Japan Long Term Visit: "Tau-Functions for Dirac Operators"

日本长期访问：“狄拉克算子的 Tau 函数”

• 批准号: 9106953
• 负责人: Craig Tracy
• 金额: $ 1.05万
• 依托单位: University of California-Davis
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-11-01 至 1992-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9106953&HistoricalAwards=false
• 关键词: Japan; Long; Term; Visit; Tau

This award will support two months of a six-month, long-term visit by Professor Craig A. Tracy and his graduate student Mr. Morris Beatty of the Department of Mathematics at the University of California, Davis, to Japan for a cooperative research project with Professor T. Miwa, Research Institute for Mathematical Sciences (RIMS) at Kyoto University. Their collaborative research will involve continued investigation into isomonodromic t-functions that arise from a holonomic quantum field theory of free fermions on manifolds. This will be important in understanding and clarifying the nature of phases for a quantum field theory in hyperbolic space; and it should permit a transparent discussion of the zero curvature limit. Results of the research should have implications for holonomic quantum fields, integrable systems and differential geometry. The research is of fundamental importance with respect to isomonodromy problems in mathematical physics. Both groups are well-respected experts in their field. RIMS is the ideal Institute for the researchers to carry out their research. At Kyoto they will be working with the inventors of the notion of a t-function; Professors Mikio Sato, Tetsuji Miwa and Michio Jimbo. They are all known for their innovative approach to holonomic quantum fields and associated isomonodromic transformations. In addition, there are many experts in Riemann surface theory at the Institute. It is expected that, following the expiration of this award, collaborations between the researchers are likely to continue.

该奖项将支持加州大学戴维斯分校数学系的 Craig A. Tracy 教授及其研究生 Morris Beatty 先生前往日本进行为期六个月的长期访问，与京都大学数学科学研究所 (RIMS) T. Miwa 教授进行合作研究项目。 他们的合作研究将涉及对等单向 t 函数的持续研究，这些 t 函数源自流形上自由费米子的完整量子场论。 这对于理解和澄清双曲空间中量子场论的相位性质非常重要； 它应该允许对零曲率极限进行透明的讨论。 研究结果应该对完整量子场、可积系统和微分几何产生影响。 该研究对于数学物理中的等单性问题具有根本重要性。 这两个小组都是各自领域备受尊敬的专家。 RIMS 是研究人员开展研究的理想研究所。 在京都，他们将与 t 函数概念的发明者合作； Mikio Sato、Tetsuji Miwa 和​​ Michio Jimbo 教授。 他们都以其完整量子场和相关等单变换的创新方法而闻名。 此外，研究所还有多名黎曼曲面理论专家。 预计该奖项到期后，研究人员之间的合作可能会继续。