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==O(3) non-linear sigma model==
A celebrated example, of particular interest due to its topological properties, is the ''O(3)'' nonlinear {{mvar|σ}}-model in 1 +
:<math>\mathcal L= \tfrac{1}{2}\ \partial^\mu \hat n \cdot\partial_\mu \hat n </math>
where ''n̂''=(''n<sub>1</sub>, n<sub>2</sub>, n<sub>3</sub>'') with the constraint ''n̂''⋅''n̂''=1 and {{mvar|μ}}=1,2.
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Since the ''n̂''-field lives on a sphere as well, the mapping {{math|''S<sup>2</sup>→ S<sup>2</sup>''}} is in evidence, the solutions of which are classified by the second [[homotopy group]] of a 2-sphere: These solutions are called the O(3) [[Instantons]].
This model can also be considered in 1+2 dimensions, where the topology now comes only from the spatial slices. These are modelled as R^2 with a point at infinity, and hence have the same topology as the O(3) instantons in 1+1 dimensions. They are called sigma model lumps.
==See also==
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