Symplectic action around loops in $\text{Ham}(M)$

Abstract

Let $\text{Ham(M)}$ be the group of Hamiltonian symplectomorphisms of a quantizable, compact, symplectic manifold $(M,\omega)$. 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.