Complete LQG propagator: Difficulties with the Barrett-Crane vertex

By Emanuele Alesci, Carlo Rovelli. 2007

154 citations recorded by the source corpus.

Some components of the graviton two-point function have been recently computed in the context of loop quantum gravity, using the spinfoam Barrett-Crane vertex. We complete the calculation of the remaining components. We find that, under our assumptions, the Barrett-Crane vertex does not yield the correct long distance limit. We argue that the problem is general and can be traced to the intertwiner-independence of the Barrett-Crane vertex, and therefore to the well-known mismatch between the Barrett-Crane formalism and the standard canonical spin networks. In a companion paper we illustrate the asymptotic behavior of a vertex amplitude that can correct this difficulty.

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

View Paper: https://www.semanticscholar.org/paper/06a80d1c823a7b9b20100948ee7c9932f12faf94

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Citations in the corpus

A new spin foam model for 4D gravity (2007, background): “In spite of the spin foam quantization programme being far from complete, some preliminary physical computations of the type [38] are possible.”
The Spin-Foam Approach to Quantum Gravity (2012, methodology): “It was then applied to the Barrett-Crane model in [5, 4, 71], where it was discovered that certain components of the two point function could not yield the expected result compatible with Regge gravity in the semiclassical limit.”
Asymptotic analysis of the EPRL four-simplex amplitude (2009, methodology): “Similar asymptotic analysis of the 4-dimensional models [5] was initially performed by Barrett, Williams and Steele [6, 7], and formed the basis of investigations of the graviton propagator structure of these models [8, 9, 10].”
Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude (2009, methodology): “Similar asymptotic analysis of the 4-dimensional models [5] was initially performed by Barrett, Williams and Steele [6, 7], and formed the basis of investigations of the graviton propagator structure of these models [ 8 , 9, 10].”
Zakopane lectures on loop gravity (2011, methodology): “2 n-point functions The two point function of general relativity over a flat spacetime has been computed in the Euclidean [106], as well as in the Lorentzian [72] theory, following the earlier attempts in [107, 74, 108, 109, 110], and has been shown to converge to the free graviton propagator of qua”
Loop Quantum Gravity (2003, background): “The nail on the coffin of the old Barrett-Crane model was the first successful calculation of the propagator of the graviton from the theory: its diagonal components turn out to be correct, but its nondiagonal one turned out to be wrong [102].”