Imprints of the quantum world in classical mechanics

DOI10.1007/s10701-011-9544-5zbMath1235.81094arXiv1001.4632OpenAlexW2170180349WikidataQ64357949 ScholiaQ64357949MaRDI QIDQ763214

Basil J. Hiley, Maurice A. De Gosson

Publication date: 9 March 2012

Published in: Foundations of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.4632

zbMATH Keywords

quantizationHamiltonian flowsSchrödinger's equationStone's theoremsymplectic covariance of Weyl calculus

Mathematics Subject Classification ID

Geometry and quantization, symplectic methods (81S10) Geometric quantization (53D50)

Related Items (14)

Entropies from coarse-graining: convex polytopes vs. ellipsoids ⋮ Time irreversibility from symplectic non-squeezing ⋮ Irreversibility from staircases in symplectic embeddings ⋮ Coarse-graining and symplectic non-squeezing ⋮ Preferred quantization rules: Born-Jordan versus Weyl. The pseudo-differential point of view ⋮ Observing quantum trajectories: From Mott's problem to quantum Zeno effect and back ⋮ Quantum pointillism with relational identity ⋮ Born-Jordan quantization and the equivalence of the Schrödinger and Heisenberg pictures ⋮ Huygens triviality of the time-independent Schrödinger equation. Applications to atomic and high energy physics ⋮ Quantum polar duality and the symplectic camel: a new geometric approach to quantization ⋮ From Weyl to Born-Jordan quantization: the Schrödinger representation revisited ⋮ Imprints of the underlying structure of physical theories ⋮ Hamiltonian deformations of Gabor frames: first steps ⋮ Quantum Trajectories: Dirac, Moyal and Bohm

Cites Work

• Pure quantum interpretations are not viable
• Why the Hamilton operator alone is not enough
• The symplectic camel and the uncertainty principle: the tip of an iceberg?
• Pseudo holomorphic curves in symplectic manifolds
• Manifolds, tensor analysis, and applications.
• Sur la structure du groupe des difféomorphismes qui preservent une forme symplectique
• Weyl transforms
• Foundations of time-frequency analysis
• Symplectic geometry and quantum mechanics
• The \(C^ *\)-algebras of a free Boson field
• \(C^ *\)-algèbres des systèmes canoniques. I
• Feynman’s derivation of the Schrödinger equation
• Geometry and uncertainty
• Schrödinger equation from an exact uncertainty principle
• Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Imprints of the quantum world in classical mechanics