Canonical Group Quantization of Noncommutative Graphene with Symmetric and Landau Dual Magnetic Fields

The canonical group quantization approach has been used to study noncommutative graphene in the presence of dual magnetic fields. The canonical group for the phase space $\mathbb{R}^2\times \mathbb{R}^2$ with both symmetric and Landau dual gauges is shown to be equivalent to $\mathtt{H}^2\rtimes \mathbb{R}$. The representations of both symmetric and Landau dual gauges lead to similar canonical commutation relations, and we observe that the energy spectrum is corrected by both dual magnetic fields, yielding the same result.