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Why is electroweak grouped together?

  1. Jul 7, 2009 #1

    BWV

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    If I understand the standard model correctly (a big assumption)

    you have

    electromagnetism - U(1) symmetry mediated by the photon
    weak interaction - SU(2) symmetry mediated by the W+- & Z bosons
    strong interaction - SU(3) symmetry mediated by gluons

    is there any reason to view electromagnetism and the weak interaction tied together more than any other combination of the three forces there?
     
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  3. Jul 7, 2009 #2

    malawi_glenn

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    yes there is a good reason -> it works ;-)

    See http://arxiv.org/abs/0705.4264 which are very good lecture notes on this topic.

    One "can" tie all three forces together in SU(5) (GUT)

    The basic observation, which lead one to think about a U(1)xSU(2) unification was that Left and Right handed fermions and antifermions interact different in weak SU(2) interactions (no right handed neutrinos for instance).
     
    Last edited: Jul 7, 2009
  4. Jul 7, 2009 #3

    blechman

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    also, the "U(1)" in the SM gauge group is NOT electromagnetism - it is the "weak hypercharge". so in fact, a better thing to say is:

    SU(2) x U(1) == electroweak interactions mediated by W, Z, photon
    SU(3) == strong interactions mediated by gluons

    When SU(2) x U(1) is spontaneously broken by the Higgs, it breaks to the U(1) electromagnetism which is a COMBINATION of two U(1)'s - the hypercharge and also a subgroup of the SU(2).
     
  5. Jul 7, 2009 #4

    malawi_glenn

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    All SU(N) groups have a U(1) subgroup, correct me if I am wrong
     
  6. Jul 7, 2009 #5

    blechman

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    i do not correct you. in fact, they have N-1 such subgroups.
     
  7. Jul 7, 2009 #6

    nrqed

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    Which is equivalent to saying that the rank of SU(N) is N-1 (unless I am mistaken)
     
  8. Jul 7, 2009 #7

    blechman

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    quite so. each cartan generator generates a U(1) subgroup.
     
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