Mathematical Topics Between Classical and Quantum Mechanics
- Binding: Hardcover
- Publisher: Springer-Verlag
- Publish date: 12/01/1998
- ISBN: 9780387983189
- ISBN10: 038798318X
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.