The one-loop effective action from the LQG coherent state path integral is computed and found to be UV-finite, with the dynamical area j0 > 0 at the quantum level.
An Exactly Soluble Group Field Theory
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We present a Group Field Theory (GFT) quantization of the Husain-Kucha\v{r} (HK) model formulated as a non-interacting GFT. We demonstrate that the path-integral formulation of this HK-GFT provides a complete spinfoam model and a unique Fock representation that describes the quantum three-geometries of the HK model. These results provide a link to the canonical quantization of the HK model and demonstrate how GFTs can bridge distinct quantization schemes.
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The one-loop effective action from the coherent state path integral of loop quantum gravity
The one-loop effective action from the LQG coherent state path integral is computed and found to be UV-finite, with the dynamical area j0 > 0 at the quantum level.