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My understanding is that QCD has three color charges that are conserved as a result of global SU(3) invariance. What about SU(2) weak? Does it have two types of charges? What I'm getting at is:

U(1) --> 1 type of charge

SU(2) --> ?

SU(3) --> 3 types of charge

Does SU(2) have two types? If not, what is the relation between SU(N) invariance and the number of charge types?

Idea: Maybe both I and I_3 (weak isospin and its third component) are conserved before electroweak symmetry breaking? Is that true? If so, then that would answer my question.

user1247
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@Michael Brown is right. The SM has 12 exactly conserved currents.

  • All local invariances, a fortiori also imply global invariances, if you ignore (for the sake of argument) the spacetime variability of transformation parameters/angles. So SU(3) has 8, not 3 conserved charges, RG, BG, .... The group has 8 generators. Likewise, SU(2) has 3, not 2 conserved currents: you know this from spin, where each of the 3 projections of a rotationally invariant system is conserved. U(1) has one conserved charge.

  • SSB does not affect the number of conserved currents, in sharp contrast to explicit symmetry breaking: The currents are still conserved, except they have a special nonlinear form (their leading term is linear, not bilinear in the fields, so the corresponding charges shift the fields "nonlinearly"). The symmetry is hidden, and much less apparent, but it is still there, which is why these symmetries are so powerful: they control systematically the divergences of the corresponding QFT. (Actually, though, the 3 charges corresponding to the 3 broken generators are ill-defined/divergent themselves, although their corresponding currents are conserved: the symmetry is still there.)

  • There are further approximate symmetries in the SM, meaning that their charges are violated by a "small" amount (a technical characterization), or even quantum anomalies (collective quantum action of the Dirac sea of fermions coupling chirally to them).

    Further see 149324

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Cosmas Zachos
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