On the noncommutative geometry in quantum mechanics

In this paper, we presented and reviewed a formalism that plays a central role in most of the investigations concerning noncommutative geometry. We presented existing methods that successfully allow us to utilize and apply the noncommutativity of phase-space in both quantum mechanics and quantum (cid:28)eld theory. In particular, we brie(cid:29)y explained the Weyl quantization, the Moyal(cid:21)Weyl product, the Bopp-shift transformations, and the Seiberg(cid:21)Witten maps.