The Electromagnetic Interactions of Electrons in the Lowest Landau Level
The Electromagnetic Interactions of Electrons in the Lowest Landau Level
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最低朗道能级中电子的电磁相互作用
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
R. Sakita
中科院分区：
文献类型：
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作者：
R. Sakita
摘要：从垂直于平面的强磁场中的平面电子系统出发，并与扰动电磁场相互作用，导出了最低朗道能级（LLL）费米子的有效拉格朗日量。通过选择合适的背景静电势，构建了这些电子的不可压缩液滴。 LLL 中电子的规范不变有效拉格朗日量自然地分裂为液滴表面电子的 (1 + 1) 维拉格朗日量和代表液滴内部贡献的 (2 + 1) 维规范场拉格朗日量。在玻色化时，前者代表液滴的表面振动。单独来看，这两个动作都不是规范不变的，但事实证明，这两个部分的规范依赖性相互抵消。这表明边缘自由度对于保持规范不变性至关重要。
Abstract Starting from a system of planar electrons in a strong magnetic field normal to the plane and interacting with perturbing electromagnetic fields, an effective Lagrangian for the fermions in the lowest Landau level (LLL) has been derived. By choosing a suitable background electrostatic potential, an incompressible droplet of these electrons is constructed. The gauge invariant effective Lagrangian for the electrons in the LLL is shown to split naturally into a (1 + 1)-dimensional Lagrangian for the electrons on the surface of the droplet and into a (2 + 1)-dimensional gauge-field Lagrangian representing the contribution of the interior of the droplet. Upon bosonization, the former represents the surface vibrations of the droplet. Individually neither of these two actions is gauge invariant, but it is shown that the gauge dependences from the two pieces cancel out. This demonstrates that the edge degrees of freedom are essential for maintaining gauge invariance.