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Old 16th February 2013, 12:47 AM   #924
lpetrich
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Join Date: Feb 2007
Posts: 762
Seems like Farsight has been extracting Great Meaning out of the 3+1 form of Maxwell's equations, and not the general-covariant form, the one where space and time dimensions are treated alike. The g-mu-nu that he sometimes mentions, that's the metric of space-time in general-covariant form.


Now to what one finds for Grand Unified Theories. It's rather remarkable that one can get all the elementary fermions into a few GUT multiplets without a lot of extra particles. The gauge and Higgs particles do get some additional ones, however, particles that can cause proton and bound-neutron decay. From proton-decay experimental bounds, these additional particles must have GUT-scale masses.

First, the gauge symmetries that are already a part of existing theories.

Macroscopic: U(1)EM
EM = electromagnetic

Low-energy Standard Model: SU(3)C * U(1)EM
C = quantum chromodynamic (QCD)
Hidden by color confinement for length scales greater than about 10^(-15) m

Unbroken Standard Model: SU(3)C * SU(2)L * U(1)Y
L = weak isospin
Y = weak hypercharge
Electroweak symmetry breaking: the last two get reduced to U(1)EM


The simplest GUT that unifies the gauge fields is Georgi-Glashow SU(5). It does so at the price of adding gauge and Higgs particles that can cause proton decay. However, the elementary fermions do not get additional particles; all the SM ones can fit into 2 multiplets per generation, with right-handed neutrinos being a third one.

The next one up is Fritzsch-Minkowski-Georgi SO(10). It adds more gauge particles, but it unifies the Higgs particles into one multiplet with no extra particles relative to SU(5). Likewise, it unifies all the elementary fermions into one multiplet per generation, with only right-handed neutrinos added.

SO(10) breaks down into SU(5) * U(1)B-L
B-L = (baryon number) - (lepton number)

From there, the next one up is E6, which breaks into SO(10) * U(1). It can unify the elementary fermions and the Higgs particles into one multiplet, with an additional Higgs singlet and two of the three sets of Higgs particles being forced up to GUT energies by symmetry breaking.
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