Let be a symplectic manifold, a Lie group acting on that manifold, its Lie algebra, and the dual of the Lie algebra. This action induces a map where is the Lie algebra of vector fields on , such that where is the flow of . Then a moment map for the action of is a map such that
Here , that is, is a covector, so we apply it to the vector and get a scalar function , and is its Hamiltonian vector field.
Generally, the moment maps we are interested in are equivariant with respect to the coadjoint action, that is, they satisfy
|Date of creation||2013-03-22 13:14:36|
|Last modified on||2013-03-22 13:14:36|
|Last modified by||bwebste (988)|