Geometric Quantization

action BWS condition canonical coordinate canonical transformations classical cocycle coisotropic comoment complex structure components conjugate constant constraint construction coordinate system corresponding cotangent bundle curve defined denoted determined diffeomorphism dynamical trajectory element equation equivalent example foliation follows geodesic given global h₁ half-density Hamilton-Jacobi Hamiltonian vector field Hence Hilbert space holomorphic identify inner product integral invariant Kähler polarization Lagrangian submanifold Lagrangian subspace leaf LEMMA Lie algebra line bundle linear M₁ M₂ metaplectic structure n-dimensional neighbourhood nondegenerate orbits P-wave functions P₁ pairing particle phase space polarized sections positive prequantum bundle projection quantization quantum real polarization represented restriction right-handed satisfying simply connected smooth solutions space-time spinor symmetric symplectic form symplectic frame symplectic manifold symplectic potential symplectic structure symplectic vector space tangent tensor transverse trivial vanishes vector bundle w₁