Numerical computations of next-to-leading order corrections in spinfoam large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>j</mml:mi></mml:math> asymptotics
Muxin Han, Zichang Huang, Hongguang Liu, Dongxue Qu
Abstract
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 $\ensuremath{\gamma}$. We show that they, as functions of $\ensuremath{\gamma}$, stabilize to finite real constants as $\ensuremath{\gamma}\ensuremath{\rightarrow}\ensuremath{\infty}$. Lastly, we obtain the quantum corrections to the Regge action because of the $O(1/j)$ contribution to the spinfoam amplitude.