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25 January 2025
 
  » arxiv » hep-th/9210028

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Schwinger-Dyson equation in three-dimensional simplicial quantum gravity
Hirosi Ooguri ;
Date 6 Oct 1992
Journal Prog.Theor.Phys. 89 (1993) 1-22
Subject hep-th
AbstractWe study the simplicial quantum gravity in three dimensions. Motivated by the Boulatov’s model which generates a sum over simplicial complexes weighted with the Turaev-Viro invariant, we introduce boundary operators in the simplicial gravity associated to compact orientable surfaces. An amplitude of the boundary operator is given by a sum over triangulations in the interior of the boundary surface. It turns out that the amplitude solves the Schwinger-Dyson equation even if we restrict the topology in the interior of the surface, as far as the surface is non-degenerate. We propose a set of factorization conditions on the amplitudes which singles out a solution associated to triangulations of $S^3$.
Source arXiv, hep-th/9210028
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