Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory

TL;DR

This paper explores the connection between 3D quantum gravity models and Feynman diagrams, showing how the no gravity limit recovers standard quantum field theory and proposing an effective non-commutative field theory consistent with doubly special relativity.

Contribution

It demonstrates the recovery of Feynman graph amplitudes from Ponzano-Regge models in the no gravity limit and introduces an effective non-commutative field theory framework for quantum particles coupled to 3D gravity.

Findings

Feynman amplitudes emerge in the G_N -> 0 limit of Ponzano-Regge models.

The G_N expansion can be resummed into an effective non-commutative field theory.

The approach respects principles of doubly special relativity.

Abstract

We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with Hadamard propagator) expressed as an abelian spin foam model. We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be resummed. This leads to the conclusion that the dynamics of quantum particles coupled to quantum 3d gravity can be expressed in terms of an effective new non commutative field theory which respects the principles of doubly special relativity. We discuss the construction of Lorentzian spin foam models including Feynman propagators