Hi GT, I uploaded digrams at User:Tomruen/aestoe from the Dec 2010 article, and pasted your comments about them from the An exceptionally simple theory of everything talk page. As I said before, I'd like some diagrams like these added to the article, but since I'm still learning about what it all means, I'm content to wait a while, until I can better assess how the diagrams can be interelated to the existing physics and math articles on wikipedia. Hopefully when I make a new attempt at the first diagram, you can help me again sort out the uncertainties. Thanks! Tom Ruen ( talk) 02:04, 14 January 2012 (UTC)
File:Gta-3.png | Your comments: 2) This is also a correct picture. This is actually one of the most interesting pictures of all, IMHO. There are these very very nice papers, published in 2002 Exceptional Confinement in G(2) Gauge Theory http://arxiv.org/abs/hep-lat/0209093 (Journal reference: Nucl.Phys. B668 (2003) 207-236) and 2003 Confinement without a center: the exceptional group G(2) http://arxiv.org/abs/hep-lat/0302023v1 (Published in Nucl.Phys.Proc.Suppl. 119 (2003) 652-654). They not only have the same identical picture as Lisi, but they even specifically recall the weight diagrams to compare the group SU(3) and the 3 and the 3bar and their relation to SO(7) and G2 (like I was saying above). But Lisi doesn't even cite them! (of course, he thinks he's the first one to use these diagrams...) By the way, those authors all have 1000 citations or more (and the two papers together have about 60 citations, they should have been cited by Lisi). To explain: they try to use G2 and its fundamental representation 7, breaking the symmetry at a high scale, to prove how the 7 would naturally break into the 3 and the 3bar (which in their picture is natural once the bosons that move from the 3 to the 3bar become very massive). Of course it's not a TOE and their approach is different, but they even look, in their second paper, at the possibility of having G2 usually nonchiral gauginos (gluinos) as chiral fermions. Being a supersymmetric theory of course they look at the chirality issue of the gauginos and attempt a domain-wall/string-theory-like approach. This issue, far from being easy to solve, as I've been mentioning here for months, is pretty common in supersymmetric models when dealing with gauginos and their chirality. |
Thanks for those papers showing G2. I don't know enough to easily compare what they're plotting, but Lisi's 2007 paper makes it clear - 6 gluons on the outer hexagon, and 6 quark/antiquark color combinations on the inner hexagram. Are you saying these papers weight diagrams are intended represent these same particles? ALSO, the first [1] has two figures, first with a 7-dimensional fundamental representation of G(2), and second a 14-dimensional adjoint representation of G(2), with both the long and short roots of G2. Can you explain this? What is a fundamental representation? It would seem accurate to call Lisi's G3/G8 projective plane Color charge diagram - AND that a diagram like one of these deserves to be there? I also see at Gluon#Eight_gluon_colors that there are 8 gluons, while this chart only shows 6. Tom Ruen ( talk) 00:59, 15 January 2012 (UTC)
Busy couple of days, I'll try to respond tonight or tomorrow, at least briefly. ~GT~ ( talk) 04:38, 15 January 2012 (UTC)
That, in general, seems like a nice plan. So, we have a few points to figure out. First, how do we distinguish fermions (fundamental representations), from bosons (adjoint representation)? I mean, a way that is clear to a reader. The point of decomposition is quite tricky. First, we would need to see a way to indicate symmetry breaking mechanism, and secondly, it would be important to understand how to deal with the 2D, 3D projections from higher dimensional spaces. The division you mention is just a way to commonly decompose theories. Historically, because we found that the strong, the weak and the em forces are easily quantized, then we tend to group them together in GUTs before we attempt to unify them with gravity. Within the standard model group, SU(3)×SU(2)×U(1), usually we assume that the two weaker forces, the e-m and the weak force, separate from SU(3) before they separate from each other. Ultimately the only local symmetry still unbroken (that we know of) is the SU(3)c×U(1)E-M. This decomposition, though, isn't necessarily the right one. Other theories in fact have different ways of breaking a larger group into the standard model group. Usually all these decompositions include some Higgs field acquiring some vev and spontaneously break the group symmetries. Other more complex methods sometimes break supersymmetries and trigger also some other symmetry breaking... but that's not really important here. ~GT~ ( talk) 03:52, 23 January 2012 (UTC)
Hi GroupT,
You are receiving this message either because you expressed an opinion about the proposed SOPA blackout before full blackout and soft blackout were adequately differentiated, or because you expressed general support without specifying a preference. Please ensure that your voice is heard by clarifying your position accordingly.
Thank you.
