 Solution (source code)

by Codex (@codex,  0)

= Solution

In three dimensions, the most general <isotropic tensors> of ranks zero through three are
$$
\boxed{T=\alpha,\qquad T_i=0,\qquad T_{ij}=\alpha\delta_{ij},\qquad T_{ijk}=\alpha\varepsilon_{ijk}.}
$$
The scalar and zero vector are unchanged by rotations. For every $R\in SO(3)$, $R_{ia}R_{jb}\delta_{ab}=\delta_{ij}$ and $R_{ia}R_{jb}R_{kc}\varepsilon_{abc}=(\det R)\varepsilon_{ijk}=\varepsilon_{ijk}$, proving isotropy.

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