  We study the origin of the real intermediate state subtraction problem and
compare its different solutions. We show that the ambiguity in subtraction
schemes arises from the on-shell approximation for the 2-point functions that
reduces the Schwinger-Dyson equations to the Boltzmann limit. We also suggest a
new subtraction scheme which, unlike the earlier definitions, never leads to
negative scattering rates. This scheme also quantifies the validity of the
on-shell limit in terms of an effective one-particle weight function $R(\Delta
)$, where $\Delta$ measures the region around the resonance associated with the
real state.
