CP1 spinor representation ($C{P}^1$ spinor representation)

The CP1 spinor representation writes a unit vector as $n_i=z^{†}{\sigma }_{i}z$ with $z^{†}z=1$. The phase redundancy $z\mapsto e^{i\alpha }z$ identifies normalized spinors that represent the same point of the two-sphere.

The ferromagnetic Wess–Zumino term is the first-order kinetic term $i\kappa z^{†}\dot{z}$ in the CP1 description. A local phase change of $z$ changes it only by the total derivative $-\kappa \dot{\alpha }$.