B Unified Quantum Field: Is it Possible?

[Dukon]

Wikipedia says that Glashow graduated from Cornell in 1954 (before 1957 parity violation) and received his PhD from Harvard in 1959 (after parity violation). AFAIRecall the topic for Glashow's dissertation was supplied by Schwinger to extend the then familiar U(1) gauge symmetry which generates electromagnetism to now perform the more complicated version of this calculation for SU(2) symmetry. (Motivated by the 1954 Yang-Mills models then recently proposed?) If this work was completed in 1959 it was then a few years later in 1961 when Glashow proposed SU(2)xU(1) to which Weinberg later added the Higgs mechanism (1964) to arrive at the 1967 model cited today.

Performing this same gauge symmetry calculation for the SU(3) group delivers QCD and the 8 gluon (performed by others Gell-Mann?)

 

[PeterDonis]

The U(1) of electromagnetism is still there. It's sitting diagonally inside SU(2).

I don't think this is quite correct. It is true that the U(1) in SU(2) x U(1) (the electroweak gauge group) is not the U(1) of electromagnetism, it's hypercharge. But the U(1) of electromagnetism is not "inside" the electroweak SU(2) (which is weak isospin). It's a combination of part of weak isospin and part of hypercharge.

 

[David Neves]

Peter Donis is right. That would be more accurate. I was just trying to respond to his post

https://www.physicsforums.com/threads/unified-quantum-field.911768/#post-5743470

where he wrote

"The Standard Model is based on the gauge group SU3 x SU2 x U1. Thinking of three "forces" identifies each term in this tensor product as a "force": SU3 is "strong", SU2 is "weak", U1 is "electromagnetic"."

 

[PeterDonis]

I was just trying to respond to his post

Yes, you're right, I was being sloppy in that post. It should really be "SU3 is strong, SU2 is weak isospin, U1 is weak hypercharge", at least if we talk about the fundamental Lagrangian before electroweak symmetry breaking. After electroweak symmetry breaking we have a more complicated situation, where we have two charged weak gauge bosons that take up two of the SU2 degrees of freedom, and a neutral weak gauge boson and electromagnetic gauge boson (the photon) that are each linear combinations of the remaining SU2 degree of freedom and the U1 hypercharge degree of freedom.