tag:blogger.com,1999:blog-22973357.post115956852447784599..comments2021-02-28T10:01:40.676-05:00Comments on Sabine Hossenfelder: Backreaction: The Omega-Minus gets a Spin (part 1)Sabine Hossenfelderhttp://www.blogger.com/profile/06151209308084588985noreply@blogger.comBlogger23125tag:blogger.com,1999:blog-22973357.post-1159890064740604602006-10-03T11:41:00.000-04:002006-10-03T11:41:00.000-04:00Dear Thomas,thanks for the explanations, and the r...Dear Thomas,<BR/><BR/>thanks for the explanations, and the reference to the Slansky review!<BR/><BR/>However, I have to say I am still looking for a good paper or text about all this representation stuff that combines mathematical exactness with thourough physical understanding...<BR/><BR/>Dear Rob,<BR/><BR/><I>But isn't this totally awsome how real particles can be classified in abstract weight stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159886935410977752006-10-03T10:48:00.000-04:002006-10-03T10:48:00.000-04:00Dear Bee, Stefan and Thomas:Thanks so much for you...Dear Bee, Stefan and Thomas:<BR/><BR/>Thanks so much for your explanations! I think, I finally get it. Me, I come more from the mathematical side, and its equally fascinating as complicated to understand the physics behind group theory. But isn't this totally awsome how real particles can be classified in abstract weight diagrams? <BR/><BR/>This is a great blog by the way, and thanks again,<BR/><Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159883431112693562006-10-03T09:50:00.000-04:002006-10-03T09:50:00.000-04:00The best review of this is Slansky, ``Group Theory...The best review of this is Slansky, ``Group Theory for Unified Model Building'', Phys. Rep. 79 (1981) <BR/><BR/>... not having read about it for some time I can't remember the formal solution to the problem of different particles sitting at the same place in the diagram. <BR/><BR/>So far as I remember the representation can be specified by the 'state of highest weight' which is unique within eachAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159820798206111912006-10-02T16:26:00.000-04:002006-10-02T16:26:00.000-04:00cum grano salis, yes: N-1 to fix the multiplet, an...cum grano salis, yes: <BR/><BR/>N-1 to fix the multiplet, and another N-1 to fix the position within the multiplet. <BR/><BR/>However, the inner positions in a multiplet can have a multiplicity higher than 1. For these states, more numbers are necessary. For example, the central positition of the baryon octet is doubly occupied, by the Σ_0 and by the Λ. Both have Y=0 and T_3=0, but the Σ_0 has stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159819019465013432006-10-02T15:56:00.000-04:002006-10-02T15:56:00.000-04:00So in toto it takes 2*(N-1) numbers to define the ...So in toto it takes 2*(N-1) numbers to define the particle?Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159818458644468912006-10-02T15:47:00.000-04:002006-10-02T15:47:00.000-04:00Dear Bee, Rob,sorry, I didn't want to increase con...Dear Bee, Rob,<BR/><BR/>sorry, I didn't want to increase confusion... so<BR/><BR/><I>the number of Casimir invariants (independent elements of the max. abelian subgroup, rank of the group) is the dimension of the diagram</I><BR/><BR/>Yes! <BR/><BR/>For SU(N), this number (= number of Casimir invariants = dimension of the maximal abelian subgroup = rank of the group = dimension of the Cartan stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159811815950494382006-10-02T13:56:00.000-04:002006-10-02T13:56:00.000-04:00Dear Quasar,Hope you take any differences and cont...Dear Quasar,<BR/><BR/><I>Hope you take any differences and contradictory opinions with a pinch of salt - or as constructive criticism and debate.