The Spinorial Formulations of Scattering Amplitudes and Loop Quantum Gravity

Abstract

We study the Spinor Helicity formalism used to represent scattering data in the calculation of scattering amplitudes and the spinorial formulation of Loop Quantum Gravity and establish a correspondence between the two. We show that the kinematic space of the scattering of N massless particles is represented by the complex Grassmannian G(2,N) which also represents the set of U(N) invariant coherent states defined by Friedel and Livine. We further show that our correspondence implies the correspondence between the closure constraint, the Gauss’s law in the intertwiner space and the conservation of the spatial components of momenta in the scattering amplitude picture. We further show that this correspondence implies that the total energy of the scattering amplitude corresponds to the total area of the coherent state.