Abstract

The (local) invariant symplectic action functional $A$ is associated to a Hamiltonian action of a compact connected Lie group $G$ on a symplectic manifold $(M,\omega)$, endowed with a $G$-invariant Riemannian metric $\langle\cdot,\cdot\rangle_M$. It is defined on the set of pairs of loops $(x,\xi):S^1\to M\times Lie G$ for which $x$ satisfies
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