## Symplectic Manifold

A pair , where is a Manifold and is a Symplectic Form on . The Phase Space is a symplectic manifold. Near every point on a symplectic manifold, it is possible to find a set of local Darboux coordinates'' in which the Symplectic Form has the simple form

(Sjamaar 1996), where is a Wedge Product.

See also Manifold, Symplectic Diffeomorphism, Symplectic Form

References

Sjamaar, R. Symplectic Reduction and Riemann-Roch Formulas for Multiplicities.'' Bull. Amer. Math. Soc. 33, 327-338, 1996.

© 1996-9 Eric W. Weisstein
1999-05-26