I think you are reading it wrong. First, while what you say is true for QM, I don't think it would be correct todescribe the 'fields' of quantum field theory as probability waves. They are even more abstract: operators thatcan create particles. The real issue seems to be that the theories at issue have both a classical and quantum interpretation -- and the interpretationsare even -more different- than in the case of QED.In the more well-understood case of light particles (photons), both interpretations (quantum/calssical) describe massless objects, hence moving at the speed of light.The combined theory of massive charged particles and photons (QED) still describes massless photons, whichis indeed what we see in the world. But for the QCD force particles (the gluons), the classical interpretation is that they are still massless particles, but thisis not believed to be true at the quantum level (or seen in the real world). For QCD, the lightest particleseen is the pion and it has a mass > 0. There is no massless force particle like the photon seen.Physicists are convinced that the theory correctly describes this, butit is not rigorous mathematics. However, the Millenium prize, as I read it, refers not to QCD and the pion, but toa stripped down version of the theory without quarks (pure Yang-Mills in 4 dim). Even without the quarks, the lightest physical particlein the stripped down theory is supposed to have some mass > 0; the issue is to prove this rigorously. For the pion, I can visualize it as two quarks connected by a gluon flux tube: o ================= oMy question: what is the visualization for the lightest particle in the pure Yang-Mills theory of the Mass Gap prize??

Last edited by Alan on September 16th, 2008, 10:00 pm, edited 1 time in total.

QuoteFor the pion, I can visualize it as two quarks connected by a gluon flux tube: o ================= oMy question: what is the visualization for the lightest particle in the pure Yang-Mills theory of the Mass Gap prize??It could be some topologically non-trivial (and hence stable) solution of the gluon field, like a soliton or something like that, properly quantized. This would be similar to viewing the proton as a soliton of the pion field, as was originally suggested by Skyrme, and then developed by others (including Witten).

Alan thanks for your clarification. Very insightful.It always seems to be that we start with a few particles, these slowly increase until the number drops back again, we then start increasing the particles again, until it drops back again to only few... slowly that increases again...e.g.4 Elemental particles (Earth, Fire, Water, Air)Elements (approx 100)Proton Electon Neutron, Neutrino, PhotonExotic particles (Pi, Sigma etc)Quark model (udcstb) + 6 leptons (not including the anti particles) + WZ HiggsWhere now???[Please not string theory again...]

QuoteOriginally posted by: scholarQuoteFor the pion, I can visualize it as two quarks connected by a gluon flux tube: o ================= oMy question: what is the visualization for the lightest particle in the pure Yang-Mills theory of the Mass Gap prize??It could be some topologically non-trivial (and hence stable) solution of the gluon field, like a soliton or something like that, properly quantized. This would be similar to viewing the proton as a soliton of the pion field, as was originally suggested by Skyrme, and then developed by others (including Witten).Thanks -- a little googling on your keywords turned up the existence of a very recent talk by Witten summarizing this problem (supplementing what is posted at theClay Inst. site). I have written for it, but in the mean time, if anybody has it and can send a copy to my profile email address, I would muchappreciate it.

Last edited by Alan on September 17th, 2008, 10:00 pm, edited 1 time in total.

"The great epiphany was realizing that the BPST instanton was exactly the Hopf fibration".

Alan - I don't have this talk, if you get it, please send it to me as well. The other way is to glance xxx.lanl.gov for some reviews/talks. The subject "baryons as solitons" was big in 80th (Witten's paper on this is dated 1983 if I recall correctly.)TJ - instantons are Euclidean solutions, while particles live in the Minkowski space. Solitons are classical solutions in the Minkowski space.

Last edited by scholar on September 17th, 2008, 10:00 pm, edited 1 time in total.

W3ckUiD3aPc:_Yyc:aU7EaDiaMDCiUT">Transformer glitch shuts down world's largest atom smasher, but not reported for a weekQuoteThe world's largest particle collider malfunctioned within hours of its launch to great fanfare, but its operator didn't report the problem for a week.maybe that's why the world didn't end ?

