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High Quality Content by WIKIPEDIA articles! In mathematics, specifically in symplectic geometry, the moment map or momentum map is a tool associated with a Hamiltonian action of a Lie group on a symplectic manifold, used to construct conserved quantities for the action. The moment map generalizes the classical notions of linear and angular momentum. It is an essential ingredient in various constructions of symplectic manifolds, including symplectic Marsden-Weinstein quotients, discussed below, and symplectic cuts and sums.