Classical and Quantum Dilogarithm Identities

Using the quantum cluster algebra formalism of Fock and Goncharov, we present several forms of quantum dilogarithm identities associated with periodicities in quantum cluster algebras, namely, the tropical, universal, and local forms. We then demonstrate how classical dilogarithm identities naturall...

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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2011
Main Authors: Kashaev, R.M., Nakanishi, T.
Format: Article
Language:English
Published: Інститут математики НАН України 2011
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/147994
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this:Classical and Quantum Dilogarithm Identities / R.M. Kashaev, T. Nakanishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 65 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Kashaev, R.M.
Nakanishi, T.
author_facet Kashaev, R.M.
Nakanishi, T.
citation_txt Classical and Quantum Dilogarithm Identities / R.M. Kashaev, T. Nakanishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 65 назв. — англ.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description Using the quantum cluster algebra formalism of Fock and Goncharov, we present several forms of quantum dilogarithm identities associated with periodicities in quantum cluster algebras, namely, the tropical, universal, and local forms. We then demonstrate how classical dilogarithm identities naturally emerge from quantum dilogarithm identities in local form in the semiclassical limit by applying the saddle point method.
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-11-24T20:38:57Z
publishDate 2011
publisher Інститут математики НАН України
record_format dspace
spelling Kashaev, R.M.
Nakanishi, T.
2019-02-16T12:50:30Z
2019-02-16T12:50:30Z
2011
Classical and Quantum Dilogarithm Identities / R.M. Kashaev, T. Nakanishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 65 назв. — англ.
1815-0659
2010 Mathematics Subject Classification: 13F60
DOI: http://dx.doi.org/10.3842/SIGMA.2011.106
https://nasplib.isofts.kiev.ua/handle/123456789/147994
Using the quantum cluster algebra formalism of Fock and Goncharov, we present several forms of quantum dilogarithm identities associated with periodicities in quantum cluster algebras, namely, the tropical, universal, and local forms. We then demonstrate how classical dilogarithm identities naturally emerge from quantum dilogarithm identities in local form in the semiclassical limit by applying the saddle point method.
We thank Vladimir V. Bazhanov, Ludwig D. Faddeev, Kentaro Nagao, Boris Pioline, and Andrei Zelevinsky for very useful discussions and comments. We especially thank Alexander Yu. Volkov for making his result in [62] available to us prior to the publication.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Classical and Quantum Dilogarithm Identities
Article
published earlier
spellingShingle Classical and Quantum Dilogarithm Identities
Kashaev, R.M.
Nakanishi, T.
title Classical and Quantum Dilogarithm Identities
title_full Classical and Quantum Dilogarithm Identities
title_fullStr Classical and Quantum Dilogarithm Identities
title_full_unstemmed Classical and Quantum Dilogarithm Identities
title_short Classical and Quantum Dilogarithm Identities
title_sort classical and quantum dilogarithm identities
url https://nasplib.isofts.kiev.ua/handle/123456789/147994
work_keys_str_mv AT kashaevrm classicalandquantumdilogarithmidentities
AT nakanishit classicalandquantumdilogarithmidentities