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Geometric Quantization in Action: Applications of Harmonic Analysis in Quantum Statistical Mechanics and Quantum Field Theory
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Catalogue Information
Field name
Details
Dewey Class
515
Title
Geometric Quantization in Action ([EBook] :) : Applications of Harmonic Analysis in Quantum Statistical Mechanics and Quantum Field Theory / / by Norman E. Hurt.
Author
Hurt, Norman E.
Other name(s)
SpringerLink (Online service)
Edition statement
1.
Publication
Dordrecht : : Springer Netherlands, , 1983.
Physical Details
356 p. : online resource.
Series
Mathematics and its applications
; 8
ISBN
9789400969636
Summary Note
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'. 'The Hermit Clad in Crane Feathers' in R. Van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the 'tree' of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (nontrivially) in regional and theoretical economics; algebraic geo metry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical progmmming profit from homotopy theory; Lie algebras are relevant to fIltering; and prediction and electrical engineering can use Stein spaces.:
Contents note
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  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  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  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.
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Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/9789400969636
Links to Related Works
Subject References:
Analysis
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Analysis (Mathematics)
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Geometry
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Mathematical analysis
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Mathematics
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Authors:
Hurt, Norman E.
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Corporate Authors:
SpringerLink (Online service)
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Series:
Mathematics and its applications
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Classification:
515
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