  We study quantum moment maps of $G$-invariant star products, which are a
quantum analogue of the moment map for classical Hamiltonian systems.
Introducing an integral representation, we show that any quantum moment map for
a $G$-invariant star product is differentiable. This property gives us a new
method for the classification of $G$-invariant star products on regular
coadjoint orbits of compact semisimple Lie groups.
