nLab presymplectic reduction

Idea

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

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

Related concepts

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

• quantization commutes with reduction

References

• Francesco Bottacin, A Marsden-Weinstein reduction for presymplectic manifolds (pdf)

• A. Echeverría-Enríquez, M.C. Muñoz-Lecanda, N. Román-Roy, Reduction of Presymplectic Manifolds with Symmetry (arXiv:math-ph/9911008)