2 research outputs found
Ponzano-Regge model revisited III: Feynman diagrams and Effective field theory
We study the no gravity limit G_{N}-> 0 of the Ponzano-Regge amplitudes with
massive particles and show that we recover in this limit Feynman graph
amplitudes (with Hadamard propagator) expressed as an abelian spin foam model.
We show how the G_{N} expansion of the Ponzano-Regge amplitudes can be
resummed. This leads to the conclusion that the dynamics of quantum particles
coupled to quantum 3d gravity can be expressed in terms of an effective new non
commutative field theory which respects the principles of doubly special
relativity. We discuss the construction of Lorentzian spin foam models
including Feynman propagatorsComment: 46 pages, the wrong file was first submitte
Hidden Quantum Gravity in 3d Feynman diagrams
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.Comment: 35 pages, 4 figures, some comments adde