  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 conserved 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.
