Author | ลniatycki, Jศฉdrzej. author |
---|---|
Title | Geometric Quantization and Quantum Mechanics [electronic resource] / by Jศฉdrzej ลniatycki |
Imprint | New York, NY : Springer New York, 1980 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-6066-0 |
Descript | X, 230 p. online resource |
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 Schrรถdinger representation -- 1.8 Other representations -- 1.9 Time-dependent Schrรถdinger equation -- 1.10 Relativistic dynamics in an electromagnetic field -- 1.11 Pauli representation -- 2. Hamiltonian Dynamics -- 2.1 Poisson algebra -- 2.2 Local expressions -- 2.3 Relativistic charged particle -- 2.4 Non-relativistic dynamics -- 3. Prequantization -- 3.1 Connections in line bundles -- 3.2 Prequantization line bundle -- 3.3 Prequantization map -- 4. Representation Space -- 4.1 Polarization -- 4.2 The bundle ??F F -- 4.3 Square integrable wave functions -- 4.4 Bohr-Sommerfeld conditions -- 4.5 Distributional wave functions -- 5. Blattner-Kostant-Sternberg Kernels -- 5.1 Transverse polarizations -- 5.2 Strongly admissible pairs of polarizations -- 5.3 Metaplectic structure -- 5.4 Induced metaplectic structure -- 6. Quantization -- 6.1 Lifting the action of ?ft -- 6.2 Polarization preserving functions -- 6.3 Quantization via Blattner-Kostant-Sternberg kernels -- 6.4 Superselection rules -- 7. Schrรถdinger Representation -- 7.1 Single particle -- 7.2 System of particles -- 7.3 Blattner-Kostant-Sternberg kernels, quasiclassical approximations and Feynman path integrals -- 8. Other Representations -- 8.1 Bargmann-Fock representation -- 8.2 Harmonic oscillator energy representation -- 9. Time-Dependent Schrรถdinger Equation -- 10. Relativistic Dynamics in An Electromagnetic Field -- 10.1 Relativistic quantum dynamics -- 10.2 Charge superselection rules -- 10.3 Quantization in the Kaluza theory -- 11. Pauli Representation for Spin -- 11.1 Classical model of spin -- 11.2 Representation space -- 11.3 Quantization -- Glossary of Notation