Formal scattering theory by an algebraic approach

Formal scattering theory is recast in a Lie-algebraic form. The central result is an algebraic Lippmann-Schwinger equation for the wave operator from which an algebraic form of the Born series (containing only linked terms) is obtained. When a finite Lie algebra is sufficient, The Mo/ller wave operator, on the energy shell, can be solved for explicitly as an element of the corresponding group. The method is illustrated for the separable potential whose relevant algebra is found to be U(1,1).