Garrett Lisi paper subject of Baez TWF 253

[marcus]

JB starts This Week's Finds talking about the paper Garrett just presented at the Loops '07 conference

http://math.ucr.edu/home/baez/week253.html

what the Standard Model looks like
and why steps toward unification (like Garrett's) look the way the do.

 

[josh1]

JB starts This Week's Finds talking about the paper Garrett just presented at the Loops '07 conference

http://math.ucr.edu/home/baez/week253.html

what the Standard Model looks like
and why steps toward unification (like Garrett's) look the way the do.

I wouldn`t waste too much time on Garrett's work. It's baloney

 

[garrett]

I wouldn`t waste too much time on Garrett's work. It's baloney

Ha ha ha ha ha!

Hey Josh, send your real name so I can quote you on that, rather then just attributing it to "random string theorist."

 

[garrett]

I've put up an executive summary for physicists on the Deferential Geometry welcome page:

http://deferentialgeometry.org

(The reason I'm on the net right now instead of talking to conference people is because I've come down with the flu, and I don't want to spread it. :( I need to get some sleep now so I can get better and not miss too much.

 

[arivero]

Note that Baez jumps straight to C^5; it is better to start chyral, in C^4.

 

[Chronos]

I wouldn`t waste too much time on Garrett's work. It's baloney

Agreed, you won't, but I will. What specific objections have you in mind?

 

[arivero]

I like to start from C^4 instead of C^5 because in that way the structure is very much as spacetime, signature (1,3). And 1-3= 6 mod 8

The 0, 1, 2, 3, and 4 forms (The Clifford algebra, if you prefer) are generated from a charged but uncoloured and three coloured generators:

$$\nu = .$$

$$e^+= dt$$
$$d_r = dx$$
$$d_g = dy$$
$$d_b = dz$$

$$u_r = dt \wedge dx$$
$$u_g = dt \wedge dy$$
$$u_b = dt \wedge dz$$
$$\bar u_b = dx \wedge dy$$
$$\bar u_g = dx \wedge dz$$
$$\bar u_r = dy \wedge dz$$

$$e^-= dx \wedge dy \wedge dz$$
$$\bar d_r = dt \wedge dy \wedge dz$$
$$\bar d_g = dt \wedge dx \wedge dz$$
$$\bar d_b = dt \wedge dx \wedge dy$$

$$\nu = dt \wedge dx \wedge dy \wedge dz$$

This idea is based on Unified Theories For Quarks And Leptons Based On Clifford Algebras by R. Casalbuoni (CERN) , Raoul Gatto (Geneva U.) . UGVA-DPT 1979/11-227, Nov 1979 Published in Phys.Lett.B90:81,190 and Families from Spinors by Frank Wilczek , A. Zee . Phys.Rev.D25:553,1982.

The cap product by the volume form maps particle to antiparticle, or almost. Chyrality considerations pending, a volume form seems very much as a mass term (or a higgs term)

From two copies (left and right) of it, you build the C^5 Baez is speaking about. And
it is possible to built the C^4 thing from two copies in C^3, using only the coloured generators. In that way it is very close to Harari-Shupe.

 

[arivero]

http://math.ucr.edu/home/baez/week253.html

I've put up an executive summary for physicists on the Deferential Geometry welcome page:
http://deferentialgeometry.org

Also, there are further developments of this discussion here:

http://www.math.columbia.edu/~woit/wordpress/?p=572#comment-26533
https://www.physicsforums.com/showthread.php?t=175406 (or other nntp: reader, such as http://groups.google.es/group/sci.p...read/thread/680c64423923229e/0189a3018b31fcd4 )
http://golem.ph.utexas.edu/category/2007/06/this_weeks_finds_in_mathematic_14.html

 

[arivero]

Another thought: if you want to introduce triality, it can be more reasonable to build it when you add the generators to jump from SO(6) to SO(8), or from SO(8) to SO(10). But if one waits to have SO(10) and further, then one is going to need to go backwards to see the SO(8) representations hidden under the carpet.