Let $M$ be a symplectic manifold and let $f$ be a real-valued function on $M$, generating a circular action. According to quantum mechanic postulates, one wishes that there, there exists a Hilbert space $Q(M)$ and a self-adjoint operator $Q(f)$ with eigenvalues the integral values of $f$. The conjecture of Guillemin-Sternberg gives a formula for the multiplicity of an eigenvalue $\lambda $ in function of the reduced fiber of $f$ at $\lambda $. This conjecture has been proved for an action of a compact group on a compact prequantified symplectic manifold by Meinrenken-Sjamaar and Tian-Zhang.