  It is pointed out that there are some fundamental difficulties with the
frequently used continuous-time formalism of the spin-coherent-state path
integral. They arise already in a single-spin system and at the level of the
"classical action" not to speak of fluctuations around the "classical path".
Similar difficulties turn out to be present in the case of the
(boson-)coherent-state path integral as well; although partially circumventable
by an ingenious trick (Klauder's $\epsilon$-prescription) at the "classical
level", they manifest themselves at the level of fluctuations. Detailed
analysis of the origin of these difficulties makes it clear that the only way
of avoiding them is to work with the proper discrete-time formalism. The thesis
is explicitly illustrated with a harmonic oscillator and a spin under a
constant magnetic field.

Quantum Physics