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Mathematical Topics Between Classical and Quantum Mechanics

by Landsman, Nicholas P. A Landsman, N. P.

  • ISBN: 9780387983189
  • ISBN10: 038798318X

Mathematical Topics Between Classical and Quantum Mechanics

by Landsman, Nicholas P. A Landsman, N. P.

  • Binding: Hardcover
  • Publisher: Springer-Verlag
  • Publish date: 12/01/1998
  • ISBN: 9780387983189
  • ISBN10: 038798318X
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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.

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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