- #1

Anchovy

- 99

- 2

\begin{align}

\psi &= \begin{pmatrix}

\nu_{e} \\

e^{-}

\end{pmatrix}_{L}

\end{align}

[/itex] etc., we have to introduce massless gauge fields to preserve the Lagrangian's invariance. For SU(2) this demands 3 bosons referred to as [itex]W_{\mu}^{1}, W_{\mu}^{2}, W_{\mu}^{3}[/itex].

We then relate the gauge bosons [itex]W_{\mu}^{1}, W_{\mu}^{2}[/itex] with the particles we actually observed which are [itex]W^{+}, W^{-}[/itex] (for now ignoring the photon, [itex]Z^{0}[/itex] and the U(1) hypercharge gauge boson [itex]B_{\mu}^{0}[/itex], and the whole [itex]W^{+}, W^{-}, Z^{0}[/itex] Higgs mechanism mass aspect of the story).

In all the texts I'm reading the author just simply defines the [itex]W^{+}, W^{-}[/itex] as the following mixtures of [itex]W_{\mu}^{1}, W_{\mu}^{2}[/itex]:

[itex]W^{+} = \frac{1}{\sqrt{2}} (W_{\mu}^{1} - W_{\mu}^{2})[/itex]

[itex]W^{-} = \frac{1}{\sqrt{2}} (W_{\mu}^{1} + W_{\mu}^{2})[/itex]

However, the texts never give any mention of charges of the [itex]W_{\mu}^{1}, W_{\mu}^{2}, W_{\mu}^{3}[/itex] so I assume them to be neutral --> it's not clear to me why mixtures of them result in charged bosons?