Spin coherent state

A spin coherent state is obtained by rotating the maximal-weight state $|s,s⟩$ so that it is an eigenstate of spin along a chosen direction with eigenvalue $s\hslash$.

A spin coherent-state path integral inserts group-averaged resolutions of the identity between short time steps. Its kinetic term is the Spin coherent-state Berry phase, equal to $S$ times the oriented solid angle swept on the sphere.

At azimuth $\phi$, the normalized spin-$3/2$ coherent-state components are proportional to $1,\sqrt{3}{e}^{i\phi },\sqrt{3}{e}^{2i\phi },e^{3i\phi }$.

Under $H=-\gamma B{S}_z$, a coherent spin direction precesses around the $z$-axis with angular velocity $-\gamma B$.

The propagator $e^{i\gamma Bt{S}_z/\hslash }$ multiplies each magnetic component $|s,m⟩$ by $e^{im\gamma Bt}$.