超对称Landau模型
Supersymmetrizing Landau Models
摘要：
本文综述了均匀磁场中量子粒子在平面上的Landau问题的超延拓及其Halfman的$S^2$推广（{ \tt hep-th/0311159，hep-th/0404108，hep-th/0510019，hep-th/0612300}）的构造和研究的最新进展。主要研究了在非齐次超群ISU（1）下保持不变的平面超Landau模型|超群SU（2）的收缩|1），并提供最小的超扩展的原始朗道模型。它们共同的显着特征是存在一个隐藏的动力学世界线N=2超对称。它存在于经典和量子两个层次上，并且在传递到量子态空间中的新的不变内积以使所有态的范数为正时最自然地被揭示。对于其中一个平面模型，超平面朗道模型，我们提出了一个离壳世界线超场公式，其中N=2的超对称性得到体现。
英文摘要：
This is an overview of recent progress in constructing and studying superextensions of the Landau problem of a quantum particle on a plane in the uniform magnetic field, as well as of its Haldane's $S^2$ generalization ({\tt hep-th/0311159, hep-th/0404108, hep-th/0510019, hep-th/0612300}). The main attention is paid to the planar super Landau models which are invariant under the inhomogeneous supergroup ISU(1|1), a contraction of the supergroup SU(2|1), and provide minimal superextensions of the original Landau model. Their common notable feature is the presence of a hidden dynamical worldline N=2 supersymmetry. It exists at the classical and quantum levels and is revealed most naturally while passing to the new invariant inner products in the space of quantum states in order to make the norms of all states positive. For one of the planar models, the superplane Landau model, we present an off-shell worldline superfield formulation in which the N=2 supersymmetry gets manifest.
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