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We show a constrained Hamiltonian system and a gauged sigma model have astructure of a momentum section and a Hamiltonian Lie algebroid theory recentlyintroduced by Blohmann and Weinstein. We propose a generalization of a momentumsection on a pre-multisymplectic manifold by considering gauged sigma models ona higher dimensional manifold.

Momentum sections in Hamiltonian mechanics and sigma models