Message delivered as per request on ANI. -- The Helpful Bot 16:31, 14 January 2012 (UTC)
Hi GT, I uploaded digrams at User:Tomruen/aestoe from the Dec 2010 article, and pasted your comments about them from the An exceptionally simple theory of everything talk page. As I said before, I'd like some diagrams like these added to the article, but since I'm still learning about what it all means, I'm content to wait a while, until I can better assess how the diagrams can be interelated to the existing physics and math articles on wikipedia. Hopefully when I make a new attempt at the first diagram, you can help me again sort out the uncertainties. Thanks! Tom Ruen ( talk) 02:04, 14 January 2012 (UTC)
File:Gta-3.png | Your comments: 2) This is also a correct picture. This is actually one of the most interesting pictures of all, IMHO. There are these very very nice papers, published in 2002 Exceptional Confinement in G(2) Gauge Theory http://arxiv.org/abs/hep-lat/0209093 (Journal reference: Nucl.Phys. B668 (2003) 207-236) and 2003 Confinement without a center: the exceptional group G(2) http://arxiv.org/abs/hep-lat/0302023v1 (Published in Nucl.Phys.Proc.Suppl. 119 (2003) 652-654). They not only have the same identical picture as Lisi, but they even specifically recall the weight diagrams to compare the group SU(3) and the 3 and the 3bar and their relation to SO(7) and G2 (like I was saying above). But Lisi doesn't even cite them! (of course, he thinks he's the first one to use these diagrams...) By the way, those authors all have 1000 citations or more (and the two papers together have about 60 citations, they should have been cited by Lisi). To explain: they try to use G2 and its fundamental representation 7, breaking the symmetry at a high scale, to prove how the 7 would naturally break into the 3 and the 3bar (which in their picture is natural once the bosons that move from the 3 to the 3bar become very massive). Of course it's not a TOE and their approach is different, but they even look, in their second paper, at the possibility of having G2 usually nonchiral gauginos (gluinos) as chiral fermions. Being a supersymmetric theory of course they look at the chirality issue of the gauginos and attempt a domain-wall/string-theory-like approach. This issue, far from being easy to solve, as I've been mentioning here for months, is pretty common in supersymmetric models when dealing with gauginos and their chirality. |
Thanks for those papers showing G2. I don't know enough to easily compare what they're plotting, but Lisi's 2007 paper makes it clear - 6 gluons on the outer hexagon, and 6 quark/antiquark color combinations on the inner hexagram. Are you saying these papers weight diagrams are intended represent these same particles? ALSO, the first [1] has two figures, first with a 7-dimensional fundamental representation of G(2), and second a 14-dimensional adjoint representation of G(2), with both the long and short roots of G2. Can you explain this? What is a fundamental representation? It would seem accurate to call Lisi's G3/G8 projective plane Color charge diagram - AND that a diagram like one of these deserves to be there? I also see at Gluon#Eight_gluon_colors that there are 8 gluons, while this chart only shows 6. Tom Ruen ( talk) 00:59, 15 January 2012 (UTC)
Busy couple of days, I'll try to respond tonight or tomorrow, at least briefly. ~GT~ ( talk) 04:38, 15 January 2012 (UTC)
That, in general, seems like a nice plan. So, we have a few points to figure out. First, how do we distinguish fermions (fundamental representations), from bosons (adjoint representation)? I mean, a way that is clear to a reader. The point of decomposition is quite tricky. First, we would need to see a way to indicate symmetry breaking mechanism, and secondly, it would be important to understand how to deal with the 2D, 3D projections from higher dimensional spaces. The division you mention is just a way to commonly decompose theories. Historically, because we found that the strong, the weak and the em forces are easily quantized, then we tend to group them together in GUTs before we attempt to unify them with gravity. Within the standard model group, SU(3)×SU(2)×U(1), usually we assume that the two weaker forces, the e-m and the weak force, separate from SU(3) before they separate from each other. Ultimately the only local symmetry still unbroken (that we know of) is the SU(3)c×U(1)E-M. This decomposition, though, isn't necessarily the right one. Other theories in fact have different ways of breaking a larger group into the standard model group. Usually all these decompositions include some Higgs field acquiring some vev and spontaneously break the group symmetries. Other more complex methods sometimes break supersymmetries and trigger also some other symmetry breaking... but that's not really important here. ~GT~ ( talk) 03:52, 23 January 2012 (UTC)
Hi GroupT,
You are receiving this message either because you expressed an opinion about the proposed SOPA blackout before full blackout and soft blackout were adequately differentiated, or because you expressed general support without specifying a preference. Please ensure that your voice is heard by clarifying your position accordingly.
Thank you.
Message delivered as per request on ANI. -- The Helpful Bot 16:31, 14 January 2012 (UTC)