  It is shown that the semiclassical coherent state propagator takes its
simplest form when the quantum mechanical Hamiltonian is replaced by its Weyl
symbol in defining the classical action, in that there is then no need of a
Solari-Kochetov correction. It is also shown that such a correction exists if a
symbol other than the Weyl symbol is chosen, and that its form is different
depending on the symbol chosen. The various forms of the propagator based on
different symbols are shown to be equivalent provided the correspondingly
correct Solari-Kochetov correction is included. All these results are shown for
both particle and spin coherent state propagators. The global anomaly in the
fluctuation determinant is further elucidated by a study of the connection
bewteen the discrete fluctuation determinant and the discrete Jacobi equation.
