Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity

By D. Oriti. 2001

181 citations recorded by the source corpus.

This is an introduction to spin foam models for non-perturbative quantum gravity, an approach that lies at the point of convergence of many different research areas, including loop quantum gravity, topological quantum field theories, path integral quantum gravity, lattice field theory, matrix models, category theory and statistical mechanics. We describe the general formalism and ideas of spin foam models, the picture of quantum geometry emerging from them, and give a review of the results obtained so far, in both the Euclidean and Lorentzian cases. We focus in particular on the Barrett-Crane model for four-dimensional quantum gravity.

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

View Paper: https://www.semanticscholar.org/paper/b5e81985e320bdccdec733adc6d6166a129920ca

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Citations in the corpus

The Spin-Foam Approach to Quantum Gravity (2012, background): “3 A brief history of spin foams in four dimensions In this section, we briefly describe the various spin-foam models for quantum gravity in the literature (for previous reviews on spin foams, see [293, 39, 302, 301, 248, 20]).”
Flipped spinfoam vertex and loop gravity (2007, methodology): “What is the vertex of LQG? The spinfoam formalism [5, 6, 7, 8, 9] can be viewed as a tool for answering this question: the spinfoam vertex plays a role similar to the vertices of Feynman’s covariant quantum field theory.”
Asymptotic analysis of the EPRL four-simplex amplitude (2009, background): “A key step in understanding the semiclassical regime of a spin foam model [1, 2, 3] in dimension n is the analysis of the asymptotic behaviour of the n-simplex amplitude that defines the model.”
Deformed special relativity as an effective flat limit of quantum gravity (2004, background): “A similar result is also obtained in the framework of spin foam models for quantum gravity [5]: the”
Asymptotic analysis of the Engle–Pereira–Rovelli–Livine four-simplex amplitude (2009, background): “A key step in understanding the semiclassical regime of a spin foam model [1, 2, 3] in dimension n is the analysis of the asymptotic behaviour of the n-simplex amplitude that defines the model.”
Introduction to loop quantum gravity and spin foams (2004, background): “rties: Z SU(2) dg= 1, and dg= d(αg) = d(gα) = dg−1 ∀α∈ SU(2). 26 Alejandro Perez be expressed as a sum over unitary irreducible representations of SU(2), namely m f(g) = X j p 2j+1 fmm′ j j Πmm′ (g), (83) where fmm′ j = p 2j+1 Z SU(2) dg j Π m′ (g −1)f(g), (84) and dgis the Haar measure of SU(2). Th”
Loop Quantum Gravity (2003, background): “For detailed introductions to the spin-foam formalism see [50, 229, 230, 212, 64, 177].”
Solving the simplicity constraints for spinfoam quantum gravity (2007, background): “Livine, Towards a Covariant Loop Quantum Gravity, [gr-qc/0608135] [14] D.”
Colored Group Field Theory (2009, background): “GFT’s arise naturally in several discrete approaches to quantum gravity, like Regge calculus [11], dynamical triangulations [12,13] or spin foam models [14,15] (see also [16] for further details).”