The Lie-Rinehart universal Poisson algebra of classical and quantum mechanics

DOI10.1007/s11005-008-0280-5zbMath1175.81135arXiv0805.2870OpenAlexW2606835034WikidataQ115381905 ScholiaQ115381905MaRDI QIDQ1035782

Franco Strocchi, Giovanni Morchio

Publication date: 4 November 2009

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0805.2870

zbMATH Keywords

canonical quantizationclassical mechanicsLie-Rinehart algebrasnoncommutative Poisson algebrasquantum mechanics on manifolds

Mathematics Subject Classification ID

Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, (W)-algebras and other current algebras and their representations (81R10) Poisson manifolds; Poisson groupoids and algebroids (53D17) Geometry and quantization, symplectic methods (81S10) Noncommutative geometry in quantum theory (81R60) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70) Operator algebra methods applied to problems in quantum theory (81R15)

Related Items (1)

Classical and quantum mechanics from the universal Poisson-Rinehart algebra of a manifold

Cites Work

• Ring theory from symplectic geometry
• Cohomology and deformation of Leibniz pairs
• On the Poisson envelope of a Lie algebra. ``Noncommutative moment space
• Quantum mechanics on manifolds and topological effects
• Lie groupoids and Lie algebroids in physics and noncommutative geometry
• Differential Forms on General Commutative Algebras
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