2008/01/31 by Valentin Bonzom, Etera R. Livine, Etera R Livine · 3 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Advanced Mathematical Theories and Applications #Noncommutative and Quantum Gravity Theories #gr-qc
paper · pdf · doi:10.1088/0264-9381/25/19/195024
published as Class.Quant.Grav.25:195024,2008 · 14 pages, v2: one reference added, more comments on the 3d/4d comparison
arxiv created 2008/06/02 · openalex publication_date 2008/09/16 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
We study an Immirzi-like ambiguity in three-dimensional quantum gravity. It shares some features with the Immirzi parameter of four-dimensional loop quantum gravity: it does not affect the equations of motion, but modifies the Poisson brackets and the constraint algebra at the canonical level. We focus on the length operator and show how to define it through non-commuting fluxes. We compute its spectrum and show the effect of this Immirzi-like ambiguity. Finally, we extend these considerations to 4D gravity and show how the different topological modifications of the action affect the canonical structure of loop quantum gravity.