Geometric quantization and quantum mechanics

摘要: 1. Introduction.- 1.1 Background.- 1.2 Hamiltonian dynamics.- 1.3 Prequantization.- 1.4 Representation space.- 1.5 Blattner-Kostant-Sternberg kernels.- 1.6 Quantization.- 1.7 Schrodinger representation.- 1.8 Other representations.- 1.9 Time-dependent equation.- 1.10 Relativistic dynamics in an electromagnetic field.- 1.11 Pauli 2. Dynamics.- 2.1 Poisson algebra.- 2.2 Local expressions.- 2.3 charged particle.- 2.4 Non-relativistic 3. 3.1 Connections line bundles.- 3.2 Prequantization bundle.- 3.3 map.- 4. Space.- 4.1 Polarization.- 4.2 The bundle ??F F.- 4.3 Square integrable wave functions.- 4.4 Bohr-Sommerfeld conditions.- 4.5 Distributional 5. Kernels.- 5.1 Transverse polarizations.- 5.2 Strongly admissible pairs of 5.3 Metaplectic structure.- 5.4 Induced metaplectic 6. 6.1 Lifting the action ?ft.- 6.2 Polarization preserving 6.3 Quantization via 6.4 Superselection rules.- 7. Representation.- 7.1 Single 7.2 System particles.- 7.3 kernels, quasiclassical approximations and Feynman path integrals.- 8. Representations.- 8.1 Bargmann-Fock 8.2 Harmonic oscillator energy 9. Time-Dependent Equation.- 10. Dynamics An Electromagnetic Field.- 10.1 quantum 10.2 Charge superselection 10.3 Kaluza theory.- 11. for Spin.- 11.1 Classical model spin.- 11.2 11.3 Glossary Notation.