Absence of particle production and factorization of the S-matrix in 1 + 1 dimensional models

In massive, 1 + 1 dimensional, local, quantum field theories the existence of two conserved charges is shown to be a sufficient condition for the absence of particle production and factorization of the S-matrix. These charges must commute and be integrals of local current densities. Their transformation properties under the Lorentz group must be different and also different from the transformation properties of a vector or a scalar. Also, they must not annihilate any single-particle momentum eigenstate.