Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory

By L. Freidel, Etera R. Livine. 2005

267 citations recorded by the source corpus.

We study the no-gravity limit GN → 0 of the Ponzano–Regge amplitudes with massive particles and show that we recover in this limit Feynman graph amplitudes (with the Hadamard propagator) expressed as an Abelian spin foam model. We show how the GN expansion of the Ponzano–Regge amplitudes can be resummed. This leads to the conclusion that the effective 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 propagators.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/c3a64797086b2666de385acd584c517c960ab151

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Citations in the corpus

Loop Quantum Gravity (2003, background): “In the spin-foam formalism, an interesting line of investigation has studied the coupling of particles in 3D, treated as topological defects [118, 119, 209, 117, 116, 220, 108].”
The Ponzano–Regge model (2008, methodology): “It is convenient to use the set of functions given by the character formula [11] sin ( (2j + 1) θ2 )”
κ-Minkowski spacetime and the star product realizations (2007, background): “The line of consideration which is carried out here may appear useful in 2+1 dimensional models of quantum gravity where the corresponding Lie algebra is SU(2) or SU(1, 1), [44].”
Group field theory and simplicial gravity path integrals: A model for Holst-Plebanski gravity (2011, methodology): “2 on, based on the SO(3) Fourier transform1 [36], we further assume an invariance of group functions under g → −g, so that they are effectively functions on SO(3)×SO(3).”
New realizations of Lie algebra kappa-deformed Euclidean space (2006, background): “This means that a given ϕ-realization induces a natural basis for monomials, i.e. a natural ordering prescription, and vice versa, an ordering uniquely defines the ϕ-realization.”
The Spin-Foam Approach to Quantum Gravity (2012, background): “These theories have been shown by Freidel and Livine to be dual, in a suitable sense, to certain non-commutative fields theories in three dimensions [185, 184].”