Journal of Physical Studies 24(2), Article 2002 [10 pages] (2020) DOI: https://doi.org/10.30970/jps.24.2002 ON THE NONCOMMUTATIVE GEOMETRY IN QUANTUM MECHANICS Ilyas Haouam  Laboratoire de Physique Mathématique et de Physique Subatomique (LPMPS), Université Frères Mentouri, Constantine, Algeria Received 20 December 2019; in final form 12 March 2020; accepted 07 April 2020; published online 03 May 2020

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 field theory. In particular, we briefly explained the Weyl quantization, the Moyal-Weyl product, the Bopp-shift transformations, and the Seiberg-Witten maps.

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