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 7227) 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. 1. Summary In this note of reply to Grossmann and Herman’s comment (GH) [Gro02], we sincerely hope that we can clear up the serious misunderstanding that has arisen between us. Perhaps we should begin by acknowledging now, rather than at the end of the paper, the efforts of the referee and the editor of this journal, who insiste dt hat this misunderstanding be aired out. We se et wo points of contention between GH and us. One is a fundamental point of physics. The other is a relatively trivial question of interpretation. Our first point is that the Herman–Kluk approximation (HK) [Her84], irrespective of its considerable other virtues, is not a semiclassical approximation in the strict sense of the term. About this we are certain. We have shown it already in our paper [Bar01] in great detail, and we are going to show it again in section 3 in at otally different way. Therefore, every statement by GH about HK being correctly semiclassical is misleading. If the H Ka pproximation is not semiclassical, then what