nLab Giuseppe Marmo

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Selected writings

On fiber bundles in physics:

• Aiyalam P. Balachandran, Giuseppe Marmo, Bo-Sture Skagerstam, A. Stern, Gauge Symmetries and Fibre Bundles, Lect. Notes in Physics 188 Springer (1983) [arXiv:1702.08910]

and with emphasis on solitons and Skyrmions:

• Aiyalam P. Balachandran, Giuseppe Marmo, Bo-Sture Skagerstam: Classical Topology and Quantum States, World Scientific (1991) [doi:10.1142/1180]

On the spin-statistics theorem for non-relativistic particles via the topology of their configuration spaces of points:

• Aiyalam P. Balachandran, A. Daughton, Z. C. Gu, Giuseppe Marmo, Rafael D. Sorkin Spin statistics theorems without relativity or field theory, Int. J. Mod. Phys. A 8 (1993) 2993-3044 [doi:10.1142/S0217751X93001223]

On canonical commutation relations:

• Elisa Ercolessi, Giuseppe Marmo Giuseppe Morandi, From the Equations of Motion to the Canonical Commutation Relations, Riv. Nuovo Cim. 33 (2010) 401-590 [arXiv:1005.1164, doi:10.1393/ncr/i2010-10057-x]

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: 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],

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