Schwinger-Dyson Equation in Three-Dimensional Simplicial Quantum Gravity
- Creators
-
Ooguri, Hirosi
Abstract
We study the 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, as far as the surface is no-degenerate. We propose a set of factorization conditions on the amplitudes which singles out a solution associated to triangulations of S^3.
Additional Information
© 1992 The Physical Society of Japan. Received October 11, 1992. I would like to thank J Ambjørn, B. Durhuus, T. Eguchi, A. Jevicki and T. Matsumoto for discussions and comments. I would also like to thank M. Atiyah and P. Goddard for their hospitality at the Isaac Newton Institute for Mathematical Sciences, University of Cambridge, where part of this work was done. This research is supported in part by the Grant-in-Aid for Scientific Research on Priority Areas 231 "Infinite Analysis" from the Minstry of Education, Science and Culture of Japan.Attached Files
Published - Prog._Theor._Phys.-1993-Ooguri-1-22.pdf
Submitted - 9210028v1.pdf
Files
| Name | Size | Download all |
|---|---|---|
|
md5:2064f93ebefe95f32912c12bf42c59b5
|
254.0 kB | Preview Download |
|
md5:e6652f61e28a22dea62e056b8238d058
|
2.2 MB | Preview Download |
Additional details
- Eprint ID
- 73096
- Resolver ID
- CaltechAUTHORS:20161221-133310666
- Ministry of Education, Culture, Sports, Science and Technology (MEXT)
- Created
-
2016-12-21Created from EPrint's datestamp field
- Updated
-
2021-11-11Created from EPrint's last_modified field