  The applicability of bosonization and the Anderson-Yuval (AY) approach at
strong coupling is investigated by considering two generic impurity models: the
multichannel interacting resonant-level and the anisotropic Kondo models. The
two methods differ in the renormalization of the conduction-electron density of
states (DoS) near the impurity site. Reduction of the DoS, absent in
bosonization but accounted for in the AY approach, is shown to be vital in some
models yet redundant in others. The criterion being the stability of the
strong-coupling fixed point. Renormalization of the DoS is essential for an
unstable fixed point, but redundant when a decoupled entity with local dynamics
is formed. This rule can be used to boost the accuracy of both methods at
strong coupling.
