Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams

TL;DR

This paper demonstrates how Feynman amplitudes in quantum field theory can be reformulated as spin foam models, revealing a connection to quantum gravity and topological invariants in four dimensions.

Contribution

It introduces a spin foam model derived from standard QFT Feynman diagrams, establishing gauge-fixing procedures and invariance under Pachner moves, linking quantum field theory to quantum gravity.

Findings

Feynman amplitudes can be expressed as spin foam observables.

The model's partition function is invariant under Pachner moves.

The algebraic structure relates to a zero Newton constant limit of 4d gravity.

Abstract

We show how Feynman amplitudes of standard QFT on flat and homogeneous space can naturally be recast as the evaluation of observables for a specific spin foam model, which provides dynamics for the background geometry. We identify the symmetries of this Feynman graph spin foam model and give the gauge-fixing prescriptions. We also show that the gauge-fixed partition function is invariant under Pachner moves of the triangulation, and thus defines an invariant of four-dimensional manifolds. Finally, we investigate the algebraic structure of the model, and discuss its relation with a quantization of 4d gravity in the limit where the Newton constant goes to zero.