Hidden quantum gravity in 4D Feynman diagrams: emergence of spin foams

We show how Feynman amplitudes of standard quantum field theory on flat and homogeneous space can naturally be recast as the evaluation of observables for a specific spin foam model, which provides the 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 G(N) -> 0.