Neumann's principle

A physical property tensor must be invariant under every symmetry operation of the material's point group. For a polar rank-$r$ tensor, $T_{i_1\dots i_r}=R_{i_1{j}_1}\cdots R_{i_r{j}_r}{T}_{j_1\dots j_r}$. Taking $R=-I$ proves that an odd-rank polar tensor vanishes in a centrosymmetric material. A susceptibility of order $n$ has rank $n+1$, so local bulk even-order electric-dipole response is forbidden there. The name refers to Franz Ernst Neumann.