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: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2011
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| 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| _version_ | 1862542629026136064 |
|---|---|
| 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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| first_indexed | 2025-11-24T20:38:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147994 |
| 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 |