Arcadian Functor

occasional meanderings in physics' brave new world

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Marni D. Sheppeard

Wednesday, November 14, 2007

M Theory Lesson 122

Speaking of Garrett Lisi's paper, recall the pretty picture from lesson 119. This picture turns up on slide number 30 from Garrett's recent talk (slides here).

Lisi points out that in this picture we see the 27 elements of the exceptional Jordan algebra, converging for each color and anti-color. The central cluster of leptons and gauge fields are the 72 roots of the E6 subgroup of E8. It is also interesting that Lisi links the Dark Force directly to the fairy field.


Blogger L. Riofrio said...

It is very promising that Garrett Lisi's work is now getting discussed and restored on arxiv. It gives hope, for new ideas should be judged on their merits. I would love to interview him sometime.

November 15, 2007 9:41 AM  
Blogger CarlBrannen said...

The 3x3 matrices of Feynman diagrams I am using (in Koide calculations and also in the non perturbative calculations in dmfound.pdf) also treat the diagonal and off diagonal elements in an unusual way. The diagonal elements are the fermion propagators. The off diagonal elements are the propagators interrupted by a gauge boson interaction.

A basic problem in writing a simple and consistent foundation for particle physics is that you have to find a way of representing both fermions and bosons in the same structure. Of these, the most critical are the fermions, as you can always suppose that the bosons are composites made from fermions.

To characterize a gauge boson, you can name what it does to a fermion. For instance, a red anti-blue gluon converts a blue quark to a red quark. So it's representation in the fermions is arranged by taking a product of two quarks, a red quark and a blue antiquark. To get this to work you have to arrange for the colors to not annihilate, which is another justification for the "snuark algebra".

Taking the analogy to my 3x3 matrices of Feynman diagrams (which uses snuark algebra), you end up with the diagonal elements as fermions and the off diagonal elements as bosons. This is not how Garrett mixes fermions and bosons, but I wonder if there is a connection.

A sort of loose connection would have the octonions represent the gauge bosons, and simpler elements of the group representing the fermions.

In the exceptional Jordan algebra, the diagonal elements are real and the off diagonal elements are octonions.

November 15, 2007 4:55 PM  

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