</I><BR/><BR/>Thanks, I appreciate your contributions, and I find your opinions undoubtedly interesting. I just honestly didn't know what further to say to your comments. But the world is not just black and white, so its always good to have different Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159810656748200822006-10-02T13:37:00.000-04:002006-10-02T13:37:00.000-04:00Dear Stefan,now I am also confused. I also thought...Dear Stefan,<BR/><BR/>now I am also confused. I also thought the number of Casimir invariants (independent elements of the max. abelian subgroup, rank of the group) is the dimension of the diagram. The operators themselves however are not uniquely defined, since you can always redefine the base, or, change the axis in the diagram. There is a way to define the operators such that the diagrams are Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159809128111360842006-10-02T13:12:00.000-04:002006-10-02T13:12:00.000-04:00Hi bee,I completely agree :-)Hi Lubos,I also agree...Hi bee,<BR/><BR/>I completely agree :-)<BR/><BR/><BR/>Hi Lubos,<BR/><BR/>I also agree: the experimental result as such is neither cutting edge physics, nor is there the tiniest reason to doubt that the result could be anything else than what was eventually measured.<BR/><BR/>But I was quite surprised, nevertheless, that such a comparably elementary property as the spin of the Omega-Minus has not stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159805518185831782006-10-02T12:11:00.000-04:002006-10-02T12:11:00.000-04:00Dear Rob,no, that's no dumb question at all, there...Dear Rob,<BR/><BR/>no, that's no dumb question at all, there is, IMHO, quite a lot of confusing nomenclature around...<BR/><BR/>So, first of all, the multiplets of SU(N) can be uniquely described by N-1 nonnegative integers, but these are in no immeditate relation to the N-1 Casimir operators of the Cartan subalgebra, I think.<BR/><BR/>For SU(3), I have used the quite standardized notation (p,q)stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159802874545537062006-10-02T11:27:00.000-04:002006-10-02T11:27:00.000-04:00Hi Stefan, It's not that I'd doubt the spin was 3/...Hi Stefan, <BR/><BR/>It's not that I'd doubt the spin was 3/2, I just found it an interesting sociological speculation what might have happened if. Yes, they would have measured again and again. Can reality be in contradiction to what we thought all the time? I guess it would have severely traumatized a whole generation of particle physicist.<BR/><BR/>Hi Lubos,<BR/><BR/>No, it's certainly not Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159801728349105282006-10-02T11:08:00.000-04:002006-10-02T11:08:00.000-04:00Come on, Stefan.It's great if hundreds of skillful...Come on, Stefan.<BR/><BR/>It's great if hundreds of skillful people have well-defined tasks to do so that experimental physics is kept in good shape but I am sure that every reasonable member of the collaboration knows that this is not a new discovery or overly interesting result, and most citations of them will likely be self-citations for some time.<BR/><BR/>How could a member of the decuplet Luboš Motlhttps://www.blogger.com/profile/17487263983247488359noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159801210394449982006-10-02T11:00:00.000-04:002006-10-02T11:00:00.000-04:00Dear Thomas, dear Stefan:Thanks so much for your a...Dear Thomas, dear Stefan:<BR/><BR/>Thanks so much for your answers. In the danger of appearing even more dumb, I still don't completely understand it. I know that the group SU(N) has N-1 Casimir Operators. In my understanding the quantum numbers belonging to these operators are needed to uniquely specify the multiplet. <A HREF="http://pdg.lbl.gov/2006/reviews/youngrpp.pdf" REL="nofollow">Thats Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159796429508667322006-10-02T09:40:00.000-04:002006-10-02T09:40:00.000-04:00Hi Paul,thanks fo the links to the news BECs... Al...Hi Paul,<BR/><BR/><BR/>thanks fo the links to the news BECs... All this is a bit off-topic here, but just two comments:<BR/><BR/><I>BEC is forbidden only in two dimensions for an infinite system without disorder.</I><BR/><BR/>I guess they are alluding to the <A HREF="http://en.wikipedia.org/wiki/Mermin-Wagner_theorem" REL="nofollow">Mermin-Wagner-Hohenberg theorem</A>, which states that there is stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159794509823157572006-10-02T09:08:00.000-04:002006-10-02T09:08:00.000-04:00Hi Thomas,thanky you for your answer! Hi Rob, yes,...Hi Thomas,<BR/><BR/>thanky you for your answer! <BR/><BR/>Hi Rob, <BR/><BR/>yes, as Thomas has explained, the multiplets of SU(N) can be drawn in N-1 dimensions. Physically speaking, this means that if an interaction Hamiltonian has SU(N) symmetry, there are N-1 conserved quantum numbers, which are plotted along the N-1 axis of the multiplet diagrams. For the strong interactions, its isospin forstefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159792718374868682006-10-02T08:38:00.000-04:002006-10-02T08:38:00.000-04:00Dear bee,What do you think would have happend if t...Dear bee,<BR/><BR/><I>What do you think would have happend if they had measured a spin 1?