Schwinger-Dyson equation in three-dimensional simplicial quantum gravity

Details Schwinger-Dyson equation in three-dimensional simplicial quantum gravity Schwinger-Dyson equation in three-dimensional simplicial quantum gravity

1992-10-06

arxiv.org/abs/hep-th/9210028v1

Prog.Theor.Phys.89:1-22,1993

Physics

High Energy Physics

High Energy Physics - Theory

32 pages, harvmac, HUTP-92/A051

Scientific paper

10.1143/PTP.89.1

We 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 $S^3$.

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