= Vacuum-preserving symmetry of the Skyrme model
{title2=$L=R$}
The massless derivative <Skyrme model> has <chiral symmetry> $U\mapsto LUR^\dagger$. For the fixed finite-energy boundary condition $U(\infty)=1$, a transformation preserves the same vacuum exactly when $LR^\dagger=1$, or $L=R$. This leaves conjugation $U\mapsto AUA^\dagger$, the <isospin> action. Since $A$ and $-A$ act identically, its effective group is $SO(3)$. Together with spatial translations and rotations it generates the localized zero-mode orbit of a <Skyrmion>. Independent axial rotations change the massless vacuum and are not additional normalizable rigid orientation modes in that fixed-vacuum sector. A usual positive pion-mass term preserves only conjugation even before the boundary condition is imposed.
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