Landau-Yang theorem

A massive spin-one state cannot decay into two identical on-shell photons. In their centre-of-momentum frame, opposite photon helicities have helicity difference two and require $J\ge 2$. Equal helicities have difference zero; exchanging the two identical bosons multiplies their total-angular momentum wave by $(-1{)}^J$, so Bose-Einstein statistics requires even $J$. Neither case permits $J=1$. The on-shell and identical-particle assumptions are essential; the theorem does not exclude a decay with one virtual photon.