On algebraic models of relativistic scattering

In this paper we develop an algebraic technique for building relativistic models in the framework of direct-interaction theories. The interacting mass operator M in the Bakamjian-Thomas construction is related to a quadratic Casimir operator C of a non-compact group G. As a consequence, the S matrix can be gained from an intertwining relation between Weyl-equivalent representations of G. The method is illustrated by explicit application to a model with SO(3,1) dynamical symmetry.