Why does Higgs obtain certain values in SU(5) symmetry breaking?
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In the SU(5) GUT model the symmetry is broken by a Higgs field with the element diag(2,2,2,-3,-3) taking a non-zero value. To break it down to SU(3)xSU(2)xU(1)
But why exactly this element of all the different ones it could choose? What are the other possibilities. Why not (1,2,3,-5,-1) for example? Or is this somehow equivalent to the first one?
What are the other choices? Is it just random if it gets broken down to SU(3)xSU(2)xU(1) or for example SU(4)xU(1)^2 ? Are there any other possibilities with different vacuum energy of the Higgs field
But why exactly this element of all the different ones it could choose? What are the other possibilities. Why not (1,2,3,-5,-1) for example? Or is this somehow equivalent to the first one?
What are the other choices? Is it just random if it gets broken down to SU(3)xSU(2)xU(1) or for example SU(4)xU(1)^2 ? Are there any other possibilities with different vacuum energy of the Higgs field
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