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

Andrés Viña
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Abstract

Let $\text{Ham(M)}$ 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.

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Andrés Viña. 2003-05-20. Symplectic action around loops in $\text{Ham}(M)$. https://arxiv.org/abs/math/0111095

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