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
Famous quotes containing the words moment and/or map:
“Of all the riddles of a married life, said my father ... there is not one that has more intricacies in it than this—that from the very moment the mistress of the house is brought to [child]bed, every female in it ... becomes an inch taller for it....
I think rather, replied my uncle Toby, that ‘tis we who sink an inch lower.”
—Laurence Sterne (1713–1768)
“You can always tell a Midwestern couple in Europe because they will be standing in the middle of a busy intersection looking at a wind-blown map and arguing over which way is west. European cities, with their wandering streets and undisciplined alleys, drive Midwesterners practically insane.”
—Bill Bryson (b. 1951)