Aspects of the evolution dynamics of GR in the chiral formalism

这个项目的目的是将最近发展的手征形式用于四维GR中的微扰计算。在这种形式中，有两个传播场，一个是有16个分量的四分体场，另一个是手征规范场，它在规范固定后也有16个分量。这种形式主义是杨-米尔斯的手性形式主义的重力类比，他的名字叫查尔默斯-西格尔作用力。在这两种形式中，作用都是多项式的，因此只有有限数量的顶点-在ym中是三次的，在gr中是三次和四次的。这种形式主义的另一个显著特征是辅助场不传播，即从连接理论的两个场的三个可能的传播子中，一个精确地消失了。这大大简化了费曼图的计算。在参考文献中描述了YM和GR的手性形式的某些方面。这个项目的目的是应用这个手征GR微扰理论，并计算一些感兴趣的散射幅度。该项目将从4点引力子树级散射的预热计算开始(使用旋量螺旋度公式)。一个更具挑战性的计算是回路振幅的计算，特别是那些与非相对论极限相关的振幅，这是分析GR中有效的两体问题所需的(用于产生来自BH合并的引力波)。该项目的目标是使用计算功能强大的引力手征微扰理论来简化产生引力波形所需的计算。

The aim of this project is to put to use the recently developed chiral formalism for perturbative calculations in 4D GR. In this formalism, there are two propagating fields, which are a tetrad field with its 16 components, and a chiral gauge field, which after gauge-fixing also has 16 components. This formalism is the gravity analog of the chiral formalism for Yang-Mills known by the name of Chalmers-Siegal action. In both formalism the action is polynomial, and so there is only a finite number of vertices - just cubic in YM, cubic and quartic in GR. The other distinguishing feather of this formalism is that the auxiliary fields do not propagate, i.e. from the 3 possible propagators connecting the two fields of the theory one vanishes exactly. This significantly simplifies Feynman diagram calculations. Some aspects of the chiral formalism for both YM and GR are described in reference. The aim of this project is to put this chiral GR perturbation theory to use, and compute some scattering amplitudes of interest. The project will start with warm up calculations of the 4-point graviton tree-level scattering (using the spinor helicity formalism). A more challenging computation is that of loop amplitudes, in particular those relevant in the non-relativistic limit that is needed for analysing the effective 2-body problem in GR (that is used for producing the gravitational wave-forms from BH mergers). THe project will aim to use the computationally powerful chiral perturbative formalism for gravity to simplify the calculations needed for producing the gravitational wave-forms.