# What electric charges do the $SU(2)$ weak isospin bosons carry?

The $SU(2)$ weak isospin group has three bosons, before symmetry breaking: The $W^1$, $W^2$, and $W^3$ weak isospin bosons.

The $W^1$ and $W^2$ mix to form the $W^+$ and $W^-$ bosons with electric charges $+1$ and $-1$, respectively.

So far, I can assume that the $W^3$ boson carries a neutral charge. However, I am not sure what the electric charges (which are somewhat present before the photon exists) of the $SU(2)$ triplet bosons ($W^1$, $W^2$, and $W^3$) are.

According to Wikipedia, the $SU(2)$ triplet bosons form a Weak Isospin triplet (so one boson has Weak Isospin $+1$, another one has $-1$, and the last one has 0). Also, the formula for electric charge is $Q=T_3+\frac12 Y_w$.

$W^1,W^2$ do not have well defined electric charge. They are not charge eigenstates: \begin{aligned} Q|W^1\rangle&=+i|W^2\rangle\\ Q|W^2\rangle&=-i|W^1\rangle \end{aligned}
On the other hand, $W^\pm\propto W^1\pm iW^2$ do have well-defined charge: $$Q|W^\pm\rangle=\pm |W^\pm\rangle$$
• $W^\pm$ has $T_3=\pm1$, and $W^3$ has $T_3=0$. They all have zero hypercharge. – AccidentalFourierTransform Dec 19 '16 at 21:11
• $W^\pm$ don't have well defined isospin, but their hypercharge is zero. – AccidentalFourierTransform Dec 19 '16 at 21:16
• $W^\pm$ or $W^{1,2}$? – fuenfundachtzig Feb 9 '17 at 13:57
• @fuenfundachtzig ah, yes. I meant $W^{1,2}$. Thanks! – AccidentalFourierTransform Feb 9 '17 at 13:59