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Every term in the free energy contracts the vector components with the Euclidean inner product: it depends only on $|\mathbf{p}{|}^2$, $|\mathbf{p}{|}^4$, $({\nabla }_i{p}_j)({\nabla }_i{p}_j)$, and $|{\nabla }^2\mathbf{p}{|}^2$. A constant $\mathcal{R}\in SO(3)$ preserves all these contractions and commutes with spatial differentiation. Thereforeso every constant rotation of candidate (ii) has the same free energy. The orientation of the rotation plane of the polar helical smectic is thus continuously degenerate.

A polar helical smectic has a vector order parameter of constant magnitude whose direction rotates at a nonzero wavevector. For an isotropic Brazovskii free energy, all constant rotations of the helical plane are degenerate until a longitudinal-gradient term such as $|\nabla \cdot \mathbf{p}{|}^2$ selects its orientation.