Non-Abelian elastic collisions, associated difference systems of equations and discrete analytic functions

We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these generic equations. Furthermore, we show that these equations can be reinterpreted as difference systems defined on the Z2 graph and this reinterpretation relates (unifies) the linear and the non-linear approach of discrete analytic functions.