Malaysian Journal of Mathematical Sciences, June 2014, Vol. 8(S)
Special Issue: The 6th Asia-Pacific Conference and Workshop in Quantum Information Science 2012 (APCWQIS2012)
On the Group Theory of 2-Dimensional Noncommutative Quantum Mechanics
S. Twareque Ali and S. Hasibul Hassan Chowdhury
Corresponding Email: [email protected]
Received date: -
Accepted date: -
Abstract:
We examine here, in some detail, the symmetry groups of a non-relativistic quantum system of 2 spatial degrees of freedom. It is argued that the (2+1) centrally extended Galilei group $G_{Gal}^{ext}$ can be considered as one of the underlying symmetry groups from the algebraic point of view. Later, the phase space variables of a particle moving on a 2 dimensional plane are quantized using the coherent states arising from the unitary dual of $G_{Gal}^{ext}$. The resulting quantized variables are found to satisfy the set of commutation relations which are postulated in the existing literatures of noncommutative quantum mechanics. We also consider a further extension resulting in the noncommutativity between the underlying momentum coordinates and explore how this is connected to the triple central extension of the abelian group of translations in $\mathbb{R}^{4}$ and its unitary irreducible representations.
Keywords: -
