Double quantization

In a quantum gravity theory, it is expected that the classical notion of spacetime disappears, leading to structure with new properties. A possible way take into account these effects through noncommutativity coordinates. literature, there not clear describe at same time and phase-space mechanics. this paper we address issue by constructing Drinfel'd twist in phase space which deals both quantizations. This method can be applied involves only space, leaving aside. We apply our construction so-called $\ensuremath{\lambda}$-Minkowski ${\mathbb{R}}_{\ensuremath{\lambda}}^{3}$ noncommutative spaces.