  We show that the WKB approximation gives the exact result in the trace
formula of ``$CQ^N$'', which is the non-compact counterpart of $CP^N$, in terms
of the ``multi-periodic'' coherent state. We revisit the symplectic 2-forms on
$CP^N$ and $CQ^N$ and, especially, construct that on $CQ^N$ with the unitary
form. We also revisit the exact calculation of the classical patition functions
of them.

Quantum Physics