Prove that the generators (left(tau_{1}, tau_{2}, K ight)) of Eq. (19.17) for the local (mathrm{SU}(2)_{mathrm{w}} times mathrm{U}(1)_{y})

Prove that the generators \(\left(\tau_{1}, \tau_{2}, K\right)\) of Eq. (19.17) for the local \(\mathrm{SU}(2)_{\mathrm{w}} \times \mathrm{U}(1)_{y}\) standard electroweak symmetry annihilate the vacuum state but that the charge generator \(Q\) does not.

Data from Eq. 19.17

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K 0 91 = (1 1) 12 = ( ; 0 ) = ( 4 ) 2 = (60) > 0-1