nLab Poisson reduction

Idea

The generalization of symplectic reduction from symplectic manifolds to Poisson manifolds.

Related concepts

• gauge reduction, symplectic reduction, presymplectic reduction, BV-BRST formalism

Reductions of (pre-)symplectic manifolds:

symplectic geometry	physics
presymplectic manifold	covariant phase space
$\downarrow$ gauge reduction	$\downarrow$ quotient by gauge symmetry
symplectic manifold	reduced phase space
$\downarrow$ symplectic reduction	$\downarrow$ quotient by global symmetry
symplectic manifold	reduced phase space

• quantization commutes with reduction

References

• Juan-Pablo Ortega, Tudor S. Ratiu, Poisson reduction (arXiv:math/0508635)