Asymptotic analysis of spin foam amplitude with timelike triangles
Liu H, Han M (2019)
Publication Type: Journal article
Publication year: 2019
Journal
Book Volume: 99
Article Number: 084040
Journal Issue: 8
DOI: 10.1103/PhysRevD.99.084040
Abstract
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.
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APA:
Liu, H., & Han, M. (2019). Asymptotic analysis of spin foam amplitude with timelike triangles. Physical Review D, 99(8). https://dx.doi.org/10.1103/PhysRevD.99.084040
MLA:
Liu, Hongguang, and Muxin Han. "Asymptotic analysis of spin foam amplitude with timelike triangles." Physical Review D 99.8 (2019).
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