عنوان

Mathematical Topics Between Classical and Quantum Mechanics /

(Number (ISBN

146121680X

(Number (ISBN

9781461216803

Erroneous ISBN

146121680X

Erroneous ISBN

1461272424

Erroneous ISBN

9781461272427

Title Proper

Mathematical Topics Between Classical and Quantum Mechanics /

General Material Designation

[Book]

First Statement of Responsibility

by N.P. Landsman.

Place of Publication, Distribution, etc.

New York, NY :

Name of Publisher, Distributor, etc.

Springer New York,

Date of Publication, Distribution, etc.

1998.

Specific Material Designation and Extent of Item

1 online resource (xix, 529 pages)

Series Title

Springer Monographs in Mathematics,

ISSN of Series

1439-7382

Text of Note

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

0

Text of Note

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.

International Standard Book Number

9781461272427

Physics.

Physics.

PHU

SCI040000

Number

Edition

Class number

Landsman, N. P.

Date of Transaction

20200823024427.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y