tag:blogger.com,1999:blog-22973357.post10474528026131207..comments2019-08-23T10:01:21.443-04:00Comments on Sabine Hossenfelder: Backreaction: Asymptotic Freedom and the Coupling Constant of QCDSabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger35125tag:blogger.com,1999:blog-22973357.post-39511635104187566482007-12-18T09:07:00.000-05:002007-12-18T09:07:00.000-05:00Hi Steve:Yeah, I just thought the refs could be us...Hi Steve:<BR/><BR/>Yeah, I just thought the refs could be useful to see what others have done, techniques etc. Good luck, and let us know from time to time how its going! Best,<BR/><BR/>B.Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-34575475088459305172007-12-18T04:11:00.000-05:002007-12-18T04:11:00.000-05:00In what way can diagrams be useful? A picture is ...In what way can diagrams be useful?<BR/><BR/> A picture is worth a thousand words, while a equation reduces the complexity to a lessor entropic valuation.:)<BR/><BR/><A HREF="http://superstringtheory.com/basics/anims/photon2.gif" REL="nofollow">The particle view of nature is a description that works exceedingly well to describe three of the four observed forces of nature</A><BR/><BR/><A HREF="Platohttps://www.blogger.com/profile/00849253658526056393noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-35501062299785831642007-12-18T03:40:00.000-05:002007-12-18T03:40:00.000-05:00Don't mind me.I've been criticized on my thinking ...Don't mind me.<BR/><BR/>I've been criticized on my thinking of <A HREF="http://universe-review.ca/I15-15-topology2.jpg" REL="nofollow">circles</A> many times:)<BR/><BR/>The <A HREF="http://www.physics.ucsb.edu/~strings/superstrings/kktower.gif" REL="nofollow">KK tower</A> is equally interesting, although this had been dismissed from the conversation early on.<BR/><BR/><I>The familiar extended Platohttps://www.blogger.com/profile/00849253658526056393noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-64874060967420241262007-12-17T22:12:00.000-05:002007-12-17T22:12:00.000-05:00Thanks, Bee, for the papers. They are interesting...Thanks, Bee, for the papers. They are interesting and it's nice to know the Cauchy problem has a solution in YM. Not sure these papers directly address confinement... But I will enjoy reading them.<BR/><BR/>Thanks Stefan for the comments. I've only seen Wilson loops in use in a lattice QCD context, but they are classical objects that apparently were designed to address the confinement problem.Steve Brysonnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-78249920988704395472007-12-17T18:51:00.000-05:002007-12-17T18:51:00.000-05:00Dear all,thanks for these interesting contribution...Dear all,<BR/><BR/>thanks for these interesting contributions! <BR/><BR/>As for confinement, I am not sure how one would measure it in a purely classical theory - would the Wilson Loop criterion work? <BR/><BR/>I guess as a starter, it would be "natural" - as coming from electrodynamics - to look at the theory in 3+1D and with massive charges - after all, electrons have mass as well? It would stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-83272883188490281852007-12-17T17:40:00.000-05:002007-12-17T17:40:00.000-05:00Well, I don't know. As I said earlier, since the c...Well, I don't know. As I said earlier, since the confinement comes with particle-antiparticle production I can't quite see how one could address it classically. I mean, one can investigate the classical solutions but I wouldn't know really what to conclude from it. I think there are some solutions known to classical YM theory, let me see if I find a reference, I had one at hand recently...<BR/><Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-59386301516802672872007-12-17T17:24:00.000-05:002007-12-17T17:24:00.000-05:00From Bee: If it's massless.Interesting point here:...From Bee: <I>If it's massless.</I><BR/><BR/>Interesting point here: pure QCD in the standard model is massless, but is my proposed (and probably too-difficult-to-do) classical study constrained to be massless? I think it would be easier with massive quarks. The formalism doesn't care.<BR/><BR/>steveSteve Brysonnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-8889335318567537642007-12-17T13:12:00.000-05:002007-12-17T13:12:00.000-05:00Thomas' point is interesting and goes beyond my co...<I>Thomas' point is interesting and goes beyond my competence. Is the classical theory really scale invariant?</I><BR/><BR/>If it's massless.Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-80430525237698083232007-12-17T13:07:00.000-05:002007-12-17T13:07:00.000-05:00Good morning - For the most recent Anonymous - I w...Good morning - <BR/><BR/>For the most recent Anonymous - I would be very surprised if we could find a 1/r or any other specific potential with a classical analysis. The equations are very non-linear and it's hard for me to imagine anything other than a numerical study making headway. As I said before, I would be content with purely qualitative results, like "the energy diverges as the quarks Steve Brysonnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-31730143053336406292007-12-17T09:40:00.000-05:002007-12-17T09:40:00.000-05:00Classical QCD (with massless fermions) is a scale ...Classical QCD (with massless fermions) is a scale invariant theory, so it cannot have a string tension or a mass gap. Scale invariance is broken by quantum effects. The QCD scale comes from the running coupling and dimensional transmutation. <BR/><BR/>cheers<BR/><BR/>thomasthomasnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-9718718664879903542007-12-17T09:26:00.000-05:002007-12-17T09:26:00.000-05:00Hi Steve:Thanks for your explanation. I guess I sh...Hi Steve:<BR/><BR/>Thanks for your explanation. I guess I share Anonymous' confusion above. I certainly don't say the fibre bundle formalism is useless. I as many others find it attractive because of the similarity to GR. Yes, if you construct your gauge bundle with a Lie-Group then the tangential space of the group is the Lie-Algebra. Fields over the manifolds are cuts in the bundle. The Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-20965014004071658492007-12-17T00:32:00.000-05:002007-12-17T00:32:00.000-05:00Theres nothing useless about the bundle formalism,...Theres nothing useless about the bundle formalism, thats really the fundamental mathematics of Yang Mills theory. Be sure most HEP theorists are intimately familiar with it.<BR/><BR/>Huge progress was made in the eighties using this geometrical picture, particularly with respect to topological field theories.<BR/><BR/>Not that it really told us something new, just that it made the physical Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-3190745130439765202007-12-16T23:39:00.000-05:002007-12-16T23:39:00.000-05:00Oops - when I said ... The connection is (sort of)...Oops - when I said <I>... The connection is (sort of) on the tangent space of the fiber in the bundle space...</I> I should have just said <I>... The connection is (sort of) on the tangent space of the bundle space...</I><BR/><BR/>steveSteve Brysonnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-67207199361809628452007-12-16T23:26:00.000-05:002007-12-16T23:26:00.000-05:00Hi Bee - Great discussion! I can see that to some...Hi Bee - Great discussion! I can see that to some extent we're talking past each other, and I hope resolving this will be interesting to anyone listening. <BR/><BR/>The bundle formalism I'm describing is <I>not</I> Kaluza-Klein, though the superficial resemblance has led many authors to confuse them. KK posits structure beyond the standard model (whatever that is at the time) in the hopes of Steve Brysonnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-580872609205327802007-12-16T21:58:00.000-05:002007-12-16T21:58:00.000-05:00Hi Steve:Sorry, the 'frame bundle' was a typo, I m...Hi Steve:<BR/><BR/>Sorry, the 'frame bundle' was a typo, I meant to say 'fibre bundle', apologies for the confusion.<BR/><BR/><I>In other words the only point of mentioning the Lorentz force law is that this non-geometrical equation (in the old way of thinking) can be derived from a geometrical picture in exactly the same way that the motion of a particle under gravity can be explained by Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-45498420231314543952007-12-16T21:45:00.000-05:002007-12-16T21:45:00.000-05:00Hi Bee - First off I'll agree: there's a really ne...Hi Bee - First off I'll agree: there's a really neat question here involving an awful lot of physics, and one way to address it is to try to separate out some simpler parts and see if the interesting stuff is still there. <BR/><BR/>I want to clarify a couple things: The picture I'm referring to is not on the frame bundle, it's instead a principle bundle with the appropriate gauge group. The Steve Brysonnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-68837937788196610482007-12-16T20:28:00.000-05:002007-12-16T20:28:00.000-05:00Hi Steve:That's an interesting question, one I've ...Hi Steve:<BR/><BR/>That's an interesting question, one I've asked myself, and I still have no really satisfactory answer for this. Sure, you can write down classical SU(3) Yang-Mills theory, and I think there are general ways to find solutions to this kind of theory. The formalism for this is the frame bundle over the base-manifold how you describe. <BR/><BR/>You need in addition however the Beehttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-43503563431528731302007-12-16T20:03:00.000-05:002007-12-16T20:03:00.000-05:00Steve my guess is no. You can get confining theor...Steve my guess is no. You can get confining theories even for abelian models in lower dimensions.