A moment map for the G-action on (M, ω) is a map such that
for all ξ in . Here is the function from M to R defined by . The moment map is uniquely defined up to an additive constant of integration.
A moment map is often also required to be G-equivariant, where G acts on via the coadjoint action. If the group is compact or semisimple, then the constant of integration can always be chosen to make the moment map coadjoint equivariant; however in general the coadjoint action must be modified to make the map equivariant (this is the case for example for the Euclidean group).
Read more about Moment Map: Hamiltonian Group Actions, Examples, Symplectic Quotients
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