  In a series of recent articles, Liu, Yang, Pan, et al. claim to have
determined the exact dressed electron-boson vertex for a number of very general
interacting many-body problems by inverting certain Ward-Takahashi identities.
Here, we point out that their Ward-Takahashi identities are missing terms which
make the inversion of the identities impossible. One therefore cannot formulate
exact self-contained integral equations for the dressed electron propagator. In
addition, the proposed vertex expressions do not reproduce well-established
results for the leading perturbative corrections.