Large Hadron Collider to be turned off for two months following damage

QuoteOriginally posted by: scholarQuoteFor the pion, I can visualize it as two quarks connected by a gluon flux tube: o ================= oMy question: what is the visualization for the lightest particle in the pure Yang-Mills theory of the Mass Gap prize??It could be some topologically non-trivial (and hence stable) solution of the gluon field, like a soliton or something like that, properly quantized. This would be similar to viewing the proton as a soliton of the pion field, as was originally suggested by Skyrme, and then developed by others (including Witten).I found this discussion over at Physics Forums useful.In particular, these comments reproduced from Polyakov's book on the possible role (or not) of instantons were interesting:QuoteSo : here are quotations from "Gauge Fields and strings". Even the negative results are interesting, remember that it is an excellent book to read.(from intro §6)We have seen in the previous chapters that in Abelian systems the problem of charge confinement is solved by instantons.In Non-Abelian theories instantons are also present. However, due to the large perturbative fluctuations, dicussed in Chapter 2, it is difficult to judge whether they play a decisive role in forming a mass gap and a confining regime. In such theories we had a kind of instanton liquid which is difficult to treat. It is possible that due to some hidden symmetries, present in these systems, instantons may form a useful set of variables for an exact description of the system, but this has not yet been shown.At the same time, due to the fact that instantons carry non-trivial topology (they describe configurations of the fields which cannot be "disentangled"), some manifestations of instantons cannot be mixed up with perturbative fluctuations.[...](from end of §6.2)As happened in the case of n-fields, the instanton contribution has an infrared divergence. This implies that in the multi-instanton picture, individual instantons tend to grow and to overlap. The vaive dilute gas approximation is certainly inapplicable then, and we should expect somethig like dissociation of dipole-like instantons to their elementary constituents, as happened in the case of n-fields. However, even one loop computations on the multi-instanton background have not yet been performed, and nothing similar to the Coulomb plasma of the previous section has been discovered. This is connected partly with the fact that multi-instanton solutions have not yet been explicitely parameterized up to now. I expect many interesting surprises await us, even on the one loop level, in this hard problem.[...](from end of §6.2)So, our conclusion is that on the present level of understanding of instanton dynamics, we cannot obtain any exact dynamical statements concerning Non-Abelian gauge theory. In the case of n-fields the situation is slightly better, since we were able to demonstrate the apearance of the mass-gap on a qualitative level. Even in this case one would like to have much deeper understanding of the situation. There are reasons to believe that some considerable progress will be achieved in the near future. In the case of gauge fields we have to pray for luck.At the same time, the existence of fields with topological charge has a deep qualitative influence on the dynamical structure of the theory. [...](from end of §6.3)(...) exchange of a massless fermion pair leads to long-range forces between instantons and anti-instantons. The result of this may have several alternative consequences. The first one is that since (6.87) implies quenching of large fluctuations in the presence of massless fermions, the system looses the confining property and we would end up with massless gauge fields together with fermions. This option seems highly improbable to me on the basis of some analogies and some model considerations. However, I am not aware of any strict statements permitting us to reject it.The second possibility, which in my opinion is realized in the theory, is the following. Due to the strong binding force between fermions the chiral symmetry gets spontaneously broken and as a result the fermions acquire mass. After that has happened, the long range force between instantons and anti-instantons disappears, being screened by the fermionic mass term in the effective lagrangian. The only remaining effect of anomalous non-conservation will consist of giving a mass to the corresponding Goldstone boson.There is also another improbable option, namely that instantons get confined but some type of large fluctuations, not suppressed by fermions, disorder the system.

Last edited by Alan on September 21st, 2008, 10:00 pm, edited 1 time in total.

Alan - thanks for the link. For sure Polyakov is a pure genius, no less than Witten. His book is also highly recommended as a weekend reading for quants fed up with the subprime crisis and failures of the Gaussian copula.

a better use for the LHC computerevidently, it could be put to better use speeding up the web

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QuoteOriginally posted by: ppaupera better use for the LHC computerevidently, it could be put to better use speeding up the webMaybe Wilmott site could use it as well?

and the helium from LHC could be used to flare up the sky with 1 billion orange balloons

Last edited by quantmeh on September 28th, 2008, 10:00 pm, edited 1 time in total.

They had a great party for the Collider earlier this week - Party Time at CERN - Physics WorldWonder if they had a live performance of the Large Hadron Rap

GZIP: On