  We show how the time-continuous coherent state path integral breaks down for
both the single-site Bose-Hubbard model and the spin path integral.
Specifically, when the Hamiltonian is quadratic in a generator of the algebra
used to construct coherent states, the path integral fails to produce correct
results following from an operator approach. As suggested by previous authors,
we note that the problems do not arise in the time-discretized version of the
path integral.
