Mathematical Topics Between Classical and Quantum Mechanics - Springer Monographs in Mathematics (Paperback)
  • Mathematical Topics Between Classical and Quantum Mechanics - Springer Monographs in Mathematics (Paperback)
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Mathematical Topics Between Classical and Quantum Mechanics - Springer Monographs in Mathematics (Paperback)

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£109.99
Paperback 529 Pages / Published: 30/10/2012
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This monograph draws on two traditions: the algebraic formulation of quantum mechanics as well as 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, which leads on to a discussion of the theory of quantization and the classical limit 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. Accessible to mathematicians with some prior knowledge of classical and quantum mechanics, and to mathematical physicists and theoretical physicists with some background in functional analysis.

Publisher: Springer-Verlag New York Inc.
ISBN: 9781461272427
Number of pages: 529
Weight: 836 g
Dimensions: 235 x 155 x 28 mm
Edition: Softcover reprint of the original 1st ed. 199

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