Hidden Quantum Gravity in 3d Feynman diagrams

Details Hidden Quantum Gravity in 3d Feynman diagrams Hidden Quantum Gravity in 3d Feynman diagrams

2006-04-04

arxiv.org/abs/gr-qc/0604016v2

Class.Quant.Grav.24:1993-2026,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

35 pages, 4 figures, some comments added

Scientific paper

10.1088/0264-9381/24/8/006

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.

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