Hamiltonian and Lagrangian formalisms of mutations in cluster algebras and application to dilogarithm identities
Hamiltonian and Lagrangian formalisms of mutations in cluster algebras and application to dilogarithm identities
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DOI：
10.1093/integr/xyx005
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发表时间：
2016-11
期刊：
影响因子：
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通讯作者：
M. Gekhtman;T. Nakanishi;Dylan Rupel
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文献类型：
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作者：
M. Gekhtman;T. Nakanishi;Dylan Rupel
我们引入并研究了一种基于正则变量的簇代数中突变的Hamilton形式，其中的Hamilton由欧拉双对数给出。相应的拉格朗日量，限制在相空间的某个子空间，符合罗杰斯双对数。作为一个应用程序，我们展示了如何双对数的身份与一个时期的集群代数的突变产生的哈密顿/拉格朗日的观点。
We introduce and study a Hamiltonian formalism of mutations in cluster algebras using canonical variables, where the Hamiltonian is given by the Euler dilogarithm. The corresponding Lagrangian, restricted to a certain subspace of the phase space, coincides with the Rogers dilogarithm. As an application, we show how the dilogarithm identity associated with a period of mutations in a cluster algebra arises from the Hamiltonian/Lagrangian point of view.