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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# I Charges in SU(2) gauge QFT

Have something to add?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**