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Mathematical Topics between Classical and Quantum Mechanics
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Mathematical Topics between Classical and Quantum Mechanics * Publisher: Springer * Number Of Pages: 556 * Publication Date: 1998-12-07 * Sales Rank: 1655372 * ISBN / ASIN: 038798318X * EAN: 9780387983189 * Binding: Hardcover * Manufacturer: Springer * Studio: Springer * Average Rating: * Total Reviews: Book Description: ) 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. [ Last edited by cuplgz on 2007-5-3 at 14:12 ] |
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