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oai:riubu.ubu.es:10259/72222023-03-24T13:07:23Zcom_10259.4_2557com_10259_5086com_10259_2604col_10259_7221

Gubitosi, Giulia 695 600 0000-0001-6107-639X Ballesteros Castañeda, Ángel 46 600 0000-0003-4085-3094 Herranz Zorrilla, Francisco José 280 600 0000-0002-5323-616X 2023-01-09T11:55:21Z 2023-01-09T11:55:21Z 2020-08 1824-8039 http://hdl.handle.net/10259/7222 10.22323/1.376.0190 Trabajo presentado en: Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019) - Workshop on Quantum Geometry, Field Theory and Gravity, 31 August - 25 September, Corfù, Greece Given a group of kinematical symmetry generators, one can construct a compatible noncommutative spacetime and deformed phase space by means of projective geometry. This was the main idea behind the very first model of noncommutative spacetime, proposed by H.S. Snyder in 1947. In this framework, spacetime coordinates are the translation generators over a manifold that is symmetric under the required generators, while momenta are projective coordinates on such a manifold. In these proceedings we review the construction of Euclidean and Lorentzian noncommutative Snyder spaces and investigate the freedom left by this construction in the choice of the physical momenta, because of different available choices of projective coordinates. In particular, we derive a quasi-canonical structure for both the Euclidean and Lorentzian Snyder noncommutative models such that their phase space algebra is diagonal although no longer quadratic. This work has been partially supported by Ministerio de Ciencia, Innovación y Universidades (Spain) under grant MTM2016-79639-P (AEI/FEDER, UE), by Junta de Castilla y León (Spain) under grants BU229P18 and BU091G19. The authors acknowledge the contribution of the COST Action CA18108. application/pdf eng Sissa Proceedings of Science. 2020, V. 376, p. 190-205 https://doi.org/10.22323/1.376.0190 info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/MTM2016-79639-P/ES/GRUPOS CUANTICOS, ALGEBRAS DE POISSON Y SISTEMAS INTEGRABLES info:eu-repo/grantAgreement/Junta de Castilla y León//BU229P18//Modelización matemática en tecnologías cuánticas y nanomateriales info:eu-repo/grantAgreement/Junta de Castilla y León//BU091G19//Grupos cuánticos, modelos integrables y aplicaciones en tecnologías cuánticas info:eu-repo/grantAgreement/COST//CA18108/EU/Quantum gravity phenomenology in the multi-messenger approach/QG-MM/ Attribution-NonCommercial-NoDerivatives 4.0 Internacional http://creativecommons.org/licenses/by-nc-nd/4.0/ info:eu-repo/semantics/openAccess Física Physics Generalized noncommutative Snyder spaces and projective geometry info:eu-repo/semantics/conferenceObject info:eu-repo/semantics/publishedVersion Proceedings of Science 376 190 205 THUMBNAIL Herranz-pos_2020.pdf.jpg Herranz-pos_2020.pdf.jpg IM Thumbnail image/jpeg 4253 https://riubu.ubu.es/bitstream/10259/7222/4/Herranz-pos_2020.pdf.jpg d78bafdb96e91b0805844437c9e55f0a MD5 4 LICENSE license.txt license.txt text/plain; charset=utf-8 998 https://riubu.ubu.es/bitstream/10259/7222/3/license.txt aa90105e1c90a1b4fe810649aa967b7d MD5 3 CC-LICENSE license_rdf license_rdf application/rdf+xml; charset=utf-8 805 https://riubu.ubu.es/bitstream/10259/7222/2/license_rdf 4460e5956bc1d1639be9ae6146a50347 MD5 2 ORIGINAL Herranz-pos_2020.pdf Herranz-pos_2020.pdf application/pdf 511430 https://riubu.ubu.es/bitstream/10259/7222/1/Herranz-pos_2020.pdf 8ddbf5070213cdeb2ce204bf4b99cc35 MD5 1 10259/7222 oai:riubu.ubu.es:10259/7222 2023-03-24 14:07:23.943 Repositorio Institucional de la Universidad de Burgos bubrep@ubu.es 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