Relativistic interactions without fields or potentials

Abstract

Employing Poincaré degrees of freedomM ^jk=(¯K,¯J) andP ^k=(E,¯p) transforming linearly (but inhomogeneously) under the action of the Poincaré group we define a number of quantities which we later identify with physical observables. The identifications are consistent with the nonrelativistic limit and with other requirements following from the Poincaré covariance. Next, we treat a free relativistic particle as composed of two interacting parts. Relativistic quantum commutation relations for their Poincaré algebras and a kind of (inverse) relativistic correspondence principle are used to generate (quasi-) classical equations of their relative motion. A simple example based on these ideas is explicitly solved.