Abstract We consider the scattering matrices of massive quantum field theories with no bound states and a global O(N) symmetry in two spacetime dimensions. In particular we explore the space of two-to-two S-matrices of particles of mass m transforming in the vector representation as restricted by the general conditions of unitarity. crossing. analyticity and O(N) symmetry. https://danddcollectiblers.shop/product-category/train-case/