Numerical computations of next-to-leading order corrections in spinfoam largej asymptotics

We numerically study the next-to-leading order corrections of the Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) 4-simplex amplitude in the large-j expansions. We perform large-j expansions of Lorentzian EPRL 4-simplex amplitudes with two different types of boundary states, the coherent intertwiners and the coherent spin-network, and numerically compute the leading-order and the next-to-leading order O(1 / j) contributions of these amplitudes. We also study the dependences of these O(1 / j) corrections on the Barbero-Immirzi parameter γ . We show that they, as functions of γ, stabilize to finite real constants as γ →∞ . Lastly, we obtain the quantum corrections to the Regge action because of the O(1 / j) contribution to the spinfoam amplitude.