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Schwinger-Dyson Equation in Three-Dimensional Simplicial Quantum Gravity

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Book cover Low-Dimensional Topology and Quantum Field Theory

Part of the book series: NATO ASI Series ((NSSB,volume 315))

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Abstract

We study simplicial quantum gravity in three dimensions. Motivated by 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, so long 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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Author information

Authors and Affiliations

  1. Research Institute for Mathematical Sciences, Kyoto University, Kyoto, 606-01, Japan

    Hirosi Ooguri

  2. Lyman Laboratory of Physics, Harvard University, Cambridge, MA, 02138, USA

    Hirosi Ooguri

Authors
  1. Hirosi Ooguri
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Editor information

Editors and Affiliations

  1. University of Cambridge, Cambridge, UK

    Hugh Osborn

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© 1993 Springer Science+Business Media New York

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Ooguri, H. (1993). Schwinger-Dyson Equation in Three-Dimensional Simplicial Quantum Gravity. In: Osborn, H. (eds) Low-Dimensional Topology and Quantum Field Theory. NATO ASI Series, vol 315. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-1612-9_4

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  • DOI: https://doi.org/10.1007/978-1-4899-1612-9_4

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4899-1614-3

  • Online ISBN: 978-1-4899-1612-9

  • eBook Packages: Springer Book Archive

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