doi:10.1103/PhysRevD.105.126013engGubitosi, G.Lizzi, F.Relancio, J. J.Vitale, P.Double quantizationART-2022-129576In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to a quantum structure with new properties. A possible way to take into account these quantum effects is through a noncommutativity of spacetime coordinates. In the literature, there is not a clear way to describe at the same time a noncommutativity of spacetime and the phase-space noncommutativity of quantum mechanics. In this paper we address this issue by constructing a Drinfel''d twist in phase space which deals with both quantizations. This method can be applied to a noncommutativity which involves only space, leaving time aside. We apply our construction to the so-called ?-Minkowski and R?3 noncommutative spaces. © 2022 authors. Published by the American Physical Society.2022http://zaguan.unizar.es/record/11818810.1103/PhysRevD.105.126013http://zaguan.unizar.es/record/118188oai:zaguan.unizar.es:118188info:eu-repo/grantAgreement/ES/AEI/PID2019-105614GB-C21Physical Review D 105, 12 (2022), 126013 [12 pp]byhttp://creativecommons.org/licenses/by/3.0/es/info:eu-repo/semantics/openAccess