Mathematical Topics Between Classical and Quantum Mechanics
- List Price: $219.99
- Binding: Hardcover
- Publisher: Springer-Verlag
- Publish date: 12/01/1998
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.
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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 and 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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