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Item Details
| Title:
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MATHEMATICAL TOPICS BETWEEN CLASSICAL AND QUANTUM MECHANICS
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| By: |
N. P. Landsman |
| Format: |
Hardback |
| List price:
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£159.99 |
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We currently do not stock this item, please contact the publisher directly for
further information.
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| ISBN 10: |
038798318X |
| ISBN 13: |
9780387983189 |
| Publisher: |
SPRINGER-VERLAG NEW YORK INC. |
| Pub. date: |
1 December, 1998 |
| Edition: |
1998 ed. |
| Series: |
Springer Monographs in Mathematics |
| Pages: |
529 |
| Description: |
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. |
| Synopsis: |
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. |
| Illustrations: |
2 black & white tables, biography |
| Publication: |
US |
| Imprint: |
Springer-Verlag New York Inc. |
| Returns: |
Returnable |
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