عنوان

Mathematical Topics Between Classical and Quantum Mechanics /

146121680X

9781461216803

146121680X

1461272424

9781461272427

Mathematical Topics Between Classical and Quantum Mechanics /

[Book]

by N.P. Landsman.

New York, NY :

Springer New York,

1998.

1 online resource (xix, 529 pages)

Springer Monographs in Mathematics,

1439-7382

Introductory overview -- Observables and pure states -- Quantization and the classical limit -- Groups, bundles, and groupoids -- Reduction and induction -- Notes -- References -- Index.

0

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.

9781461272427

Physics.

Physics.

PHU

SCI040000

Landsman, N. P.

20200823024427.0

pn

[Book]

Y