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Description - Mathematical Topics Between Classical and Quantum Mechanics by N. P. Landsman

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.

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Book Details

ISBN: 9780387983189
ISBN-10: 038798318X
Format: Hardback
(235mm x 155mm x mm)
Pages: 529
Imprint: Springer-Verlag New York Inc.
Publisher: Springer-Verlag New York Inc.
Publish Date: 1-Dec-1998
Country of Publication: United States

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