The Geometry of Quantum Mechanics

Abstract

A recent notion in theoretical physics is that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. These facts find strong evidence in string duality and M-theory, and it has been suggested that they should also have a counterpart in quantum mechanics. In view of these developments we propose "dequantisation", a mechanism to render a quantum theory classical. Specifically, we present a geometric procedure to "dequantise" a given quantum mechanics (regardless of its classical origin, if any) to possibly different classical limits, whose quantisation gives back the original quantum theory. The standard classical limit $\hslash \to 0$ arises as a particular case of our approach.

15 pages, LaTeX

References in corpus (3)

• Operads and Motives in Deformation Quantization
• Equivalence Principle, Higher Dimensional Moebius Group and the Hidden Antisymmetric Tensor of Quantum Mechanics
• Constructing Hamiltonian quantum theories from path integrals in a diffeomorphism invariant context

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• A General Theory of Quantum Relativity
• Time and M-theory
• Algebraic hierarchy of logics unifying fuzzy logic and quantum logic
• A short introduction to the quantum formalism[s]
• Geometric quantization in the framework of algebraic lagrangian geometry
• Quantum and Classical Phase Space: Separability and Entanglement