Geometric quantum states and Lagrangian polar duality: quantum mechanics without wavefunctions

DOI10.1007/978-3-031-38299-4_43OpenAlexW4385434597MaRDI QIDQ6179032

Maurice A. De Gosson

Publication date: 16 January 2024

Published in: Lecture Notes in Computer Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-031-38299-4_43

zbMATH Keywords

Lagrangian planeuncertainty principleJohn ellipsoidpolar dualityWigner transform

Mathematics Subject Classification ID

Approximation in the complex plane (30E10) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Frames, locales (06D22) Polar geometry, symplectic spaces, orthogonal spaces (51A50) Natural dualities for classes of algebras (08C20) Uncertainty relations, also entropic (81S07)

Cites Work

• Unnamed Item
• Quantum indeterminacy and polar duality
• Quantum blobs
• From symplectic measurements to the Mahler conjecture
• The symplectic camel and the uncertainty principle: the tip of an iceberg?
• Ellipsoids of maximal volume in convex bodies
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• Symplectic coarse-grained dynamics: chalkboard motion in classical and quantum mechanics
• Polar duality between pairs of transversal Lagrangian planes; applications to uncertainty principles
• Quantum polar duality and the symplectic camel: a new geometric approach to quantization
• Symplectic geometry and quantum mechanics
• Spacetime symmetries and the uncertainty principle
• Pointillisme à la Signac and construction of a quantum fiber bundle over convex bodies

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