= Spinor sign under a full spatial rotation
For a <Dirac spinor> a spatial rotation acts in each chiral block by a <matrix exponential> $e^{\pm i\theta\mathbf n\cdot\boldsymbol\sigma/2}$, depending on angle orientation. Since $(\mathbf n\cdot\boldsymbol\sigma)^2=I_2$ for a unit axis, the <Pauli matrix multiplication law> gives this exponential as $\cos(\theta/2)I_2\pm i\sin(\theta/2)\mathbf n\cdot\boldsymbol\sigma$. At $\theta=2\pi$ it is $-I_2$, and at $4\pi$ it is $I_2$. A <vector> returns already at $2\pi$. This describes the lift of the rotation loop to the <Spin group>, rather than a single-valued representation of the ordinary rotation group on spinors.
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