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John G
#56
Dec8-07, 06:32 PM
P: 24
Garrett, hi, that Baez link mentioned earlier is actually a link in your paper (apparently four brilliant minds thinking alike (you, Baez, Tits & kneemo and actually a 5th since I think Baez originally got Tits' idea via Tony Smith). You mentioned your E8 idea in simpler form is kind of an F4 one (with real vectors/spinors), and as you mention in your paper you make complex vectors/spinors via E6 and it seems what you get by going up to E8 is a big Jordan Algebra. That big Jordan algebra along with your MacDowell-Mansouri gravity and your D4xD4 bosons are three really interesting things that justify the hype for me and should hopefully stay no matter what you have to change as far as fermions are concerned. Smolin wrote about a big Jordan Algebra for string theory:

http://xxx.lanl.gov/abs/hep-th/0104050

and I know Tony Smith like it for string theory/spin foam too (and Smolin certainly likes spin foam-type models). Smith and Ark Jadczyk are the two physicists I've read about the most. Ark isn't in to Jordan Algebras but he is in to Clifford Algebra and Dirac Gammas and Tony I know can talk about an E8 model using Gammas instead of Jordan Algebra so in my mind string theory, spin foams, Jordan Algebra, and Dirac Gammas are all kind of related and found in E8 above E6. You seem to be using Jordan Algebra in a spin foam sense too, is that true?

That D4xD4 for bosons is something I've never seen before. Cause of your use of D4xD4, Tony Smith actually added a way of looking at his model in a D4XD4 way so now I've got not only your model but a new version of Tony's to try and learn the best I can (thanks I think). I think I really like the use of D4xD4 though perhaps not for the reason you use it. It seems like even though you only have a 4-dim spacetime that extra D4 kind of creates an extra 4-dim spacetime. Tony actually has an 8-dim spacetime but I don't fully understand yet his D4xD4 (or yours) as well as I understand Tony's version using only one D4. Anyways thank you very very much for making this kind of stuff more mainstream, mainstream physics no longer seems so depressing to me!!!