Hidden Quantum Gravity in 3d Feynman diagrams

TL;DR

This paper demonstrates that 3d Feynman amplitudes in quantum field theory can be represented as expectation values of a topological spin foam model, providing a background-independent perspective and linking to 3d gravity quantization.

Contribution

It introduces a framework connecting 3d Feynman diagrams with a Poincare group-based spin foam model, extending the understanding of background independence in quantum field theories.

Findings

Feynman amplitudes expressed as spin foam expectation values

Spin foam model encodes flat spacetime geometry algebraically

Relation established between spin foam quantization and 3d gravity

Abstract

In this work we show that 3d Feynman amplitudes of standard QFT in flat and homogeneous space can be naturally expressed as expectation values of a specific topological spin foam model. The main interest of the paper is to set up a framework which gives a background independent perspective on usual field theories and can also be applied in higher dimensions. We also show that this Feynman graph spin foam model, which encodes the geometry of flat space-time, can be purely expressed in terms of algebraic data associated with the Poincare group. This spin foam model turns out to be the spin foam quantization of a BF theory based on the Poincare group, and as such is related to a quantization of 3d gravity in the limit where the Newton constant G_N goes to 0. We investigate the 4d case in a companion paper where the strategy proposed here leads to similar results.