Clarification of the phase space structure of the tropical integrable systems

2016 Fiscal Year Final Research Report

• Project/Area Number: 25400122
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工学群)
• Principal Investigator: Takagi Taichiro 防衛大学校(総合教育学群、人文社会科学群、応用科学群、電気情報学群及びシステム工, 応用科学群, 教授 (00531766)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 可積分系 / 組合せ論 / 離散戸田格子 / トロピカル幾何学 / ソリトン / ベーテ仮説 / 共形場理論

Outline of Final Research Achievements

We clarified several properties of the phase space structures of the tropical periodic Toda lattice. This model is defined as a tropical limit of the discrete periodic Toda lattice, a variation of the Toda lattice which is one of the most famous models in the field of classical integrable systems. Especially, we proved that the Young diagrams defined through the Lax representation of the discrete periodic Toda lattice coincide with the Young diagrams defined as continuous limits of the corresponding diagrams defined in the combinatorial theory of the Bethe ansatz of the quantum spin chains. In addition, during a process of widening the author’s vision to find a breakthrough in future studies, we considered somehow different kind of problems in the field of integrable systems and found a new result on generalized Wick theorems in conformal field theory.

Free Research Field

数理物理学