Download - Grand Unification
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Leptons as a fourth color?
lepton number as fourth color?
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ddde
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ddde
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numberleptonL
numberbaryonB
LBTTQ RLEM
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133
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SU(3)xSU(2)xU(1) < SU(5)(Georgi, Glashow, 1974)
SU(3)xSU(2)xU(1) < SO(10)(Fritzsch, Minkowski, 1975 )
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SU(3) x SU(2) x U(1) < SU(5)
fermions of one family in
two different representations:
)5()10(
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e
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5 )()10( e
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guburu
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Gauge bosons in SU(5) > SU(2) x U(1):
adjoint representation ~ (24)
5 x 5* = 24 + 1
24 = (8,1) + (1,3) + (1,1) + (3,2) + (3*,2)
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Grand unification takes placeabove a very high unified mass scale M.Above this energy there is only one unified coupling constant g. The coupling constants for QCD and for the SU(2) x U(1) theory are the same, apart from Clebsch-Gordan coefficients.
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The rather different values
of the three coupling constants at low energies are due to renormalization effects.
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No convergence of coupling constants
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1)( i
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convergence in case of
supersymmetry
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Grand unification
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SU(3) x SU(2) x U(1) < SU(4) x SU(2,L) x SU(2,R)
~ SO(6) x SO(4)
=> SO(10)
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Representations of SO(10):16-dimensional spinor representation( => Pauli spinor ~ SO(3) )
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SO(10)
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ee uuuuuu ::: edddddde :::
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SO(10):due to the two intermediate energy scales there is no problem with the convergence of the coupling constants at the grand unified mass scale