Hidden Quantum Gravity in 3d Feynman diagrams

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.

35 pages, 4 figures, some comments added

References in corpus (4)

• Quantum gravity in terms of topological observables
• Ponzano-Regge model revisited II: Equivalence with Chern-Simons
• Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
• Spherical Tetrahedra and Invariants of 3-manifolds

Cited by in corpus (6)

• A New Spin Foam Model for 4d Gravity
• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• Fermions in three-dimensional spinfoam quantum gravity
• Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
• Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model
• Invariants of three-dimensional manifolds from four-dimensional Euclidean geometry