Towards a test particle description of transport processes for states with continuous mass spectra

Based on a first order gradient expansion a consistent transport equation is derived for a nonrelativistic system beyond the quasiparticle approximation, i.e. for a regime where the dynamically generated width of the states is allowed to be large. An exactly consented quantity is identified which is interpreted as an effective particle number obtained by coarse graining. Using a test particle ansatz for this conserved quantity allows to rewrite the transport equation into equations of motion for test particles. The two-body collision terms are formulated in terms of the test particles which gain non-trivial renormalization factors due to the coarse graining process.