超扭量理论的几何构造
Geometrical Construction of Supertwistor Theory
摘要：
超扭量理论是基于超对称霍普夫映射的几何构造。我们导出了几何超扭量理论的一个新的关联关系。本超扭量具有显著的性质：Minkowski空间不需要复杂化以引入自旋自由度，并且偶数SUSY由几何设置{自动}并入。我们还发展了闵可夫斯基超空间中的无质量自由粒子理论，它在物理上对应于几何超扭量理论。自旋自由度来源于费米子动量和费米子坐标。对几何超扭量进行量子化，再现了与原超扭量理论相同的物理内容。讨论了超自旋理论与超对称量子霍尔效应的关系。
英文摘要：
Supertwistor theory is geometrically constructed based on the SUSY Hopf map. We derive a new incidence relation for the geometrical supertwistor theory. The present supertwistor exhibits remarkable properties: Minkowski space need not be complexified to introduce spin degrees of freedom, and even number SUSY is {automatically} incorporated by the geometrical set-up. We also develop a theory for massless free particle in Minkowski superspace, which physically corresponds to the geometrical supertwistor theory. The spin degrees of freedom are originated from fermionic momenta as well as fermionic coordinates. The geometrical supertwistor is quantized to reproduce same physical contents as in the original supertwistor theory. Relationships to superspin formalism and SUSY quantum Hall effect are also discussed.
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