../0/1/0/all/0/1

hep-th/0307047
Quark confinement without a confining force
P.S. Isaac, W.P. Joyce, J. Links
5 pages

hep-th/0307046
An algebraic origin for quark confinement
P.S. Isaac, W.P. Joyce, J. Links
23 pages

hep-th/0306256
Quark State Confinement as a Consequence of the Extension of the Bose--Fermi Recoupling to SU(3) Colour
W. P. Joyce
15 pages, 4 figures

this list gives not only the one which Kea cited but also two others which are more recent---not yet in hardcopy
I have not examined these papers personally, but only helping as
an assistant librarian (I think I would not understand the papers in any case, or grasp their applicability)

regards to all

*
Kea
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#59
Nov18-04, 06:50 PM
P: 859
http://www.arxiv.org/find/math/1/au:.../0/1/0/all/0/1
selfAdjoint
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#60
Nov18-04, 11:05 PM
Emeritus
PF Gold
P: 8,147
Thank you both Kea and Marcus. I will start looking at these tomorrow. I also just found out about Google Scholar (www.scholar.google.com). I typed in topos quantization and got some very interesting results. There's hope for the old presheaf guy yet.
Chronos
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#61
Apr18-05, 01:30 AM
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Is there actually any missing mass? I don't think so. Yang-Mills suggests a slight CPT violation, but no missing energy [mass] that I can see. No matter how much you twist and turn space time around, mass does not go away. The observational evidence for its existence is fairly solid.
ohwilleke
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#62
Apr18-05, 12:11 PM
P: 632
Quote Quote by Chronos
Is there actually any missing mass? I don't think so. Yang-Mills suggests a slight CPT violation, but no missing energy [mass] that I can see. No matter how much you twist and turn space time around, mass does not go away. The observational evidence for its existence is fairly solid.
The mass isn't missing from the observational universe. The mass is missing from the theory. The gap is between the presence of mass in the observational world, and the absence of mass in the theory, not the other way around. The issue is how to get mass into the theory (with a Higgs like mechanism a possible solution) so that it can fit what we observe, because expect for the mass problem Y-M does a good job of giving us to QCD that we observe.
Lester
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#63
Aug22-10, 12:06 PM
P: 34
You can find a simple definition of mass gap on Wikipedia. A Yang-Mills theory, in the limit of the coupling gauge going to infinity, displays at the classical level a mass gap. This because there is a theorem proved in

http://arxiv.org/abs/0709.2042 (appeared in Physics Letters B)

http://arxiv.org/abs/0903.2357 (appeared in Modern Physics Letters A)

that maps classical solutions of a massless quartic scalar field on the Yang-Mills field. These solutions appear to describe free massive fields notwithstanding we started from massless theories. One can use these solutions to build a quantum field theory and obtain an identical situation once is proved that quantum corrections do not modify it.


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