</I> <BR/><BR/>I really do not know. Probably they would have checked again everything, and again, and again...<BR/><BR/>I cannot think of any explanation of spin 1 that would be possible within the quark model. Even if you consider possible contributions to spin through angular momentum or glue, it's not stefanhttps://www.blogger.com/profile/09495628046446378453noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159790119480640522006-10-02T07:55:00.000-04:002006-10-02T07:55:00.000-04:00question:> What do these multiplet diagrams look >...question:<BR/><BR/>> What do these multiplet diagrams look <BR/>> like for SU(N) groups with N>3? Are <BR/>> they higher dimensional? <BR/><BR/>--- good question!<BR/><BR/>It is convenient for us that the largest group (to be more precise, Lie algebra) that is so far compulsory to understand particle physics has rank 2, which means that its representations can be drawn on a two-dimensional Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159729275895904532006-10-01T15:01:00.000-04:002006-10-01T15:01:00.000-04:00Dear Stefan: This is an interesting story. What do...Dear Stefan: <BR/><BR/>This is an interesting story. What do these multiplet diagrams look like for SU(N) groups with N>3? Are they higher dimensional? Sorry for the dumb question. Yours,<BR/><BR/>RobAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159726815975987382006-10-01T14:20:00.000-04:002006-10-01T14:20:00.000-04:00Stefan, another great post!This:http://physicsweb....Stefan, another great post!<BR/><BR/>This:<BR/>http://physicsweb.org/articles/news/10/9/16<BR/><BR/>Thus:<BR/>http://blogs.nature.com/nature/peerreview/trial/2006/09/boseeinstein_condensation_of_m.html<BR/><BR/>and this:<BR/><BR/>http://en.wikipedia.org/wiki/Heat_equation<BR/><BR/>can have interesting consequences.<BR/><BR/>1-D, 2-D and 3-D factors ?<BR/><BR/>Form the first link:"But Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159700786612338782006-10-01T07:06:00.000-04:002006-10-01T07:06:00.000-04:00PS - loved Bee's previous post on microstate bhs t...PS - loved Bee's previous post on microstate bhs too.<BR/>I read all the links too, Thanks!<BR/>Just that it would not be fair for me not to expess differences of point of view, from the macroscale.<BR/><BR/>Hope you take any differences and contradictory opinions with a pinch of salt - or as constructive criticism and debate. <BR/><BR/>Hope You Are Having Fun. <BR/>Laters ...Legacy Userhttps://www.blogger.com/profile/16367376204730068104noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159700706606964302006-10-01T07:05:00.000-04:002006-10-01T07:05:00.000-04:00Hi Stefan, excellent postMost informative, laced a...Hi Stefan, excellent post<BR/>Most informative, laced and flavoured with historical facts.<BR/>Particle Physics is becoming more and more excitingLegacy Userhttps://www.blogger.com/profile/16367376204730068104noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159639323652444062006-09-30T14:02:00.000-04:002006-09-30T14:02:00.000-04:00Hi Stefan, thanks for that very informative post! ...Hi Stefan, thanks for that very informative post! What do you think would have happend if they had measured a spin 1? Best, B.Sabine Hossenfelderhttps://www.blogger.com/profile/06151209308084588985noreply@blogger.comtag:blogger.com,1999:blog-22973357.post-1159575148123988092006-09-29T20:12:00.000-04:002006-09-29T20:12:00.000-04:00The Standard Model begins massless and requires al...The Standard Model begins massless and requires almost two dozen parameter inserts (mostly particle masses) plus the Higgs mechanism. That is disturbing. Standard Model extensions are disasters of empirical absence. If the Higgs remains invisible in the LHC, what originates mass?<BR/><BR/>Is the vacuum isotropic and angular momentum thereby conserved (Noether)? A counterexample with 0.27x10^(Anonymousnoreply@blogger.com