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• W3102511735 endingPage "165012" @default.
• W3102511735 startingPage "165012" @default.
• W3102511735 abstract "The present paper studies the large-j asymptotics of the Lorentzian EPRL spinfoam amplitude on a 4d simplicial complex with an arbitrary number of simplices. The asymptotics of the spinfoam amplitude is determined by the critical configurations. Here we show that, given a critical configuration in general, there exists a partition of the simplicial complex into three type of regions R_{Nondeg}, R_{Deg-A}, R_{Deg-B}, where the three regions are simplicial sub-complexes with boundaries. The critical configuration implies different types of geometries in different types of regions, i.e. (1) the critical configuration restricted into R_{Nondeg}$ implies a nondegenerate discrete Lorentzian geometry, (2) the critical configuration restricted into R_{Deg-A}$ is degenerate of type-A in our definition of degeneracy, but implies a nondegenerate discrete Euclidean geometry on R_{Deg-A}, (3) the critical configuration restricted into R_{Deg-B} is degenerate of type-B, and implies a vector geometry on R_{Deg-B}. With the critical configuration, we further make a subdivision of the regions R_{Nondeg} and R_{Deg-A} into sub-complexes (with boundary) according to their Lorentzian/Euclidean oriented 4-simplex volume V_4(v), such that sgn(V_4(v)) is a constant sign on each sub-complex. Then in the each sub-complex, the spinfoam amplitude at the critical configuration gives the Regge action in Lorentzian or Euclidean signature respectively on R_{Nondeg} or R_{Deg-A}. The Regge action reproduced here contains a sign factor sgn(V_4(v)) of the oriented 4-simplex volume. Therefore the Regge action reproduced here can be viewed a discretized Palatini action with on-shell connection. Finally the asymptotic formula of the spinfoam amplitude is given by a sum of the amplitudes evaluated at all possible critical configurations, which are the products of the amplitudes associated to different type of geometries." @default.
• W3102511735 created "2020-11-23" @default.
• W3102511735 creator A5027369269 @default.
• W3102511735 creator A5073086952 @default.
• W3102511735 date "2013-07-22" @default.
• W3102511735 modified "2023-10-05" @default.
• W3102511735 title "Asymptotics of spinfoam amplitude on simplicial manifold: Lorentzian theory" @default.
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• W3102511735 doi "https://doi.org/10.1088/0264-9381/30/16/165012" @default.
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