Why Are Quarks and Leptons Grouped in the Antisymmetric Representation of SU(5)?

[Sombrero]

Dear PF,

I have very simple question, it is due to my poor understanding of group theory. WhY in antisymmetric 5*5 representation of SU(5) (there are 10 states) one puts quarks and leptons, since having product of two SU(5) fundamental representations we get a composed antisymmetric ten states. So they are composed ten states built from fundamentals of SU (5), but assigned to simply quarks and leptons.

If I express my question not properly pls tell me and Ill be more specific.

Thanks very much

 

[Sombrero]

Not "correct" question... :(

 

[Haelfix]

I can't quite make out what's bothering you.
Let me review the model quickly

The vector bosons are in the adjoint 24, and the fermions are in two irreps which are the conjugate fundamental 5(bar) and the antisymmetric 10. Their is a 24 whith Higgs bosons that give masses to the unseen vector bosons, only one of of these Higgs having a nonzero VEV. There is also a 5 of higgs bosons that break the model down to the standard model (with the correct branching ratios).

Why not stick the particles in a fundamental 15 instead of 5bar and 10? Answer, such a model would be nonchiral, so its ruled out.

For a fairly brief intro with the right matrices for this GUT check out John Baez's summary (which I always found very readable)

http://math.ucr.edu/home/baez/week119.html

 

[john baez]

For a fairly brief intro with the right matrices for this GUT check out John Baez's summary (which I always found very readable)

http://math.ucr.edu/home/baez/week119.html"

I'm glad you liked it. I also wrote up a longer treatment of the SU(5) GUT for a course I taught:

http://math.ucr.edu/home/baez/qg-spring2003/"

People often underestimate the beauty of how the fermions can be described in this GUT; I tried to fix that. Zee's book Quantum Field Theory in a Nutshell also came out in 2003, and it treats this GUT very nicely.