 Faddeev-Zamolodchikov algebra

Particle operators obey a rapidity-dependent exchange rule $A_i({\theta }_1)A_j({\theta }_2)=S_{ij}^{kl}({\theta }_1-{\theta }_2)A_l({\theta }_2)A_k({\theta }_1)$, with repeated species indices summed. A consistent associative algebra must give the same coefficients when a triple product is brought to decreasing or increasing rapidity order by either sequence of adjacent exchanges. This is the Faddeev-Zamolodchikov associativity constraint. Rapidity ordering here is distinct from the creation/annihilation convention of ordinary normal ordering.