2007/11/30 by Jonathan Engle, Etera R. Livine, Etera Livine +2 · 9 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.1016/j.nuclphysb.2008.02.018
published as Nucl.Phys.B799:136-149,2008
arxiv created 2007/12/13 · openalex publication_date 2008/03/05 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We extend the definition of the "flipped" loop-quantum-gravity vertex to the case of a finite Immirzi parameter. We cover the Euclidean as well as the Lorentzian case. We show that the resulting dynamics is defined on a Hilbert space isomorphic to the one of loop quantum gravity, and that the area operator has the same discrete spectrum as in loop quantum gravity. This includes the correct dependence on the Immirzi parameter, and, remarkably, holds in the Lorentzian case as well. The ad hoc flip of the symplectic structure that was initially required to derive the flipped vertex is not anymore needed for finite Immirzi parameter. These results establish a bridge between canonical loop quantum gravity and the spinfoam formalism in four dimensions.