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:
“the beautiful changes
In such kind ways,
Wishing ever to sunder
Things and things’ selves for a second finding, to lose
For a moment all that it touches back to wonder.”
—Richard Wilbur (b. 1921)
“When I had mapped the pond ... I laid a rule on the map lengthwise, and then breadthwise, and found, to my surprise, that the line of greatest length intersected the line of greatest breadth exactly at the point of greatest depth.”
—Henry David Thoreau (1817–1862)