= Derrick dimension test for the Skyrme model
{c}
{title2=$E(L)=L^{d-2}E_2+L^{d-4}E_4$}
For a spatially dilated <Skyrme model> field $U_L(x)=U(x/L)$, the quadratic and quartic derivative energies scale as shown. A static stationary field must satisfy $(d-2)E_2+(d-4)E_4=0$. In three spatial dimensions this permits $E_2=E_4$ and a positive second variation along scale. In two dimensions it requires $E_4=0$, and in four or more it forces a constant finite-energy smooth field. In one dimension the commutator term vanishes identically. <Derrick scaling> tests a necessary variational condition, not existence or stability under all deformations.
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