Mathematical Topics Between Classical and Quantum Mechanics /
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 probabi...
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| Format: | eBook |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
1998.
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| Series: | Springer monographs in mathematics.
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| Online Access: | Connect to the full text of this electronic book |
| Summary: | 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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| Item Description: | Electronic resource. |
| Physical Description: | 1 online resource (xix, 529 pages) |
| ISBN: | 9781461216803 (electronic bk.) 146121680X (electronic bk.) |
| ISSN: | 1439-7382 |