Relativistic Landau Models and Generation of Fuzzy Spheres
Relativistic Landau Models and Generation of Fuzzy Spheres
复制标题
相对论朗道模型和模糊球的生成
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
K. Hasebe
中科院分区：
文献类型：
--
作者：
K. Hasebe
作为水平投影的结果，非交换几何自然地出现在朗道模型的低能物理中。在这项工作中，我们主动利用水平投影作为生成模糊几何的有效工具。能级投影专门应用于相对论朗道模型。论文的前半部分详细分析了球面上的相对论朗道问题，基于代数方法得到了狄拉克-朗道算子本征态的简洁表达式。我们在相对论朗道模型和泡利-薛定谔非相对论量子力学之间建立了 SU(2)“规范”变换。经过SU(2)变换后，发现狄拉克算子和角动量算子满足SO(3, 1)代数。后半部分阐明了相对论朗道能级产生的模糊几何，阐明了相对论模糊几何的独特性质。我们考虑相对论朗道模型的质量变形，并证明其对模糊几何的几何影响。超模糊几何也是从超对称量子力学构造为狄拉克-朗道算子的平方。最后，我们将水平投影方法应用于真实的石墨烯系统来生成谷模糊球。
Noncommutative geometry naturally emerges in low energy physics of Landau models as a consequence of level projection. In this work, we proactively utilize the level projection as an effective tool to generate fuzzy geometry. The level projection is specifically applied to the relativistic Landau models. In the first half of the paper, a detail analysis of the relativistic Landau problems on a sphere is presented, where a concise expression of the Dirac–Landau operator eigenstates is obtained based on algebraic methods. We establish SU(2) “gauge” transformation between the relativistic Landau model and the Pauli–Schrodinger nonrelativistic quantum mechanics. After the SU(2) transformation, the Dirac operator and the angular momentum operators are found to satisfy the SO(3, 1) algebra. In the second half, the fuzzy geometries generated from the relativistic Landau levels are elucidated, where unique properties of the relativistic fuzzy geometries are clarified. We consider mass deformation of the relativistic Landau models and demonstrate its geometrical effects to fuzzy geometry. Super fuzzy geometry is also constructed from a supersymmetric quantum mechanics as the square of the Dirac–Landau operator. Finally, we apply the level projection method to real graphene system to generate valley fuzzy spheres.
DOI：
10.1515/9781400846733
发表时间：
2013-04
期刊：
--
影响因子：
--
作者：
B. Bernevig
通讯作者：
B. Bernevig
基于 Atiyah-Singer 指数定理的电荷量化条件
DOI：
--
发表时间：
2006
期刊：
Progress of Theoretical Physics 115
影响因子：
--
作者：
S.Deguchi;K.Kitsukawa
通讯作者：
K.Kitsukawa