= Theta-angle shift of a sigma-model kink charge
{title2=$Q_\theta=Q_0-\theta T/(2\pi)$}
With $\epsilon^{01}=+1$, the Noether density for the angular shift gains $\theta\partial_x\cos\phi/(4\pi)$. Its integral gives the displayed topological shift. Mechanical charge $Q_0$ determines the classical rotating-kink <energy>, while canonical symmetry charge $Q_\theta$ is conjugate to the periodic angle and is integral after quantization. Reversing the epsilon convention reverses the theta sign.
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