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Partition functions and topology-changing amplitudes in the three-dimensional lattice gravity of Ponzano and Regge

Ooguri, Hirosi (1992) Partition functions and topology-changing amplitudes in the three-dimensional lattice gravity of Ponzano and Regge. Nuclear Physics B, 382 (2). pp. 276-304. ISSN 0550-3213. doi:10.1016/0550-3213(92)90188-H. https://resolver.caltech.edu/CaltechAUTHORS:20161220-160213579

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Abstract

We define a physical Hilbert space for the three-dimensional lattice gravity of Ponzano and Regge and establish its isomorphism to the one in the ISO(3) Chern-Simons theory. It is shown that, for a handlebody of any genus, a Hartle-Hawking-type wave function of the lattice gravity transforms into the corresponding state in the Chern-Simons theory under this isomorphism. Using the Heegaard splitting of a three-dimensional manifold, the partition functions of each of these theories is expressed as an inner product of such wave functions. Since the isomorphism preserves the inner products, the partition functions of the two theories are the same for any closed orientable manifold. We also discuss a class of topology-changing amplitudes in the lattice gravity and their relation to the ones in the Chern-Simons theory.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/0550-3213(92)90188-HDOIArticle
http://www.sciencedirect.com/science/article/pii/055032139290188HPublisherArticle
https://arxiv.org/abs/hep-th/9112072arXivDiscussion Paper
ORCID:
AuthorORCID
Ooguri, Hirosi0000-0001-6021-3778
Alternate Title:Partition Functions and Topology-Changing Amplitudes in the 3D Lattice Gravity of Ponzano and Regge
Additional Information:© 1992 Elsevier. Received 27 December 1991, Accepted 15 April 1992. The author would like to thank N. Sakakura for discussions. He is also thankful to T. Maskawa for explaining him some group theoretical facts and to L. Kauffman for encouragements.
Issue or Number:2
DOI:10.1016/0550-3213(92)90188-H
Record Number:CaltechAUTHORS:20161220-160213579
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20161220-160213579
Official Citation:Hirosi Ooguri, Partition functions and topology-changing amplitudes in the three-dimensional lattice gravity of Ponzano and Regge, Nuclear Physics B, Volume 382, Issue 2, 7 September 1992, Pages 276-304, ISSN 0550-3213, http://dx.doi.org/10.1016/0550-3213(92)90188-H. (http://www.sciencedirect.com/science/article/pii/055032139290188H)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73018
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:21 Dec 2016 17:50
Last Modified:11 Nov 2021 05:10

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