2010/08/24 by Maïté Dupuis, Maité Dupuis, Etera R. Livine
Mathematics · Physics and Astronomy · #Algorithm #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geometry #Group field theory #Immirzi parameter #Loop quantum gravity #Mathematics #Noncommutative and Quantum Gravity Theories #Parameterized complexity #Physics #Quantum #Quantum gravity #Quantum mechanics #Scalar (mathematics) #Spin (aerodynamics) #Spin foam #Spin network #gr-qc #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.82.064044
published as Phys.Rev.D82:064044,2010 · 14 pages
arxiv created 2010/08/24 · openalex publication_date 2010/09/30 · arxiv updated 2014/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Projected spin network states are the canonical basis of quantum states of geometry for the recent EPRL-FK spinfoam models for quantum gravity introduced by Engle-Pereira-Rovelli-Livine and Freidel-Krasnov. They are functionals of both the Lorentz connection and the time-normal field. We analyze in detail the map from these projected spin networks to the standard SU(2) spin networks of loop quantum gravity. We show that this map is not one to one and that the corresponding ambiguity is parameterized by the Immirzi parameter. We conclude with a comparison of the scalar products between projected spin networks and SU(2) spin network states.