The groupoidal picture of quantum mechanics

DOI10.1016/j.geomphys.2023.105095MaRDI QIDQ6146400

Giuseppe Marmo, Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort

Publication date: 5 February 2024

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

zbMATH Keywords

von Neumann algebraquantum mechanicsmeasure groupoidsFeynman's sum

Mathematics Subject Classification ID

Operator algebra methods applied to problems in quantum theory (81R15) Topological groupoids (including differentiable and Lie groupoids) (22A22) Groupoids (i.e. small categories in which all morphisms are isomorphisms) (20L05) Groupoids, semigroupoids, semigroups, groups (viewed as categories) (18B40)

Cites Work

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• Riemannian metrics on Lie groupoids
• On A. Connes' noncommutative integration theory
• A groupoid approach to C*-algebras
• Integrability of Lie brackets
• Theory of operator algebras. II
• Schwinger's picture of quantum mechanics: 2-groupoids and symmetries
• A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics
• Ergodic theory and virtual groups
• Virtual groups and group actions
• Lie groupoids and Lie algebroids in physics and noncommutative geometry
• Families of induced representations
• On rings of operators. Reduction theory
• Postulates for general quantum mechanics
• Algèbres quasi-unitaires
• Categorical quantum mechanics
• Picturing Quantum Processes
• Haar Measure for Measure Groupoids
• The Regular Representations of Measure Groupoids
• A gentle introduction to Schwinger’s formulation of quantum mechanics: The groupoid picture
• A quantum route to the classical Lagrangian formalism
• Feynman’s propagator in Schwinger’s picture of Quantum Mechanics
• Schwinger’s picture of quantum mechanics I: Groupoids
• Space-Time Approach to Non-Relativistic Quantum Mechanics
• The sources of Schwinger's Green's functions
• An Algebraic Approach to Quantum Field Theory
• THE ALGEBRA OF MICROSCOPIC MEASUREMENT
• Operator algebras and Poisson manifolds associated to groupoids
• Groupoid and algebra of the infinite quantum spin chain