= O3 nonlinear sigma model
{c}
{title2=$O(3)$ nonlinear sigma model}
= CP1 nonlinear sigma model
{c}
{synonym}
In two spatial dimensions, a unit-vector field $\mathbf n:\mathbb R^2\to S^2$ has static energy $E=\int|\nabla\mathbf n|^2d^2x/2$. The sphere is also the <complex projective line>, so its <stereographic projection> gives the equivalent complex field description. A constant value at spatial infinity compactifies a regular configuration to a map $S^2\to S^2$, whose <degree of a map between oriented manifolds> is its <topological charge>.
Back to article page
