Geometric Quantization in Action : Applications of Harmonic Analysis in Quantum Statistical Mechanics and Quantum Field Theory
Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then, is that they can't see the problem. one day, perhaps you will fmd the final question. G. K. Chesterton, The Scandal of Father Brown 'The Point of a Pin'....
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Format:  eBook 
Language:  English 
Published: 
Dordrecht
Springer Netherlands
1983, 1983

Edition:  1st ed. 1983 
Series:  Mathematics and Its Applications

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Online Access:  
Collection:  Springer Book Archives 2004  Collection details see MPG.ReNa 
Table of Contents:
 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
 10. Geometry of CSpaces and RSpaces
 The Geometry of CManifolds
 Kirillov Character Formula
 Geometry of RSpaces
 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
 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
 RiemanrrRoch 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. BorelWeil Theory
 Representation Theory for Compact Semisimple Lie Groups
 BorelWei! Theory
 Cocompact Nilradical Groups
 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 PeterWeyl 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