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

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.

28 pages (RevTeX4), 7 figures, references added

References in corpus (2)

• Group Integral Techniques for the Spinfoam Graviton Propagator
• Hidden Quantum Gravity in 3d Feynman diagrams

Cited by in corpus (6)

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• Discretization independence implies non-locality in 4D discrete quantum gravity
• Hidden Quantum Gravity in 3d Feynman diagrams
• A 2-categorical state sum model
• Lorentzian quantum cosmology from effective spin foams
• Poincare group spin networks