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

DOI10.1016/S0034-4877(09)90018-0zbMath1204.81103arXiv0901.0870OpenAlexW3104236148MaRDI QIDQ963200

Franco Strocchi, Giovanni Morchio

Publication date: 8 April 2010

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0901.0870

zbMATH Keywords

quantizationPoisson algebrasLie-Rinehart algebras

Mathematics Subject Classification ID

Poisson manifolds; Poisson groupoids and algebroids (53D17) Geometry and quantization, symplectic methods (81S10) Relativistic dynamics for problems in Hamiltonian and Lagrangian mechanics (70H40) Poisson algebras (17B63) Differential geometric methods, including holonomy, Berry and Hannay phases, Aharonov-Bohm effect, etc. in quantum theory (81Q70)

Cites Work

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• Quantization of Nonlinear Systems
• QUANTIZATION AND SUPERSELECTION SECTORS I: TRANSFORMATION GROUP C*-ALGEBRAS
• QUANTIZATION METHODS: A GUIDE FOR PHYSICISTS AND ANALYSTS
• Differential Forms on General Commutative Algebras

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