Is Loop Quantum Gravity a QFT ?

Martin Rainer

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Is Loop Quantum Gravity a QFT ?

Martin Rainer

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Abstract

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.

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Martin Rainer. 2000-01-31. Is Loop Quantum Gravity a QFT ?. https://arxiv.org/abs/gr-qc/9912011

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