Diffeomorphisms and spin foam models

By L. Freidel, David Louapre. 2002

160 citations recorded by the source corpus.

Abstract We study the action of diffeomorphisms on spin foam models. We prove that in 3 dimensions, there is a residual action of the diffeomorphisms that explains the naive divergences of state sum models. We present the gauge fixing of this symmetry and show that it explains the original renormalization of Ponzano–Regge model. We discuss the implication this action of diffeomorphisms has on higher dimensional spin foam models and especially the finite ones.

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

View Paper: https://www.semanticscholar.org/paper/ebaf536c91a784c013839f346d3065fb9407470d

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Citations in the corpus

Ponzano–Regge model revisited: III. Feynman diagrams and effective field theory (2005, methodology): “Then, following the analysis of [ 10 , 3], we know that the spin foam amplitude is in general ill-defined and that it requires a gauge-fixing in order to give a finite amplitude.”
Introduction to loop quantum gravity and spin foams (2004, background): “φ1 mn(gh[A]) = j Πmq (g) φ j qn(h[A]) (96) the action of P0 G can be written as P0 G φ j1 m1n1(he1 [A]) · · ·φ4 m4n4(he4 [A]) = = P0 m1···m4,q1···q4 φ j1 q1n1(he1 [A]) · · ·φ4 q4n4(he4 [A]), (97) where P0 m1···m4,q1···q4 = ∫ dg j1 Πm1q1 (g) · · · j4 Πm4q4 (g).”
Phase space descriptions for simplicial 4D geometries (2008, background): “Although there is a considerable amount of work addressing these questions in different frameworks [11, 14, 15, 16, 17, 18, 19, 20], in our view the issue is not yet settled, even at the classical level.”
The Ponzano–Regge model (2008, methodology): “This regularisation was proposed for the PonzanoRegge model in [8].”
Quantum gravity in terms of topological observables (2005, background): “The gauge fixing procedure of BF is now well understood in the spin foam context [18].”
The Spin-Foam Approach to Quantum Gravity (2012, background): “This is illustrated precisely in the simplest scenario of 3D gravity, where it is well known that bubble divergences are directly linked to the infinite volume of the gauge orbits generated by the curvature constraint [186].”
Improved and Perfect Actions in Discrete Gravity (2009, methodology): “Just as the discretization of one-dimensional systems replaces the search for smooth solutions to the equations by piecewise linear ones, Regge calculus replaces smooth curved metrics by piecewise linear flat ones.”
Group Field Theory: An Overview (2005, background): “It was argued in [37] (and exemplified in the context of 3d gravity) that diffeomorphism symmetry should act as a gauge symmetry on the spin foam amplitudes.”
Solving the simplicity constraints for spinfoam quantum gravity (2007, unknown): “17 (2000) 3101-3118 [gr-qc/9904025] [3] L.”
Ponzano–Regge model revisited: I. Gauge fixing, observables and interacting spinning particles (2004, methodology): “The jacobian for fixing the translational symmetry has been computed in [29].”
Three-dimensional loop quantum gravity: physical scalar product and spin-foam models (2004, background): “We have also shown that our regularization of the generalized projector P implies the Ponzano-Regge amplitudes automatically in its gauge fixed form in the language of reference [25].”
The continuum limit of loop quantum gravity - a framework for solving the theory (2014, background): “This is indeed confirmed for (topological) 3D spin foams with the link to the diffeomorphism symmetry made explicit [55].”