Mathematical Topics Between Classical and Quantum Mechanics / by N.P. Landsman.
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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Full Text (via Springer) |
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| Main Author: | |
| 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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| Subjects: |
MARC
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| 245 | 1 | 0 | |a Mathematical Topics Between Classical and Quantum Mechanics / |c by N.P. Landsman. |
| 260 | |a New York, NY : |b Springer New York, |c 1998. | ||
| 300 | |a 1 online resource (xix, 529 pages) | ||
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| 490 | 1 | |a Springer Monographs in Mathematics, |x 1439-7382. | |
| 505 | 0 | |a Introductory overview -- Observables and pure states -- Quantization and the classical limit -- Groups, bundles, and groupoids -- Reduction and induction -- Notes -- References -- Index. | |
| 520 | |a 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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