= Rotational quantization of a unit Skyrmion
{title2=$E_j=M+j(j+1)\hbar^2/(2\Lambda)$}
Write $U=A U_0 A^{-1}$, $A\in SU(2)$, and $A^{-1}\dot A=i\boldsymbol\omega\cdot\boldsymbol\sigma/2$. The rotational kinetic energy is $\Lambda|\boldsymbol\omega|^2/2$. Since $A$ and $-A$ give the same classical field, the physical orientation space is $SO(3)$, covered by $SU(2)$. For fermionic unit baryons the <Finkelstein-Rubinstein constraints> require $\Psi(-A)=-\Psi(A)$. The <SU(2) representations> then give half-integer $j$, with <spin angular momentum> and <isospin> both of magnitude $j$. The rigid-rotor energies are $M+j(j+1)\hbar^2/(2\Lambda)$; the lowest multiplets model the <nucleon> and <Delta baryon>. Large rotational energies can excite deformation and radiation, beyond the rigid approximation.
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