标题： 扭量空间上的δ函数及其符号因子 显示英文标题

标题： Delta functions on twistor space and their sign factors

摘要： 在将杨-米尔斯理论中的散射振幅从动量空间进行傅里叶变换到实扭量空间时，我们会遇到破坏全局共形不变性的符号因子。先前的研究推测，这些符号因子是对应于分裂签名时空的实扭量空间的固有属性；因此，在对应于洛伦兹签名时空的复扭量空间中它们不会出现。在本研究中，我们通过研究实扭量空间上δ函数的定义域，对这些符号因子提出了新的几何解释。此外，我们提出了一种新的复扭量空间上δ函数的定义，该定义基于Čech上同调群，且没有任何符号因子，并证明这些δ函数具有共形不变性。此外，我们证明了这些δ函数的逆傅里叶变换就是杨-米尔斯理论中的散射振幅。因此，符号因子不会出现在复扭量空间中。 显示英文摘要

摘要： When performing the Fourier transform of the scattering amplitudes in Yang-Mills theory from momentum space to real twistor space, we encounter sign factors that break global conformal invariance. Previous studies conjectured that the sign factors are intrinsic in the real twistor space corresponding to the split signature space-time; hence, they will not appear in the complex twistor space corresponding to the Lorentzian signature space-time. In this study, we present a new geometrical interpretation of the sign factors by investigating the domain of the delta functions on the real twistor space. In addition, we propose a new definition of delta functions on the complex twistor space in terms of the Cech cohomology group without any sign factors and show that these delta functions have conformal invariance. Moreover, we show that the inverse Fourier transforms of these delta functions are the scattering amplitudes in Yang-Mills theory. Thus, the sign factors do not appear in the complex twistor space.