ENGLISH

Mathematical topics between classical and quantum mechanics

By Nicholas P. Landsman

Book information

Publisher
Springer
Year
1998
ISBN
038798318X, 9780387983189
LCC
QC174.17.M35 L36 1998
Open Library ID
OL358436M
Language
english
Format
DJVU
Filesize
6 MB (5999137 bytes)
Series
Springer monographs in mathematics
Edition
1
Pages
547\547
Library
Kolxo3
DPI
300
Time added
2009-07-20 03:45:11

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.

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