Quantum mechanics on manifolds and topological effects

DOI10.1007/s11005-007-0188-5zbMath1189.81095arXiv0707.3357OpenAlexW2080720742MaRDI QIDQ2475206

Giovanni Morchio, Franco Strocchi

Publication date: 11 March 2008

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

Full work available at URL: https://arxiv.org/abs/0707.3357

zbMATH Keywords

observable algebraLie-Rinehart algebrasquantum mechanics on manifoldsquantum topological effects

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) General quantum mechanics and problems of quantization (81S99) 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

Background potentials and superselection sectors, Gauge invariance and symmetry breaking by topology and energy gap, Aharonov-Bohm superselection sectors, Classical and quantum mechanics from the universal Poisson-Rinehart algebra of a manifold, Quantum charges and spacetime topology: the emergence of new superselection sectors, The Lie-Rinehart universal Poisson algebra of classical and quantum mechanics, Manifold topology, observables, and gauge group

Cites Work

• \(C^*\)-algebraic quantization and the origin of topological quantum effects
• Topological factors derived from Bohmian mechanics
• Lie groupoids and Lie algebroids in physics and noncommutative geometry
• Quantization of Nonlinear Systems
• QUANTIZATION AND SUPERSELECTION SECTORS I: TRANSFORMATION GROUP C*-ALGEBRAS
• Differential Forms on General Commutative Algebras
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