Classical and Quantum Dilogarithm Identities

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Фізико-технічні та математичні науки
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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7
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Symmetry, Integrability and Geometry: Methods and Applications, 2011, том 7, випуск за цей рік
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dc.contributor.author	Kashaev, R.M.
dc.contributor.author	Nakanishi, T.
dc.date.accessioned	2019-02-16T12:50:30Z
dc.date.available	2019-02-16T12:50:30Z
dc.date.issued	2011
dc.identifier.citation	Classical and Quantum Dilogarithm Identities / R.M. Kashaev, T. Nakanishi // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 65 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 13F60
dc.identifier.other	DOI: http://dx.doi.org/10.3842/SIGMA.2011.106
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/147994
dc.description.abstract	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.	uk_UA
dc.description.sponsorship	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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	Classical and Quantum Dilogarithm Identities	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA