Mathematical Topics Between Classical and Quantum Mechanics

✍ Scribed by Nicholas P. Landsman

• Publisher: Springer, Berlin
• Year: 1998
• Tongue: English
• Leaves: 547
• Series: Springer Monographs in Mathematics
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Subjects

Физика;Матметоды и моделирование в физике;