Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-$\Delta_3$ complex
Abstract
The complex critical points are analyzed in the 4-dimensional Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam model in the large- regime. For the 4-simplex amplitude, taking into account the complex critical point generalizes the large- asymptotics to the situation with non-Regge boundary data and relates to the twisted geometry. For generic simplicial complexes, we present a general procedure to derive the effective theory of Regge geometries from the spinfoam amplitude in the large- regime by using the complex critical points. The effective theory is analyzed in detail for the spinfoam amplitude on the double- simplicial complex. We numerically compute the effective action and the solution of the effective equation of motion on the double- complex. The effective theory reproduces the classical Regge gravity when the Barbero-Immirzi parameter is small.
Cite
@article{arxiv.2301.02930,
title = {Complex critical points in Lorentzian spinfoam quantum gravity: 4-simplex amplitude and effective dynamics on double-$\Delta_3$ complex},
author = {Muxin Han and Hongguang Liu and Dongxue Qu},
journal= {arXiv preprint arXiv:2301.02930},
year = {2023}
}
Comments
29 pages, 15 figures