nLab
prequantum circle n-bundle

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Context

Geometric quantization

geometric quantization higher geometric quantization

geometry of physics: Lagrangians and Action functionals + Geometric Quantization

Prerequisites

Prequantum field theiry

Geometric quantization

Theorems

Bundles

bundles

Context

Classes of bundles

Universal bundles

Presentations

Examples and Applications

Contents

Idea

In higher geometric prequantization (see there for more details for the moment) the notion of prequantum circle bundle is refined to that of a prequantum circle n-bundle with connection for all n∈ℕ.

extended prequantum field theory

0≤k≤n(off-shell) prequantum (n-k)-bundletraditional terminology
0differential universal characteristic maplevel
1prequantum (n-1)-bundleWZW bundle (n-2)-gerbe
kprequantum (n-k)-bundle
n−1prequantum 1-bundle(off-shell) prequantum bundle
nprequantum 0-bundleaction functional

Revised on March 30, 2013 15:05:37 by Urs Schreiber (82.113.99.161)
Edit | Back in time (7 revisions) | See changes | History | Views: Print | TeX | Source | Linked from: BV-BRST formalism, Courant algebroid, AKSZ sigma-model, bundle gerbe, principal bundle, vector bundle, principal 2-bundle, principal infinity-bundle, fiber bundle, symplectic geometry, geometric quantization, Borel-Weil theorem, symplectic vector space, symplectic manifold, Poisson manifold, line bundle, action functional, Chern-Simons theory, symplectic groupoid, symplectic Lie n-algebroid, Poisson Lie algebroid, multisymplectic geometry, bibundle, circle bundle, Maslov index, Poisson Lie group, symplectomorphism, lagrangian submanifold, deformation quantization, determinant line bundle, n-plectic geometry, groupoid principal bundle, associated infinity-bundle, circle n-bundle with connection, principal 3-bundle, Heisenberg group, quantization via the A-model, Poisson n-algebra, over-(infinity,1)-topos, spinor bundle, over-topos, n-vector bundle, Lagrangian subspace, isotropic subspace, presymplectic structure, isotropic submanifold, moment map, higher geometric quantization, prequantum line bundle, orbit method, 2-gerbe, polarization, symplectic field theory, symplectic geometry - contents, higher symplectic geometry, symplectic infinity-groupoid, geometric quantization of symplectic groupoids, Hamiltonian action, space of states (in geometric quantization), Hamiltonian vector field, complex vector bundle, Bohr-Sommerfeld leaf, theta function, quantum observable, Hopf fibration, double cover, gauge reduction, Planck's constant, 2-plectic geometry, metaplectic structure, canonical momentum, coherent state in geometric quantization, bundles - contents, local coefficient bundle, fiber infinity-bundle, metaplectic representation, quantomorphism group, contact manifold, geometric quantization - contents, quantum operator (in geometric quantization), symplectic leaf, symplectomorphism group, Poisson Lie 2-algebra, symplectic reduction, presymplectic reduction, holomorphic vector bundle, metaplectic correction (in geometric quantization), C-star algebraic deformation quantization, metalinear group, metalinear structure, prequantum circle n-bundle, Heisenberg Lie n-algebra, Weinstein symplectic category, Heisenberg n-group, associated bundle, Hamiltonian form, geometry of physics, groupoid-principal infinity-bundle, Dirac manifold, Liouville integrable system, Poisson bracket Lie n-algebra, prequantum field theory, Lie-Poisson structure, stable vector bundle, geometric quantization of non-integral forms, prequantum 0-bundle, 2-vector bundle, line 2-bundle, Guillemin-Sternberg geometric quantization conjecture, extended Lagrangian, Moyal quantization, density, Hopf construction, symplectic connection, adjoint bundle, Lagrangian Grassmannian, centrally extended groupoid, Poisson geometry, symplectic realization, higher Atiyah groupoid, prequantum geometry, Kostant-Souriau extension, Poisson tensor, Poisson cohomology, semiclassical state