nLab symplectic reduction - table

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