标题： ER = EPR 在环量子引力中的情况：伊米里参数和连续极限 显示英文标题

标题： ER = EPR in Loop Quantum Gravity: the Immirzi Parameter and the Continuum Limit

摘要： 我们将支撑ER=EPR计划的爱因斯坦方程的有限区域分析重新表述为环量子引力（LQG）框架。 通过将曲率-能量不确定性关系转化为全息通量运动学，并将普朗克尺度的爱因斯坦-罗森喉与自旋网络上的单穿刺切割相联系，我们得到了纠缠和量子几何之间的精确字典。 在这个字典中，我们直接从最小桥的纠缠/面积增量中推导出Barbero-Immirzi参数，并表明边界边模式构造使Bekenstein-Hawking熵系数具有普遍性，并且在自然复极化下与$\gamma$无关。 我们进一步建立了一个由有限区域曲率能量界限驱动的自旋泡沫振幅精炼重整化流，该流抑制了泡状发散，并在显式条件下给出了与调节器无关的连续极限。 最后，我们指出从$N$方广义不确定性关系中得出的观测后果。 显示英文摘要

摘要： We recast the finite-region analysis of Einstein's equations that underpins the ER=EPR program into the loop quantum gravity (LQG) framework. By translating curvature-energy uncertainty relations into holonomy-flux kinematics, and by identifying Planckian Einstein-Rosen throats with single-puncture cuts through spin networks, we obtain a precise dictionary between entanglement and quantum geometry. Within this dictionary we derive the Barbero-Immirzi parameter directly from the entanglement/area increment of a minimal bridge, and show that a boundary edge-mode construction renders the Bekenstein - Hawking entropy coefficient universal and independent of $\gamma$ under a natural complex polarization. We further establish a refinement renormalization flow for spin-foam amplitudes driven by the finite-region curvature energy bound, which suppresses bubble divergences and yields a regulator-independent continuum limit under explicit conditions. Finally, we indicate observational consequences that follow from an $N$-party generalized uncertainty relation.