Wess–Zumino term

For a spin coherent-state history, a Wess--Zumino term records the oriented target-sphere area bounded by the spin path. Its variation is local even though a single gauge-patch expression for the area need not be global.

In a bipartite antiferromagnet, the smooth staggered contributions to the spin Wess--Zumino terms cancel between sublattices. Their term linear in uniform canting is proportional to $\mathbf{m}\cdot (\mathbf{n}\times {\partial }_t\mathbf{n})$.