Aspects of the evolution dynamics of GR in the chiral formalism

本项目的目的是将最近发展的手性形式用于4D GR的微扰计算。在该形式中，有两个传播场，一个是具有16个分量的四分场，一个是具有16个分量的手性规范场，该规范场在规范固定后也具有16个分量。这种形式主义是Yang-Mills手性形式主义的重力类比，也就是Chalmers-Siegal行为。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中只有三次，在GR中只有三次和四次。这种形式的另一个区别在于辅助场不传播，即从连接理论的两个场的3个可能的传播量中，一个完全消失。这大大简化了费曼图的计算。在参考文献中描述了YM和GR的手性形式的一些方面。这个项目的目的是把这个手性GR微扰理论应用，并计算一些感兴趣的散射振幅。该项目将从4点引力子树级散射的预热计算开始（使用旋量螺旋度形式）。一个更具挑战性的计算是环路振幅的计算，特别是那些与非相对论性极限相关的计算，这是分析GR中有效的二体问题（用于产生黑洞合并的引力波形式）所需要的。该项目旨在使用计算能力强大的引力手性微扰形式来简化产生引力波形式所需的计算。

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.