Reply to 'Comment on "Semiclassical approximations in phase space with coherent states"'

The Herman-Kluk (HK) formula was shown in (Baranger et al J. Phys. A: Math. Gen. 34 1227) not to be a correct semiclassical limit of an exact quantum mechanical formula. Two previous attempts to derive it using semiclassical arguments contain serious errors. These statements are left totally untouched by Herman and Grossmann's comment. They argue that the formula which we found to be at fault is not the one that should be called the HK formula. However, the formula we criticized is definitely one of the steps, in fact the main step, in these two published derivations of the HK formula. Very recently, a new derivation was published by Miller. It is interesting, but it is not semiclassical.