Conformal invariant two particle processes

For the conformal group (essentially the SO2(n,2)group) in n-dimensional Minkowsi-space homogeneous spaces are studied which can be interpreted as 2-particle configuration spaces, and 2-particle representations are induced (both participants are spin 0 particles). The eigensolutions of the Casimir-operator in momentum space are Clebsch-Gordan coefficients in momentum basis. The separation of a complete set of comuting operators from the Casimir eigenvalue equations results in all cases in differential equations with 2 variables (a direct consequence of the rank 2 of the homogen spaces), which can be classified as 'generalized hypergeometric differential operators in 2 variables' (this type, as the author supposes, has not been delt with in the literature so far). In the second part the classical conform invariant (relativistic) 2-particle problem, corresponding to the common quantum mechanical (or quantum field theoretical) problem, is presented and solved completely. It is shown for example that for participant momentums (reasonable in the classic sens) on the forward - or on the zero cone only scattering and no bound states are found. (orig./WBU)