闭环：从EPRL-FK自旋泡沫到Regge动力学
Closing the Loop: from EPRL-FK spinfoams to Regge dynamics
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中文总结 AI 辅助
本文针对EPRL-FK自旋泡沫模型半经典极限仅描述平坦几何的局限，通过引入几何闭合约束，证明其与Regge微积分等价，从而重构弯曲时空并导出长度-Regge方程。
中文摘要 AI 辅助
EPRL-FK自旋泡沫模型在固定离散化下的半经典区域面临一个重大限制：其主导构型仅描述平坦几何。我们探究变分原理需要何种附加条件才能重现Regge微积分（广义相对论的标准离散化）的运动方程。我们将EPRL-FK模型改写为楔形-和乐变量，并识别出几何闭合是缺失的条件。我们证明，将几何闭合作为附加约束与局部平坦性一起施加，能够重构弯曲几何。在具有类空四面体的规则、非退化洛伦兹分支上，模去规范，它们定义了一个与长度-Regge几何空间等价的约束面。限制在该面上的楔形作用变为Regge作用，其切向变分产生长度-Regge方程。最后，我们提出一种直接在自旋泡沫振幅中实现几何闭合的方法。借助这一附加约束，EPRL-FK模型在其半经典区域因此等价于Regge微积分。
英文摘要
The EPRL-FK spinfoam model in its semiclassical regime at fixed discretization faces a big limitation: its dominant configurations describe only flat geometries. We ask what additional condition is needed for the variational principle to reproduce the equations of motion of Regge calculus, the standard discretization of General Relativity. We recast the EPRL-FK model in wedge-holonomy variables and identify geometric closure as the missing condition. We prove that imposing geometric closure as an additional constraint alongside local flatness allows us to reconstruct curved geometries. On a regular, nondegenerate Lorentzian branch with spacelike tetrahedra, modulo gauge, they define a constraint surface equivalent to the space of length-Regge geometries. The wedge action restricted to this surface becomes the Regge action, and its tangent variations yield the length-Regge equations. Finally, we propose a way to implement geometric closure directly in the spinfoam amplitude. With this additional constraint, the EPRL-FK model is therefore equivalent to Regge calculus in its semiclassical regime.
发表机构
- Aix-Marseille Univ, Universit\'e de Toulon, CNRS, CPT, Marseille, France
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