Neumann's principle
= Neumann's principle
{c}
A physical property <tensor> must be invariant under every symmetry operation of the material's <point group>. For a polar rank-$r$ <tensor>, $T_{i_1\ldots i_r}=R_{i_1j_1}\cdots R_{i_rj_r}T_{j_1\ldots j_r}$. 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>.