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" Mathematical Topics Between Classical and Quantum Mechanics / "
by N.P. Landsman.
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BL
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| Record Number
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849794
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| Main Entry
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Landsman, N. P.
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| Title & Author
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Mathematical Topics Between Classical and Quantum Mechanics /\ by N.P. Landsman.
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| Publication Statement
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New York, NY :: Springer New York,, 1998.
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| Series Statement
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Springer Monographs in Mathematics,
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| Page. NO
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1 online resource (xix, 529 pages)
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| ISBN
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146121680X
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: 9781461216803
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146121680X
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1461272424
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9781461272427
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| Contents
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Introductory overview -- Observables and pure states -- Quantization and the classical limit -- Groups, bundles, and groupoids -- Reduction and induction -- Notes -- References -- Index.
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| Abstract
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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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Physics.
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Physics.
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| Dewey Classification
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530.1
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| LC Classification
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QC19.2-20.85
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