= Collective-rotation constraints for a Skyrmion
{title2=$\widehat D^J(R)\widehat D^I(A)\Psi=\chi_{\rm FR}\Psi$}
A rigid <Skyrmion> orientation is quantized on a cover of its <Skyrmion collective-coordinate orbit>. A lifted combined rotation in the static field's <stabilizer subgroup> identifies the same classical field and imposes $\widehat D^J(R)\widehat D^I(A)\Psi=\chi_{\rm FR}\Psi$, where the sign is the chosen <Finkelstein-Rubinstein constraints> character of that configuration-space loop. Choosing the nontrivial character models unit baryons as fermions. A $2\pi$ spatial rotation or <isorotation> of charge $B$ then has sign $(-1)^B$: deforming the field to separated unit lumps adds the unit-lump loop classes in the <fundamental group> $\mathbb Z_2$, while the labelled orbital paths can be contracted in three dimensions. The resulting <Finkelstein-Rubinstein constraints> sign is the product of the unit-lump signs. Hence spin and <isospin> are half-integer for odd $B$ and integer for even $B$. Further stabilizer constraints restrict which pairs $(J,I)$ and which body-fixed states occur. The <energy> operator comes from the <inertia tensors> on the orbit; symmetry selects allowed states but does not by itself determine their energies. A bosonic choice of the trivial topological character is mathematically possible but does not model a fermionic <nucleon>.
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