  Quantum field theory provides us with the means to calculate scattering
amplitudes. In recent years a dramatic new development has lead to great
simplification of such calculations. This is based on the discovery of
the``amplituhedron'' in the context of scattering of massless gauge bosons in
Yang-Mills theory. One of the main challenges facing Loop Quantum Gravity is
the lack of a clear description of particle scattering processes and a
connection to flat space QFT. Here we show a correspondence between the space
of kinematic data of the scattering $ N $ massless particles and $ U(N) $
coherent states in LQG. This correspondence allows us to provide the outlines
of a theory of quantum gravity based upon the dynamics of excitations living on
the the positive Grassmannian.
