Author | Hurt, Norman E. author |
---|---|
Title | Geometric Quantization in Action [electronic resource] : Applications of Harmonic Analysis in Quantum Statistical Mechanics and Quantum Field Theory / by Norman E. Hurt |
Imprint | Dordrecht : Springer Netherlands, 1983 |
Edition | 1 |
Connect to | http://dx.doi.org/10.1007/978-94-009-6963-6 |
Descript | 356 p. online resource |
O. Survey of Results -- Some Elementary Quantum Systems -- Examples of Group Representations in Physics -- Asymptotics in Statistical Mechanics -- More Spectral Geometry -- Statistical Mechanics and Representation Theory -- Transformation Groups in Physics -- Fiber Bundles -- Orbit Spaces in Lie Algebras -- Scattering Theory and Statistical Mechanics -- Quantum Field Theory -- 1. Representation Theory -- Basic Ideas of Representation Theory -- Induced Representations -- Schur and Peter-Weyl Theorems -- Lie Groups and Parallelization -- Spectral Theory and Representation Theory -- 2. Euclidean Group -- The Euclidean Group and Semidirect Products -- Fock Space, An Introduction -- 3. Geometry of Symplectic Manifolds -- Elementary Review of Lagrangian and Hamiltonian Mechanics: Notation -- Connections on Principal Bundles -- Riemannian Connections -- Geometry of Symplectic Manifolds -- Classical Mechanics and Symmetry Groups -- Homogeneous Symplectic Manifolds -- 4. Geometry of Contact Manifolds -- Contact Manifolds -- Almost Contact Metric Manifolds -- Dynamical Systems and Contact Manifolds -- Topology of Regular Contact Manifolds -- Infinitesimal Contact Transformations -- Homogeneous Contact Manifolds -- Contact Structures in the Sense of Spencer -- Homogeneous Complex Contact Manifolds -- 5. The Dirac Problem -- Derivations of Lie Algebras -- Geometric Quantization: An introduction -- The Dirac Problem -- Kostant and Souriau Approach -- 6. Geometry of Polarizations -- Polarizations -- Riemanrr-Roch for Polarizations -- Lie Algebra Polarizations -- Spin Structures, Metaplectic Structures and Square Root Bundles -- 7. Geometry of Orbits -- Orbit Theory -- Complete Integrability -- Morse Theory of Orbit Spaces -- 8. Fock Space -- Fock Space and Cohomology -- Nilpotent Lie Groups -- 9. Borel-Weil Theory -- Representation Theory for Compact Semisimple Lie Groups -- Borel-Wei! Theory -- Cocompact Nilradical Groups -- 10. Geometry of C-Spaces and R-Spaces -- The Geometry of C-Manifolds -- Kirillov Character Formula -- Geometry of R-Spaces -- Schubert Cell Decompositions -- 11. Geometric Quantization -- Geometric Quantization of Complex Manifolds -- Harmonic Oscillator -- The Kepler Problem - Hydrogen Atom -- Maslov Quantization -- 12. Principal Series Representations -- Representation Theory for Noncompact Semisimple Lie Groups. Part I: Principal Series Representations -- Applications to the Toda Lattice -- 13. Geometry of De Sitter Spaces -- De Sitter Spaces -- 14. Discrete Series Representations -- Representations of Noncompact Semisimple Lie Groups. Part II: Discrete Series -- 15. Representations and Automorphic Forms -- Geometric Quantization and Automorphic Forms -- Bounded Symmetric Domains and Holomorphic Discrete Series -- 16. Thermodynamics of Homogeneous Spaces -- Density Matrices and Partition Functions -- Epstein Zeta Functions -- Asymptotes of the Density Matrix -- Zeta Functions on Compact Lie Groups -- Ising Models -- 17. Quantum Statistical Mechanics -- Quantum Statistical Mechanics on Compact Symmetric Spaces -- Zeta Functions on Compact Lie Groups -- 18. Selberg Trace Theory -- The Selberg Trace Formula -- The Partition Function and the Length Spectra -- Noncompact Spaces with Finite Volume -- 19. Quantum Field Theory -- Applications to Quantum Field Theory -- Static Space Times and Periodization -- Examples of Zeta Functions in Quantum Field Theory -- 20. Coherent States and Automorphic Forms -- 20.1. Coherent States and Automorphic Forms -- References and Historical Comments