Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy
Abstract
Spinfoam amplitudes with small spins can have interesting semiclassical behavior and relate to semiclassical gravity and geometry in 4 dimensions. We study the generalized spinfoam model (Spinfoams for all loop quantum gravity (LQG)) with small spins but a large number of spin degrees of freedom (DOFs), and find that it relates to the simplicial Engle-Pereira-Rovelli-Livine-Freidel-Krasnov (EPRL-FK) model with large spins and Regge calculus by coarse-graining spin DOFs. Small- generalized spinfoam amplitudes can be employed to define semiclassical states in the LQG kinematical Hilbert space. Each of these semiclassical states is determined by a 4-dimensional Regge geometry. We compute the entanglement R\'enyi entropies of these semiclassical states. The entanglement entropy interestingly coarse-grains spin DOFs in the generalized spinfoam model, and satisfies an analog of the thermodynamical first law. This result possibly relates to the quantum black hole thermodynamics in arXiv:1107.1320.
Keywords
Cite
@article{arxiv.1906.05536,
title = {Semiclassical Behavior of Spinfoam Amplitude with Small Spins and Entanglement Entropy},
author = {Muxin Han},
journal= {arXiv preprint arXiv:1906.05536},
year = {2019}
}
Comments
30 pages, 7 figures