The relativistic Vlasov equation with non-radiating meson fields

Abstract

The relativistic Vlasov equation which is coupled to wave equations for massive classical fields is solved in the spirit of the action-at-a-distance theory. It is argued that the acceleration of the nucleon due to the Hartree mean field is too small to produce free on-shell mesons by bremsstrahlung. An appropriate Green function allows one to construct radiation free solutions even for classical wave equations. The assumption of small accelerations is also used to achieve covariant equations of motion for test-particles which are the representatives of phase space cells. First results for the collision of two 16O nuclei are presented.