Groupoidal picture of Quantum Mechanics

This project aims to investigate the use of groupoids in the context of quantum mechanics, quantum information theory, and quantum field theory. The idea of associating a groupoid with a quantum system may be traced back to Schwinger’s seminal work.

The list is ordered according to the date of publication/arXiv submission, and not the date of creation.

F.M. Ciaglia, A. Ibort, and G. Marmo: A gentle introduction to Schwinger’s formulation of quantum mechanics: The groupoid picture: Modern physics letters a 33(20): 2018-06: doi: 10.1142/S0217732318501225. Available at: https://arxiv.org/abs/1807.00519

F.M. Ciaglia, A. Ibort, and G. Marmo: Schwinger’s picture of quantum mechanics I: Groupoids: International journal of geometric methods in modern physics 16(08): 2019-08: doi: 10.1142/S0219887819501196. Available at: https://arxiv.org/abs/1905.12274

F.M. Ciaglia, A. Ibort, and G. Marmo: Schwinger’s picture of quantum mechanics II: Algebras and observables: International journal of geometric methods in modern physics 16(09): 2019-09: doi: 10.1142/S0219887819501366. Available at: https://arxiv.org/abs/1907.03883

F.M. Ciaglia, A. Ibort, and G. Marmo: Schwinger’s picture of quantum mechanics III: The statistical interpretation: International journal of geometric methods in modern physics 16(11): 2019-11: doi: 10.1142/S0219887819501652. Available at: https://arxiv.org/abs/1909.07265

F.M. Ciaglia, F. Di Cosmo, A. Ibort, and G. Marmo: Schwinger’s picture of quantum mechanics: International journal of geometric methods in modern physics 17(04): 2020-03: doi: 10.1142/S0219887820500541. Available at: https://arxiv.org/abs/2002.09326

F.M. Ciaglia, F. Di Cosmo, A. Ibort, and G. Marmo: Schwinger’s picture of quantum mechanics IV: Composition and independence: International journal of geometric methods in modern physics 17(04): 2020-03: doi: 10.1142/S0219887820500589. Available at: https://arxiv.org/abs/2004.02472

F.M. Ciaglia, F.D. Di Cosmo, A. Ibort, and G. Marmo: Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics: Entropy 22(11): 2020-11: doi: 10.3390/e22111292. Available at: https://arxiv.org/abs/2012.10284

F.M. Ciaglia, F. Di Cosmo, A. Ibort, G. Marmo, L. Schiavone, and A. Zampini: A quantum route to the classical Lagrangian formalism: Modern physics letters a 36(15): 2021-05: doi: 10.1142/S0217732321500917. Available at: https://arxiv.org/abs/2106.00998

F.M. Ciaglia, F. Di Cosmo, A. Ibort, G. Marmo, L. Schiavone, and A. Zampini: Feynman’s propagator in Schwinger’s picture of Quantum Mechanics: Modern physics letters a 36(26): 2021-08: doi: 10.1142/S021773232150187X. Available at: https://arxiv.org/abs/2109.05756

F.M. Ciaglia, F.D. Cosmo, A. Ibort, G. Marmo, and L. Schiavone: Schwinger’s picture of quantum mechanics: 2-groupoids and symmetries: Journal of geometric mechanics 13(3): 2021-09: doi: 10.3934/jgm.2021008. Available at: https://arxiv.org/abs/2104.13880

F.M. Ciaglia, F. Di Cosmo, A. Ibort, G. Marmo, L. Schiavone, and A. Zampini: Causality in Schwinger’s Picture of Quantum Mechanics: Entropy 24(1): 2022-01: doi: 10.3390/e24010075. Available at: https://www.mdpi.com/1099-4300/24/1/75

F.M. Ciaglia, F. Di Cosmo, A. Ibort, and G. Marmo: Quantum tomography and Schwinger’s picture of quantum mechanics: Journal of physics a: Mathematical and theoretical 55(27): 2022-07: doi: 10.1088/1751-8121/ac7591. Available at: https://arxiv.org/abs/2205.00170

F.M. Ciaglia, F. Di Cosmo, A. Ibort, and G. Marmo: Dynamical Maps and Symmetroids: Open systems & information dynamics 28(04): 2022-07: doi: 10.1142/S1230161221500190. Available at: https://arxiv.org/abs/2205.06734

F.M. Ciaglia, F. Di Cosmo, P. Facchi, A. Ibort, A. Konderak, and G. Marmo: Groupoid and algebra of the infinite quantum spin chain: Journal of geometry and physics 191: 2023-06: doi: 10.1016/j.geomphys.2023.104901. Available at: https://arxiv.org/abs/2302.01050

F.M. Ciaglia, F. Di Cosmo, A. Ibort, and G. Marmo: The groupoidal picture of quantum mechanics: Journal of geometry and physics 197: 2024-01: doi: 10.1016/j.geomphys.2023.105095. Available at: https://doi.org/10.1016/j.geomphys.2023.105095