2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62597Let $\text{Ham(M)}$ be the group of Hamiltonian symplectomorphisms of a quantizable, compact, symplectic manifold $(M,ω)$. We prove the existence of an action integral around loops in $\text{Ham(M)}$, and determine the value of this action integral on particular loops when the manifold is a coadjoint orbit.Expanded version. To appear in Geometriae DedicataSymplectic Geometrytext