Mathematical Topics Between Classical and Quantum Mechanics (Hardcover, 1998 ed.)

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.

General

Imprint:	Springer-Verlag New York
Country of origin:	United States
Series:	Springer Monographs in Mathematics
Release date:	December 1998
First published:	December 1998
Authors:	Nicholas P. Landsman
Dimensions:	235 x 155 x 35mm (L x W x T)
Format:	Hardcover
Pages:	529
Edition:	1998 ed.
ISBN-13:	978-0-387-98318-9
Categories:	Books > Science & Mathematics > Mathematics > Applied mathematics > General Books > Science & Mathematics > Physics > Classical mechanics > General Books > Science & Mathematics > Physics > Quantum physics (quantum mechanics) > General
LSN:	0-387-98318-X
Barcode:	9780387983189

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