= Skyrmion hedgehog ansatz
{c}
{title2=$U_0(\mathbf x)=\cos f(r)+i\sin f(r)\widehat{\mathbf x}\cdot\boldsymbol\sigma$}
The unit <Skyrmion> has a spherically symmetric ansatz with <Pauli matrices> $\boldsymbol\sigma$, $f(0)=\pi$ and $f(\infty)=0$. The <baryon number> is
$$
B=-\frac2\pi\int_0^\infty f'\sin^2f\,dr=1.
$$
The radial profile is obtained from the <Skyrme model> variational equation. Spatial rotations and <isospin> rotations act on the same hedgehog orientation, leaving only three independent rotational <collective coordinates>.
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