Exact S-matrices for anomaly-free non-linear sigma models on symmetric spaces

The existence of a conserved quantum non-local charge is used to prove the factorization equations for the two-body S-matrix pertaining to the following five classical series of non-linear σ models on symmetric spaces: SU(N) (A), SO(N) (BD), Sp(N) (C), SU(N)/SO(N) (AI) and SU(2N)/Sp(N) (AII). For the last two cases, this proof is new. The relevant S-matrices are computed explicitly, and the bound state problem is discussed. © 1988.