Theta term in a spherical sigma model
= Theta term in a spherical sigma model
{title2=$\mathcal L_\theta=-\frac{\theta}{4\pi}\epsilon^{\mu\nu}\partial_\mu\cos\phi\,\partial_\nu\alpha$}
Locally this density is a total derivative, so it changes neither the bulk field equations nor the <energy>. Its contribution to the angular <canonical momentum> is a spatial boundary derivative. With $\epsilon^{01}=+1$, it produces the <theta-angle shift of a sigma-model kink charge>.