  Partial wave analysis is an important tool for analyzing large data sets in
hadronic decays of light and heavy mesons. It commonly relies on the isobar
model, which assumes multihadron final states originate from successive
two-body decays of well-known undisturbed intermediate states. Recently,
analyses of heavy-meson decays and diffractively produced states have attempted
to overcome the strong model dependences of the isobar model. These analyses
have overlooked that model-independent, or freed-isobar, partial-wave analysis
can break the orthogonality of partial waves and introduce mathematical
ambiguities into results. We show how these ambiguities arise and present
general techniques for identifying their presence and for correcting for them.
We demonstrate these techniques with specific examples in both heavy-meson
decay and pion--proton scattering.
