论文标题
在非交通相空间中狄拉克汉顿人的代数结构
Algebraic Structure of Dirac Hamiltonians in Non-Commutative Phase Space
论文作者
论文摘要
在本文中，我们从代数的角度研究了在坐标和动量的二维迪拉克汉密尔顿人。为此，我们考虑了由Hermitian双线性形式产生的分级谎言代数$ \ Mathfrak {sl}（2 | 1）$在非交换性动力学变量中生成的，而Dirac矩阵则以$ 2+1 $的尺寸为单位。通过进一步定义一个全角动量操作员，我们能够完全按照这些操作员来表达一类Dirac Hamiltonians。通过这种方式，我们通过构建和研究分级谎言代数$ \ mathfrak {sl}（2 | 1）\ oplus \ mathfrak \ mathfrak {so}（so}（2）$的单位不可约形表示的表示空间来分析某些简单模型的能量谱。作为我们结果的应用，我们考虑了有限圆柱井中的Landau模型和速度。
In this article we study two-dimensional Dirac Hamiltonians with non-commutativity both in coordinates and momenta from an algebraic perspective. In order to do so, we consider the graded Lie algebra $\mathfrak{sl}(2|1)$ generated by Hermitian bilinear forms in the non-commutative dynamical variables and the Dirac matrices in $2+1$ dimensions. By further defining a total angular momentum operator, we are able to express a class of Dirac Hamiltonians completely in terms of these operators. In this way, we analyze the energy spectrum of some simple models by constructing and studying the representation spaces of the unitary irreducible representations of the graded Lie algebra $\mathfrak{sl}(2|1)\oplus \mathfrak{so}(2)$. As application of our results, we consider the Landau model and a fermion in a finite cylindrical well.
