Aspects of the evolution dynamics of GR in the chiral formalism

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.