= Polar-frame parallel spinor
{title2=$\epsilon(\phi)=e^{\phi\gamma^1\gamma^2/2}\epsilon_0$}
In flat three-dimensional spacetime with polar spatial <orthonormal coframe> $(dT,d\rho,\rho d\phi)$, the <spin connection> has $\omega_{12}=-d\phi$. Thus every <parallel spinor> has the displayed components. Since $(\gamma^1\gamma^2)^2=-1$, these components change sign under $\phi\mapsto\phi+2\pi$. This is the lift of a full rotation to the <spin structure> extending over the disk; the polar frame itself does not extend over the origin. In a Cartesian frame the same <parallel spinors> have constant components.
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