2018/10/31 by Hongguang Liu, Muxin Han · 37 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Amplitude #Black Holes and Theoretical Physics #Classical mechanics #Combinatorics #Degenerate energy levels #Geometry #Graph #Gravitation #Massive gravity #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantum gravity #Quantum mechanics #Signature (topology) #Simplex #Spin (aerodynamics) #Spin foam #Tetrahedron #Vertex (graph theory) #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.99.084040
published in Physical review. D/Physical review. D. 99(8) (American Physical Society) · 24+28 pages, 2 figures
arxiv created 2019/04/16 · openalex publication_date 2019/04/24 · arxiv updated 2019/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The large-j asymptotic behavior of the four-dimensional spin foam amplitude is investigated for the extended spin foam model (Conrady-Hnybida extension) on a simplicial complex. We study the most general situation in which timelike tetrahedra with timelike triangles are taken into account. The large-j asymptotic behavior is determined by the critical configurations of the amplitude. We identify the critical configurations that correspond to the Lorentzian simplicial geometries with timelike tetrahedra and triangles. Their contributions to the amplitude are asymptotic phases, whose exponents equal the Regge action of gravity. The amplitude may also contains critical configurations corresponding to nondegenerate split signature 4-simplices and degenerate vector geometries. But vertex amplitudes containing at least one timelike and one spacelike tetrahedra only give Lorentzian 4-simplices, while the split signature or degenerate 4-simplex does not appear.