Arguments that the proposal of Schwinger 1969, Schwinger & Berthold-Englert 2001 for an “algebra of (selective) measurement” in quantum physics is to be understood as groupoid convolution algebra of groupoids whose morphisms reflect transitions between possible quantum measurement-outcomes:
Florio M. Ciaglia, Alberto Ibort, Giuseppe Marmo: A gentle introduction to Schwinger’s formulation of quantum mechanics: The groupoid picture, Modern Physics Letters A, 33 20 (2018) [doi:10.1142/S0217732318501225, arXiv:1807.00519]
Florio M. Ciaglia, Alberto Ibort, Giuseppe Marmo: Schwinger’s Picture of Quantum Mechanics I: Groupoids, Int. J. Geometric Methods in Modern Physics 16 08 (2019) 1950119 [doi:10.1142/S0219887819501196, arXiv:1905.12274]
Florio M. Ciaglia, Alberto Ibort, Giuseppe Marmo: Schwinger’s Picture of Quantum Mechanics II: Algebras and Observables, Int. J. Geometric Methods in Modern Physics 16 09 (2019) 1950136 [doi:10.1142/S0219887819501366, arXiv:1907.03883]
Florio M. Ciaglia, Alberto Ibort, Giuseppe Marmo: Schwinger’s Picture of Quantum Mechanics II: Algebras and Observables, Int. J. Geometric Methods in Modern Physics 16 11 (2019) 1950165 [doi:10.1142/S0219887819501652, arXiv:1909.07265]
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo: Schwinger’s Picture of Quantum Mechanics IV: Composition and independence, Int. J. Geometric Methods in Modern Physics 17 04 (2020) 2050058 [doi:10.1142/S0219887820500589, arXiv:2004.02472]
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo: Schwinger’s picture of Quantum Mechanics, Int. J. Geometric Methods in Modern Physics 17 04 (2020) 2050054 [doi:10.1142/S0219887820500541, arXiv:2002.09326]
and as such further developed in:
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo: Schrödinger’s problem with cats: measurements and states in the Groupoid Picture of Quantum Mechanics, Entropy 22 11 (2020) [doi:10.3390/e22111292, arXiv:2012.10284]
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo, Luca Schiavone: Schwinger’s picture of quantum mechanics: 2-groupoids and symmetries, Journal of Geometric Mechanics 13 3 (2021) [doi:10.3934/jgm.2021008, arXiv:2104.13880]
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo: Quantum Tomography and Schwinger’s Picture of Quantum Mechanics, Journal of Physics A: Mathematics and Theoretical 55 27 (2022) [doi:10.1088/1751-8121/ac7591, arXiv:2205.00170]
Florio M. Ciaglia, Fabio Di Cosmo, Paolo Facchi, Alberto Ibort, Arturo Konderak, Giuseppe Marmo: Groupoid and algebra of the infinite quantum spin chain, Journal of Geometry and Physics 191 (2023) [doi:10.1016/j.geomphys.2023.104901, arXiv:2302.01050],
Review:
On groupoids and their representation theory (groupoid representations, groupoid algebras):
On smooth sets as a foundation for classical field theory/variational calculus:
Last revised on October 26, 2025 at 11:01:04. See the history of this page for a list of all contributions to it.