Lorentzian spin foam amplitudes: graphical calculus and asymptotics

By John W. Barrett, R. J. Dowdall, W. Fairbairn, Frank Hellmann, Roberto Pereira. 2009

247 citations recorded by the source corpus.

The amplitude for the 4-simplex in a spin foam model for quantum gravity is defined using a graphical calculus for the unitary representations of the Lorentz group. The asymptotics of this amplitude are studied in the limit when the representation parameters are large, for various cases of boundary data. It is shown that for boundary data corresponding to a Lorentzian simplex, the asymptotic formula has two terms, with phase plus or minus the Lorentzian signature Regge action for the 4-simplex geometry, multiplied by an Immirzi parameter. Other cases of boundary data are also considered, including a surprising contribution from Euclidean signature metrics.

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

View Paper: https://www.semanticscholar.org/paper/e5edd7f21791ce367620f39f4e44e969c6b223f5

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Citations in the corpus

The Spin-Foam Approach to Quantum Gravity (2012, methodology): “However, this seems to be a peculiarity of the Riemannian theory alone as the results of [64] for the Lorentzian models show.”
A new look at loop quantum gravity (2010, background): “The analysis of the vertex (49) as well as that of its euclidean analog (55) in this limit has been carried out in great detail for the 5-valent vertex, by the Nottingham group [29, 30, 50, 51].”
Twisted geometries: A geometric parametrisation of SU(2) phase space (2010, methodology): “The next key step is the understanding that the labels of the n-valent vertex can be restricted to satisfy a certain closure condition (see below) without loosing any information [13, 14].”
The Complete 1/N Expansion of Colored Tensor Models in Arbitrary Dimension (2011, methodology): “The semiclassical limit of various GFT models [30, 31 ] has been analyzed and matter field have been added in the GFT framework [32–34].”
Zakopane lectures on loop gravity (2011, background): “31) and the action of general relativity has been first studied in the Euclidean context (not discussed here) [65, 66, 67] and then extended to the relevant Lorentzian domain [58].”
Loop Quantum Gravity (2003, unknown): “Now, it turns out [31, 36, 37], remarkably, that”
Polyhedra in loop quantum gravity (2010, background): “Specifically, in this limit the transition amplitudes are related to exponentials of the Regge action [9, 31, 56, 57].”