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the_standard_model [2017/12/06 09:33]
127.0.0.1 external edit
the_standard_model [2018/02/15 08:00] (current)
jakobadmin
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 <​blockquote>​ <​blockquote>​
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 There are thirteen connected Lie groups'​ with the There are thirteen connected Lie groups'​ with the
 same Lie algebra as $SU(3)\times SU(2) \times U(1)$. [...] We can eliminate choices 1—4 by demanding that the gauge group be compact. Choices 9—13 may be removed from consideration by using the fact that the true non Abelian group of the quarks and leptons in the standard model is $SU(3) \times SU(2)$, since color triplet and weak doublet representations exist in nature.Note that the simply connected universal covering group of all 13 groups above is $SU(3) \times ​ SU(2)  \times R$, while $SU(3) ​ \times SU(2)   ​\times U(1)$ is the covering group for groups 5—13. As discussed previously by O'​Raifeartaigh,​ there then remain four possible true symmetry groups for the standard model: same Lie algebra as $SU(3)\times SU(2) \times U(1)$. [...] We can eliminate choices 1—4 by demanding that the gauge group be compact. Choices 9—13 may be removed from consideration by using the fact that the true non Abelian group of the quarks and leptons in the standard model is $SU(3) \times SU(2)$, since color triplet and weak doublet representations exist in nature.Note that the simply connected universal covering group of all 13 groups above is $SU(3) \times ​ SU(2)  \times R$, while $SU(3) ​ \times SU(2)   ​\times U(1)$ is the covering group for groups 5—13. As discussed previously by O'​Raifeartaigh,​ there then remain four possible true symmetry groups for the standard model:
the_standard_model.txt · Last modified: 2018/02/15 08:00 by jakobadmin