Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian
  Theory   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.

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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph