= Massless limit of a transverse canonical-spin label
{title2=$u_x=\sqrt E(0,1,1,0)^T$}
Boost a massive rest <Dirac spinor> labelled by $\xi=(1,1)^T/\sqrt2$ along the third axis and take its <massless limit>. In the <Weyl representation> the result is the displayed equal superposition of helicities, not an eigenvector of the fixed transverse rotation generator $\Sigma_1/2$. For momentum $(E,0,0,E)$ the positive-energy Hamiltonian is $E\gamma^0\gamma^3$, which anticommutes with $\Sigma_1=\operatorname{diag}(\sigma_1,\sigma_1)$. A nonzero positive-energy solution cannot also be a $\Sigma_1$ eigenvector. Thus a transported canonical spin label must be distinguished from literal transverse spin at zero mass; longitudinal <helicity> remains a good quantum number.
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