2007/11/15 by Etera R. Livine, Etera R Livine, Simone Speziale · 13 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Degrees of freedom (physics and chemistry) #Eigenvalues and eigenvectors #Noncommutative and Quantum Gravity Theories #Quantum #Quantum many-body systems #Spin (aerodynamics) #Spin foam #Tetrahedron #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/25/8/085003
published in Classical and Quantum Gravity 25(8), 085003 (IOP Publishing) · 20 pages, 6 figures
arxiv created 2007/11/15 · openalex publication_date 2008/03/26 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider stability under evolution as a criterion to select a physical boundary state for the spinfoam formalism. As an example, we apply it to the simplest spinfoam defined by a single quantum tetrahedron and solve the associated eigenvalue problem at leading order in the large spin limit. We show that this fixes uniquely the free parameters entering the boundary state. Remarkably, the state obtained this way gives a correlation between edges which runs at leading order with the inverse distance between the edges, in agreement with the linearized continuum theory. Finally, we give an argument why this correlator represents the propagation of a pure gauge, consistently with the absence of physical degrees of freedom in 3d general relativity.