nLab
symplectic reduction

Skip the Navigation Links | Home Page | All Pages | Recently Revised | Authors | Feeds | Export |

Context

Symplectic geometry

symplectic geometry

higher symplectic geometry

Background

Basic concepts

Classical mechanics and quantization

Contents

Idea

This entry is being splitt-off from BRST-BV formalism. For the moment see the discussion there at Hamiltonian BFV.

Properties

The analog for presymplectic manifolds is presymplectic reduction.

Reductions of (pre-)symplectic manifolds:

symplectic geometryphysics
presymplectic manifoldcovariant phase space
↓ gauge reduction↓ quotient by gauge symmetry
symplectic manifoldreduced phase space
↓ symplectic reduction↓ quotient by global symmetry
symplectic manifoldreduced phase space

References

Reviews include

Textbook accounts include

  • Bertram Kostant, Shlomo Sternberg, Symplectic reduction, BRS cohomology and infinite-dimensional Clifford algebras, Annals of Physics Volume 176, Issue 1, 15 May 1987, Pages 49–113

Revised on April 4, 2013 23:44:38 by Urs Schreiber (82.169.65.155)
Edit | Back in time (3 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: BV-BRST formalism, Courant algebroid, AKSZ sigma-model, symplectic geometry, geometric quantization, symplectic vector space, symplectic manifold, Poisson manifold, symplectic groupoid, symplectic Lie n-algebroid, Poisson Lie algebroid, multisymplectic geometry, Maslov index, equivariant localization and elimination of nodes, Poisson Lie group, symplectomorphism, lagrangian submanifold, deformation quantization, phase space, n-plectic geometry, Heisenberg group, Poisson n-algebra, Lagrangian subspace, isotropic subspace, presymplectic structure, isotropic submanifold, moment map, polarization, symplectic field theory, symplectic geometry - contents, higher symplectic geometry, symplectic infinity-groupoid, geometric quantization of symplectic groupoids, Hamiltonian action, Hamiltonian vector field, Bohr-Sommerfeld leaf, quantum observable, gauge reduction, 2-plectic geometry, metaplectic structure, canonical momentum, metaplectic representation, contact manifold, symplectic leaf, symplectomorphism group, first class constraint, symplectic reduction, presymplectic reduction, symplectic reduction - table, C-star algebraic deformation quantization, metalinear group, metalinear structure, Heisenberg Lie n-algebra, Weinstein symplectic category, Heisenberg n-group, Hamiltonian form, motivation for higher differential geometry, Dirac manifold, Liouville integrable system, Poisson bracket Lie n-algebra, Lie-Poisson structure, geometric quantization of non-integral forms, Guillemin-Sternberg geometric quantization conjecture, Moyal quantization, symplectic connection, Lagrangian Grassmannian, extended geometric quantization of 2d Chern-Simons theory, Poisson geometry, symplectic realization, prequantum geometry, Kostant-Souriau extension, Poisson tensor, Poisson cohomology