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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| Дата: | 2011 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/147994 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Classical and Quantum Dilogarithm Identities / R.M. Kashaev, T. Nakanishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 65 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-147994 |
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dspace |
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irk-123456789-1479942019-02-17T01:23:27Z Classical and Quantum Dilogarithm Identities Kashaev, R.M. Nakanishi, T. 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. 2011 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/147994 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Kashaev, R.M. Nakanishi, T. |
| spellingShingle |
Kashaev, R.M. Nakanishi, T. Classical and Quantum Dilogarithm Identities Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Kashaev, R.M. Nakanishi, T. |
| author_sort |
Kashaev, R.M. |
| title |
Classical and Quantum Dilogarithm Identities |
| title_short |
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_sort |
classical and quantum dilogarithm identities |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/147994 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT kashaevrm classicalandquantumdilogarithmidentities AT nakanishit classicalandquantumdilogarithmidentities |
| first_indexed |
2023-05-20T17:28:21Z |
| last_indexed |
2023-05-20T17:28:21Z |
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