Lorentzian spinfoam gravity path integral and geometrical area-law entanglement entropy

本文探讨了 3+1 维 Lorentzian 协变环路量子引力 (LQG) 中的纠缠熵问题。我们计算了由 spinfoam path integral 对一族 2 复形进行求和所产生的动态状态所构成的空间区域的纠缠熵。 resulting entropy exhibits a geometric area law, $S \simeq \beta a$, where the area $a$ of the entangling surface is determined by the LQG area spectrum and the leading coefficient $\beta>0$ is independent of the underlying 2-complexes. By relating the coupling constant of the sum over 2-complexes to the Barbero-Immirzi parameter $\gamma$, we reproduce the Bekenstein-Hawking formula for the range $0 < \gamma \lesssim 1/2$. This work provides a Lorentzian path integral approach to gravitational entropy without the need for contour prescriptions.