Geometric Quantization in Action: Applications of Harmonic Analysis in Quantum Statistical Mechanics and Quantum Field Theory (Mathematics and Its Applications, 8)

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 (non-trivially) 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. 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 (non-trivially) in regional and theoretical economics; algebraic geoƯ 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 Front Matter....Pages i-xiv Survey of Results....Pages 1-40 Representation Theory....Pages 41-55 Euclidean Group....Pages 56-62 Geometry of Symplectic Manifolds....Pages 63-82 Geometry of Contact Manifolds....Pages 83-106 The Dirac Problem....Pages 107-116 Geometry of Polarizations....Pages 117-128 Geometry of Orbits....Pages 129-143 Fock Space....Pages 144-150 Borel-Weil Theory....Pages 151-165 Geometry of C-Spaces and R-Spaces....Pages 166-181 Geometric Quantization....Pages 182-189 Principal Series Representations....Pages 190-196 Geometry of De Sitter Spaces....Pages 197-200 Discrete Series Representations....Pages 201-209 Representations and Automorphic Forms....Pages 210-218 Thermodynamics of Homogeneous Spaces....Pages 219-239 Quantum Statistical Mechanics....Pages 240-262 Selberg Trace Theory....Pages 263-282 Quantum Field Theory....Pages 283-299 Coherent States and Automorphic Forms....Pages 300-308 Back Matter....Pages 309-336