<BR/><BR/>Also if you stick things on a lattice, confinement/nonconfinement is really seen as a sort of phase transition.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-46852214378292784952007-12-16T18:08:00.000-05:002007-12-16T18:08:00.000-05:00hi - i've only recently started reading Backreacti...hi - i've only recently started reading Backreaction and I really enjoy your surveys of important historical topics, especially the links to modern survey articles.<BR/><BR/>Since we're on the topic of quark confinement, let me ask something I've wondered about since the 80's, which I hope some of you will find entertaining: does quark confinement require quantum field theory, or does is show up Steve Brysonnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-55147094101725189352007-12-16T06:23:00.000-05:002007-12-16T06:23:00.000-05:00Hi Eric,thanks again - I am not so familiar with t...Hi Eric,<BR/><BR/><BR/>thanks again - I am not so familiar with the beta function, will have to check that some time... <BR/><BR/>But then, the point remains, is the non-abelian nature of QCD, in contrast to abelian QED, relevant for confinement? <BR/><BR/>OK, if in QED the coupling constant is increased to 1, there is the argument that the vacuum gets instable and that real electron-positron stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-29410145941729068352007-12-16T05:51:00.000-05:002007-12-16T05:51:00.000-05:00Hi Neil',no, Newton's gravitational constant G is ...Hi Neil',<BR/><BR/>no, Newton's gravitational constant G is not involved here, but, as you suggest, the Compton wavelength. Maybe you see better what is going on when focussing on the potential energy U between two electrical charges Q and q at distance r, which is (in SI or MKS units)<BR/><BR/>U = qQ/4πεr .<BR/><BR/>Now, you measure U in units of the rest energy of the electron, E = stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-50938105088185238812007-12-15T16:14:00.000-05:002007-12-15T16:14:00.000-05:00Stefan, Yes, QED would become confining if th...Stefan,<BR/> Yes, QED would become confining if the coupling costant were of order one at some energy and if it had a negative beta function, so that the coupling is of order one for all values below this energy. However, I think this can only happen for nonAbelian gauge symmetries. Essentially, any nonAbelian gauge group SU(N) with a negative beta function will become confining at some Ericnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-85585509097014985892007-12-15T15:27:00.000-05:002007-12-15T15:27:00.000-05:00Thanks Stefan for the clarification about units. ...Thanks Stefan for the clarification about units. Since you relate L and T to M, I suppose you need to use G to fit it all together, which I wouldn't have expected (or do you use the Compton wavelength somehow?) But what if there was no gravity to calibrate the magnitude of mass? I get the impression that the deep theoretical implications would be more than just no attraction between masses.<BR/>Neil'https://www.blogger.com/profile/04564859009749481136noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-45532214170198960562007-12-15T15:06:00.000-05:002007-12-15T15:06:00.000-05:00Hi Eric,thanks for you comment. Let me ask the que...Hi Eric,<BR/><BR/>thanks for you comment. Let me ask the question in another way: <BR/><BR/>Would QED confine electrical charges if the coupling constant was of the order of 1 instead of 0.01?stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-19026388377407509262007-12-15T14:32:00.000-05:002007-12-15T14:32:00.000-05:00Quark confinement happens when alpha_s is approxim...Quark confinement happens when alpha_s is approximately equal to unity, which you can see from the plot happens around 1 GeV. Note that hadrons and mesons all of masses around this scale.Ericnoreply@blogger.com