标题： 环量子引力是一种量子场论吗？ 显示英文标题

标题： Is Loop Quantum Gravity a QFT ?

摘要： 我们研究环量子引力的运动学设置在多大程度上可以融入代数量子场论的微分同胚不变设置，该设置推广了Wightman型量子场论的Haag-Kastler设置。 由量子几何的自旋网络态产生的局部 (Weyl-)代数立即容纳了单调性和微分同胚协变性，并且通过底层流形的锥体的微分同胚不变叶状结构可以实现因果性的表述。 在空间视界上，如果圆柱函数的支撑图在内部边界球面上以无限多个穿刺点相交，量子几何将渐近地成为具有无限自由度的真实量子场论。 显示英文摘要

摘要： We investigate up to which extend the kinematic setting of loop quantum gravity can be fit into a diffeomorphism invariant setting of algebraic QFT generalizing the Haag-Kastler setting of Wightman type QFT. The net of local (Weyl-)algebras resulting from a spin network state of quantum geometry immediately accommodates isotony and diffeomorphism covariance, and formulation of causality becomes possible via of diffeomorphism invariant foliations of the underlying manifold by cones. On a spatial horizon, quantum geometry becomes asymptotically a genuine QFT with infinitely many degrees of freedom, if the cylinder functions' supporting graphs intersect the inner boundary spheres in an infinite number of punctures.