symplectic reduction

almost symplectic structure, metaplectic structure, metalinear structure

**geometric quantization**, higher geometric quantization

This entry is being splitt-off from

BRST-BV formalism. For the moment see the discussion there atHamiltonian BFV.

The analog for presymplectic manifolds is presymplectic reduction.

The analog for Poisson manifolds is Poisson reduction.

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 |

The original influential article is

- Jerrold Marsden, Alan Weinstein,
*Reduction of symplectic manifolds with symmetry*, Reports on Math. Phys., 5, (1974), 121-130 (web)

Reviews include

- José Figueroa-O'Farrill, chapter 2+3 of PhD thesis (pdf)

Textbook accounts include

- Bertram Kostant, Shlomo Sternberg,
*Symplectic reduction, BRS cohomology and infinite-dimensional Clifford algebras*, Annals of Physics**176**:1 (15 May 1987) pp. 49–113 MR893479 doi

Last revised on September 20, 2013 at 23:55:54. See the history of this page for a list of all contributions to it.