2016/12/13 by Javier Chagoya, M. Sabido, Chagoya, Javier +1
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Curvature #Diffeomorphism #FOS: Physical sciences #Formalism (music) #General Relativity and Quantum Cosmology (gr-qc) #Geometry #Gravitation #Immirzi parameter #Loop quantum gravity #Mathematical physics #Mathematics #Physics #Pure mathematics #Quantum #Quantum gravity #Quantum mechanics #Relativity and Gravitational Theory #Theoretical physics #gr-qc
paper · pdf · doi:10.48550/arxiv.1612.04002
7 pages, no figures, RevTex
arxiv created 2016/12/13 · openalex publication_date 2016/12/13 · arxiv updated 2016/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Working in the first order formalism of gravity, we propose an action that combines the self and anti-self-dual parts of the curvature and comprises all the diffeomorphism invariant Lagrangians that one can consider in this formalism. The action that we propose is motivated by (A)dS gauge theories of gravity. We use this action to derive the (2+1)-dimensional version of the Immirzi parameter. Our derivation relates explicitly the Immirzi parameter to the existence of two classically equivalent actions for the description of gravity in (2+1) dimensions, namely the standard and exotic actions introduced by Witten in the description of (2+1) gravity as a gauge theory. This relation had been conjectured previously in the literature, but not derived.