Is Loop Quantum Gravity a QFT ?
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.
引用
@article{arxiv.gr-qc/9912011,
title = {Is Loop Quantum Gravity a QFT ?},
author = {Martin Rainer},
journal= {arXiv preprint arXiv:gr-qc/9912011},
year = {2007}
}
备注
10 pages, latex & AMS symb., presented at ERE 99 (Bilbao), v2: errors & misprints corrected at beginning/end of sec.2, and in sec. 4