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arXiv · 2404.16943

Partial absence of cosine problem in 3d Lorentzian spin foams

Alexander F. Jercher·José Diogo Simão·Sebastian Steinhaus
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Abstract

We study the semi-classical limit of the recently proposed coherent spin foam model for (2+1) Lorentzian quantum gravity. Specifically, we analyze the gluing equations derived from the stationary phase approximation of the vertex amplitude. Typically these exhibit two solutions yielding a cosine of the Regge action. However, by inspection of the algebraic equations as well as their geometrical realization, we show in this note that the behavior is more nuanced: when all triangles are either spacelike or timelike, two solutions exist. In any other case, only a single solution is obtained, thus yielding a single Regge exponential.

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Alexander F. Jercher, José Diogo Simão, Sebastian Steinhaus. 2024-04-25. Partial absence of cosine problem in 3d Lorentzian spin foams. https://doi.org/10.1088/1361-6382%2Fad9700

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