de Sitter空间中的扭转和对极
Twistors and antipodes in de Sitter space
摘要：
我们发展了德西特空间中扭量理论的基础，直到自由无质量场的彭罗斯变换。我们把德西特空间作为基本空间，就像在扭量理论的传统介绍中对闵可夫斯基空间所做的那样。这涉及到将扭子视为de Sitter群SO（4，1）的旋量。当附着在一个时空点上时，这样的扭量可以被重新解释为局域SO（3，1）狄拉克旋量。我们的方法突出了de Sitter空间中的对映映射，这引起了扭曲和时空之间的标准关系的质疑。特别地，可以从单个扭量函数生成具有两个手性符号的场。这样的场自然地存在于反足的de Sitter空间dS_4/Z_2上，该空间被认为是正宇宙学常数量子引力的理想实验室。
英文摘要：
We develop the basics of twistor theory in de Sitter space, up to the Penrose transform for free massless fields. We treat de Sitter space as fundamental, as one does for Minkowski space in conventional introductions to twistor theory. This involves viewing twistors as spinors of the de Sitter group SO(4,1). When attached to a spacetime point, such a twistor can be reinterpreted as a local SO(3,1) Dirac spinor. Our approach highlights the antipodal map in de Sitter space, which gives rise to doublings in the standard relations between twistors and spacetime. In particular, one can generate a field with both handedness signs from a single twistor function. Such fields naturally live on antipodally-identified de Sitter space dS_4/Z_2, which has been put forward as the ideal laboratory for quantum gravity with positive cosmological constant.
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