  Motivated by a quantum Zeno dynamics in a cavity quantum electrodynamics
setting, we study the asymptotics of a family of symbols corresponding to a
truncated momentum operator, in the semiclassical limit of vanishing Planck
constant $\hbar\to0$ and large quantum number $N\to\infty$, with $\hbar N$ kept
fixed. In a suitable topology, the limit is the discontinuous symbol
$p\chi_D(x,p)$ where $\chi_D$ is the characteristic function of the classically
permitted region $D$ in phase space. A refined analysis shows that the symbol
is asymptotically close to the function $p\chi_D^{(N)}(x,p)$, where
$\chi_D^{(N)}$ is a smooth version of $\chi_D$ related to the integrated Airy
function. We also discuss the limit from a dynamical point of view.
