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Mathematical Topics between Classical and Quantum Mechanics
Mathematical Topics between Classical and Quantum Mechanics
Date: 24 November 2010, 15:33

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Nicholas P. Landsman, "Mathematical Topics between Classical and Quantum Mechanics"
S--r | 1998 | ISBN: 038798318X | 556 pages | Djvu | 5,7 MB

This monograph draws on two traditions: the algebraic formulation of quantum mechanics and quantum field theory, and the geometric theory of classical mechanics. These are combined in a unified treatment of the theory of Poisson algebras of observables and pure state spaces with a transition probability. The theory of quantization and the classical limit is discussed from this perspective. A prototype of quantization comes from the analogy between the C*- algebra of a Lie groupoid and the Poisson algebra of the corresponding Lie algebroid. The parallel between reduction of symplectic manifolds in classical mechanics and induced representations of groups and C*- algebras in quantum mechanics plays an equally important role. Examples from physics include constrained quantization, curved spaces, magnetic monopoles, gauge theories, massless particles, and $theta$- vacua. The book should be accessible to mathematicians with some prior knowledge of classical and quantum! mechanics, to mathematical physicists and to theoretical physicists who have some background in functional analysis.
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