Geometric Quantization in Action: Applications of Harmonic Analysis in Quantum Statistical Mechanics and Quantum Field Theory [Paperback]

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.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.- Elementals°