= Conformal rescaling of a parallel spinor to a twistor spinor
{title2=$\epsilon=\Omega^{1/2}\epsilon_0$}
In the conformal frame for $g=\Omega^2\eta$, identify the spinor fibres using the chosen <vierbein>. If $\epsilon_0$ is a flat constant <spinor field>, the <spin connection of a conformally flat metric> gives $\nabla_a\epsilon=\widehat\gamma_a\widehat\gamma^c(\partial_c\log\Omega)\epsilon/2$. Contracting with curved $\gamma^a=\Omega^{-1}\widehat\gamma^a$ yields $\gamma^a\nabla_a\epsilon=n\Omega^{-1}\widehat\gamma^c(\partial_c\log\Omega)\epsilon/2$. Thus $\nabla_a\epsilon=\gamma_a\gamma^b\nabla_b\epsilon/n$: the rescaled parallel spinor is a <twistor spinor>.
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