= Triplet charged-current closure on electromagnetic charge
{title2=$[T^+,T^-]=4Q_\ell/e$}
For normalized triplets $(E^+,n,e)_L$ and $(E^+,N,e)_R$, let the raising matrix have ones in entries $(1,2)$ and $(2,3)$. Its commutator with its adjoint is $\operatorname{diag}(1,0,-1)$. Neutral mixing in $n=c_\alpha\nu+s_\alpha N$ leaves this result unchanged because $c_\alpha^2+s_\alpha^2=1$. With current normalization using $1\mp\gamma^5=2P_{L,R}$, <fermionic bilinear charge algebra> gives the displayed proportionality to the leptonic <electric charge> $Q_\ell=e\int:(E^{+\dagger}E^+-e^\dagger e):$. Other current normalizations change the numerical prefactor, not closure. Equal-time algebra does not itself imply conservation of a fermionic weak charge in a symmetry-broken theory.
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