Yang-Baxter equation ($R_{12}(u)R_{13}(u+v)R_{23}(v)=R_{23}(v)R_{13}(u+v)R_{12}(u)$)

For a two-body operator $R(u)$ acting on a tensor product of particle species spaces, the spectral equation is $R_{12}(u)R_{13}(u+v)R_{23}(v)=R_{23}(v)R_{13}(u+v)R_{12}(u)$. It guarantees agreement between the two ways to reorder three particles in factorized scattering. A Yang–Baxter operator is a related braid-form operator; multiplying by the permutation operator converts between the braided and unbraided conventions.