2015/03/19 by Seramika Ariwahjoedi, Jusak Sali Kosasih, Carlo Rovelli +1
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Holonomy #Isosceles triangle #Loop (graph theory) #Loop quantum gravity #Noncommutative and Quantum Gravity Theories #Quantum #Quantum gravity #Spin foam #gr-qc
paper · pdf · doi:10.1142/s0219887815501121
published in International Journal of Geometric Methods in Modern Physics 12(10), 1550112 (World Scientific) · 16 pages, 10 figures
arxiv created 2015/03/19 · openalex publication_date 2015/06/21 · openalex created_date 2016/06/24 · arxiv updated 2016/08/01 · openalex updated_date 2026/08/05
We derive the Gauss–Codazzi equation in the holonomy and plane-angle representations and we use the result to write a Gauss–Codazzi equation for a discrete (2 + 1)-dimensional manifold, triangulated by isosceles tetrahedra. This allows us to write operators acting on spin network states in (2 + 1)-dimensional loop quantum gravity, representing the 3-dimensional intrinsic, 2-dimensional intrinsic, and 2-dimensional extrinsic curvatures.