# Group theoretical foundations of Noncommutative quantum mechanics

### What is it about?

Many articles were written on Noncommutative quantum mechanics lately. If one looks at any representation of NCQM, one discovers nothing new since it is an ordinary basis change of standard quantum mechanics! We show in this paper and one coming up shortly that the unitary irreducible representations of the defining group of quantum mechanics, i.e. the Weyl-Heisenberg group are sitting inside the unitary dual of the triply extended group of translations which is the defining group of NCQM.

### Why is it important?

We quantize a 2 dimensional plane using the coherent states obtained from the unitary irreducible representations of centrally extended (2+1)-Galilei group and obtain noncommutative quantum mechanics as result. Noncommutative quantum mechanics is no less natural than the standard quantum mechanics and the unitary dual of the defining group (2 dimensional Weyl-Heisenberg group) of the former contains the UIRs of the latter (triply extended group of translations in R^4 as introduced in the paper).

The following have contributed to this page: Syed Chowdhury and Syed Chowdhury