In QCD, quark is in fundamental representation of SU(3) and thus it has to have 3 charges (what we came to call "colors"). Gauge bosons are in adjoint representation and there are 8 of them. The choice how to assign color charges to them is not unique, one popular choice is based on Gell-Mann matrices. Wiki has a good layman explanation: https://en.wikipedia.org/wiki/Gluon(adsbygoogle = window.adsbygoogle || []).push({});

Naively, I would expect that in SU(2) gauge theory, fermions are in its fundamental representation and thus have to have 2 charges. And it is "sort of" true - in SM, the "up" and "down" labels for quarks are basically those charges (and for leptons too: charged leptons carry "down" charge, neutrinos are "ups").

There are 3 gauge bosons in (unbroken) SU(2): W1, W2 and W3.

Is it possible to assign these charges, call them "flavor charges", to W1/2/3 bosons (say, based on Pauli matrices, analogously to gluons' colors)? Like this:

##(u\bar{d}+d\bar{u})/\sqrt{2}##

##-i(u\bar{d}-d\bar{u})/\sqrt{2}##

##(u\bar{u}-d\bar{d})/\sqrt{2}##

But when SU(2) gauge symmetry is mentioned in SM, this is never written like this. Somehow it simplifies to a single charge, weak isospin. This part I don't understand. How does it work?

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# I Charges in SU(2) gauge QFT

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