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Springer Mathematical Topics Between Classical and Quantum Mechanics - Springer

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Description

This Springer monograph bridges algebraic and geometric approaches to mechanics by unifying Poisson algebras of observables, pure state spaces, and transition probabilities. Drawing from both quantum field theory traditions and classical mechanical geometry, the work explores quantization theory and classical limits through a cohesive framework. The text establishes a prototype of quantization by drawing analogies between C*-algebras of Lie groupoids and Poisson algebras of corresponding Lie algebroids, revealing deep structural parallels between quantum and classical systems. Designed for mathematicians and theoretical physicists, this treatment combines rigorous algebraic formulation with geometric insights to provide a comprehensive foundation for understanding the mathematical structures underlying both classical and quantum mechanical theories.

Key Features

Combines algebraic formulation of quantum mechanics and quantum field theory with geometric classical mechanics theory into a unified treatment.

Explores Poisson algebras of observables and pure state spaces with transition probability as central mathematical objects.

Discusses quantization theory and classical limits from the perspective of Poisson algebra structures.

Uses C*-algebras of Lie groupoids as prototypes for quantization, drawing connections to Poisson algebras of Lie algebroids.

Part of Springer Monographs in Mathematics series, providing authoritative mathematical treatment for advanced study.

Addresses the foundational mathematical structures bridging classical and quantum mechanical frameworks.

Product Specifications

Format
paperback
Domain
Amazon UK
Publication Date
30 October 2012
Listed Since
03 March 2013

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