Flipped spinfoam vertex and loop gravity

By Jonathan Engle, Roberto Pereira, Carlo Rovelli. 2007

273 citations recorded by the source corpus.

Abstract We introduce a vertex amplitude for 4d loop quantum gravity. We derive it from a conventional quantization of a Regge discretization of euclidean general relativity. This yields a spinfoam sum that corrects some difficulties of the Barrett–Crane theory. The second class simplicity constraints are imposed weakly, and not strongly as in Barrett–Crane theory. Thanks to a flip in the quantum algebra, the boundary states turn out to match those of SO ( 3 ) loop quantum gravity—the two can be identified as eigenstates of the same physical quantities—providing a solution to the problem of connecting the covariant SO ( 4 ) spinfoam formalism with the canonical SO ( 3 ) spin-network one. The vertex amplitude is SO ( 3 ) and SO ( 4 ) -covariant. It rectifies the triviality of the intertwiner dependence of the Barrett–Crane vertex, which is responsible for its failure to yield the correct propagator tensorial structure. The construction provides also an independent derivation of the kinematics of loop quantum gravity and of the result that geometry is quantized.

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

View Paper: https://www.semanticscholar.org/paper/febbee02f9755d54b9dc0a050a0aae22d8ae578f

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Citations in the corpus

Loop Quantum Gravity (2003, background): “2007 The new vertex and the loop/spin-foam relation in 4D A vertex amplitude correcting some difficulties of the Barrett–Crane model is introduced in [106], and gives rise to rapid development [105, 181, 182, 227] leading to the formulation of a class of spin-foam models that provide a covariant def”
Renormalization of Tensorial Group Field Theories: Abelian U(1) Models in Four Dimensions (2012, methodology): “In this context, models for 4d quantum gravity have been developed, the most interesting ones being found in [37–42].”
Phase space descriptions for simplicial 4D geometries (2008, background): “A considerable amount of current work on spin foam models [27, 28, 29, 30] discusses the question of how to properly impose the simplicity constraints.”
Colored Group Field Theory (2009, unknown): “This line of research has been explored in [19–23], to define more realistic GFT’s whose semiclassical limit [24,25] exhibits the expected behavior.”
The Spin-Foam Approach to Quantum Gravity (2012, methodology): “8 The Engle–Pereira–Rovelli–Livine (EPRL) A modification of the Barrett–Crane model was recently introduced in [168, 169] and extended for arbitrary Immirzi parameter in [164].”
Spin-foams for all loop quantum gravity (2009, background): “Gravity 14 1753 (Preprint gr-qc/9609002) [14] Engle J, Pereira R and Rovelli C (2008), Flipped spinfoam vertex and loop gravity, Nucl.”
On the semiclassical limit of 4d spin foam models (2008, methodology): “In this section, we review the path integral representation for the EPR and FKγ models derived in ref.”
A new look at loop quantum gravity (2010, background): “In fact, there is a derivation of vertex (45) which is precisely based on Regge calculus, and a single vertex is interpreted as a flat 4-simplex [34, 41].”
Lorentzian spin foam amplitudes: graphical calculus and asymptotics (2009, methodology): “A natural gluing between neighbouring 4-simplices is given by identifying the quantum numbers that specify the boundary states in each simplex, and this was the strategy followed in both the BC model (see for instance [20]) and in [6, 7, 15].”
A new spin foam model for 4D gravity (2007, background): “While the present work was in its final stages, an extended version [20] of the paper [18] has appeared.”
Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude (2009, background): “Our thanks are due to Carlo Rovelli, who encouraged us to study this problem, and for hosting JWB and WF in Marseille, where the methods and most of the results were presented in detail on 19th November 2008 in a five-hour seminar.”
Asymptotic analysis of the EPRL four-simplex amplitude (2009, background): “Our thanks are due to Carlo Rovelli, who encouraged us to study this problem, and for hosting JWB and WF in Marseille, where the methods and most of the results were presented in detail on 19th November 2008 in a five-hour seminar.”