An Exactly Soluble Group Field Theory

TL;DR

This paper introduces a solvable Group Field Theory for the Husain-Kuchař model, establishing a complete spinfoam representation and connecting canonical and path-integral quantizations of quantum geometry.

Contribution

It presents the first exactly soluble GFT for the HK model, linking canonical and path-integral approaches in quantum gravity.

Findings

Complete spinfoam model derived from the GFT

Unique Fock representation for quantum three-geometries

Bridges canonical and path-integral quantizations

Abstract

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.