Solving the simplicity constraints for spinfoam quantum gravity

By Etera R. Livine, Simone Speziale. 2007

192 citations recorded by the source corpus.

General relativity can be written as topological BF theory plus a set of second-class constraints. Classically the constraints provide the geometric interpretation of the B variables and reduce BF to general relativity. In the quantum theory these constraints do not commute and thus cannot be imposed strongly. We use SU(2) coherent states to develop a notion of semiclassical states for the quantum geometry which allows to implement them weakly, i.e. on average with minimal uncertainty. Using the spinfoam formalism, this leads to a background independent regularized path integral for quantum gravity whose variables have a transparent geometric interpretation.

Subfields: Applied Mathematics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/72bb973463e3c5e58b6477cf20e1f2890a24c653

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In Applied Mathematics

In Nuclear and High Energy Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude (2009, background): “Meanwhile Livine and Speziale introduced coherent states to the analysis and definition of Spin Foam models [12], and suggested a a way to construct new models in [ 13 ].”
The Spin-Foam Approach to Quantum Gravity (2012, methodology): “The importance of coherent states in spin foam models was put forward in [246] and explicitly used to re-derive the EPRL model in [247].”
On the semiclassical limit of 4d spin foam models (2008, unknown): “2 & Krasnov (FKγ) [26] that incorporate any value of the Immirzi parameter γ 6= 1 and reproduce the EPR model for γ = 0 [26, 27].”
A new spin foam model for 4D gravity (2007, result): “In particular, paper [22] is very close in spirit to the present work and paper [23] studies further the finite Immirzi parameter case.”