Mathematical Topics between Classical and Quantum ...

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Title: Mathematical Topics between Classical and Quantum Mechanics
Description:
(Springer Monographs in Mathematics)

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

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1. Ebooks list page : 521
2. Mathematical Topics between Classical and Quantum Mechanics
3. Geometric Phases in Classical and Quantum Mechanics (Progress in Mathematical Physics)
4. Geometric Phases in Classical and Quantum Mechanics (Progress in Mathematical Physics)
5. Classical and Quantum Dynamics: From Classical Paths to Path Integrals by Walter Dittrich
6. Classical and Quantum Dynamics: From Classical Paths to Path Integrals (Advanced Texts in Physics)
7. Mathematical Aspects of Classical and Celestial Mechanics (Encyclopaedia of Mathematical Sciences) (Repost)
8. Mathematical Aspects of Classical and Celestial Mechanics (Encyclopaedia of Mathematical Sciences) (Repost)
9. Quantum: The Quantum Theory of Particles, Fields and Cosmology (Theoretical and Mathematical Physics)
10. Topics in Classical Analysis and Applications In Honor of Daniel Waterman
11. Chaos: Classical and Quantum
12. The Quantum Classical Theory
13. Supersymmetry In Quantum and Classical Mechanics
14. Classical Topology and Quantum States
15. Decoherence and the Quantum-To-Classical Transition
16. Decoherence and the Quantum-To-Classical Transition