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

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Cited by in corpus (25)

• A New Spin Foam Model for 4d Gravity
• An Invitation to Higher Gauge Theory
• Non-commutative flux representation for loop quantum gravity
• Regge calculus from a new angle
• 3d Spinfoam Quantum Gravity: Matter as a Phase of the Group Field Theory
• Path integral measure and triangulation independence in discrete gravity
• Infinite-Dimensional Representations of 2-Groups
• Discretization independence implies non-locality in 4D discrete quantum gravity
• Dirac's discrete hypersurface deformation algebras
• Quasi-local holographic dualities in non-perturbative 3d quantum gravity II - From coherent quantum boundaries to BMS3 characters
• Fermions in three-dimensional spinfoam quantum gravity
• 3D holography: from discretum to continuum
• Hidden Quantum Gravity in 4d Feynman diagrams: Emergence of spin foams
• Grasping rules and semiclassical limit of the geometry in the Ponzano-Regge model
• A 2-categorical state sum model
• Holographic description of boundary gravitons in (3+1) dimensions
• 2-Group Representations for Spin Foams
• Spikes and spines in 4D Lorentzian simplicial quantum gravity
• A Short and Subjective Introduction to the Spinfoam Framework for Quantum Gravity
• A New Recursion Relation for the 6j-Symbol
• Poincare group spin networks
• Invariants of three-dimensional manifolds from four-dimensional Euclidean geometry
• World quantum gravity: Quantum test objects and Synge's world function
• Lorentzian quantum gravity via Pachner moves: one-loop evaluation
• Invariance Mechanics - A new direction for quantum gravity