标题： 非交换石墨烯的规范群量子化与对称和兰道对偶磁场 显示英文标题

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

摘要： 规范群量子化方法被用来研究在双磁场存在下的非对易石墨烯。 相空间$\mathbb{R}^2\times \mathbb{R}^2$的规范群，在对称和兰道双规范下被证明等价于$\mathtt{H}^2\rtimes \mathbb{R}$。 对称和兰道双规范的表示导致类似的规范对易关系，我们观察到能谱被两个双磁场修正，得到相同的结果。 显示英文摘要

摘要： 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.