Rotational quantization of a unit Skyrmion ($E_j=M+j(j+1){\hslash }^2/(2\Lambda )$)

Write $U=A{U}_0{A}^{-1}$, $A\in SU(2)$, and $A^{-1}\dot{A}=i\mathbf{\omega }\cdot \mathbf{\sigma }/2$. The rotational kinetic energy is $\Lambda |\mathbf{\omega }{|}^2/2$. 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 $M+j(j+1){\hslash }^2/(2\Lambda )$; the lowest multiplets model the nucleon and Delta baryon. Large rotational energies can excite deformation and radiation, beyond the rigid approximation.