Studies on Dynamical systems

动力系统研究

• 批准号: 03640099
• 负责人: SUZUKI Osamu
• 金额: $ 1.02万
• 依托单位: Nihon University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for General Scientific Research (C)
• 财政年份: 1991
• 资助国家: 日本
• 起止时间: 1991 至 1993
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-03640099/
• 关键词: gauge thery; flat extension therem; devergence in quantum field theory; Symmetry structure; algebroid; anomaly; 相転移; K.M.S状態; ゲージ接続; 平坦拡張定理; 非可変微分幾何; 量子場の発散; algebroid; 指数定理; Gauss-Bonnet定理; Singular pertuvbation; flat connection; Diff.eq

A new formalism for gauge connections is given and monlinear gauge eauations are solved and the divergence of quantu field theory is discussed. The following results are obtained.(1) A gauge theory is formulated in termas of a certain kind of a decomposition of a linear space, whitch is called a "gauge decomposition." Then every gauge connection connection can be extended to a flat connection, when it admits a representation in some algebra (flat extension theorem).(2) By use of the result (1), nonlinear gauge equations can be solved by use of a decomposition of a solution of a linear equation. Symmetry structures and special class of silutions can be discussed as a "Galois thery for differntial equations". When it has a representation in "algebroids", divergece appears and anomaly and renormalization can discussed in this case.

本文给出了规范连接的一种新形式，求解了非线性规范方程，讨论了量子场论的发散性。得到了以下结果。(1)规范理论是用线性空间的某种分解来表述的，这种分解被称为“规范分解”。“那么每个规范联络都可以被扩展为平坦联络，当它允许在某个代数中的表示时（平坦扩张定理）。(2)利用结果（1），非线性规范方程可以通过利用线性方程的解的分解来求解。对称结构和特殊类的解可以作为“微分方程的伽罗瓦定理”来讨论。当它在“代数胚”中有表示时，发散就出现了，这时就可以讨论反常和重整化问题。

项目成果

西岡久美子: "Mahler関数と超越数" 慶応大学, (1991)

西冈久美子：“马勒函数和超越数”庆应义塾大学，（1991）

SUZUKI.O: The duality theorem for the Hurwitz pairs of bidimension (8,5) and the Penrose theory. Kluwer Academic Publ, 209-212 (1994)

SUZUKI.O：Hurwitz 双维 (8,5) 对的对偶定理和彭罗斯理论。

西岡久美子: "Algebraic independence mesures of values of Mahler functions" J.reine angew.Math.420. 203-214 (1991)

Kumiko Nishioka：“马勒函数值的代数独立性测度”J.reine angew.Math.420（1991）。

鈴木理: "Supercomplex structures,surface soliton equations and quasiconformal mappings" Ann.Polo.Math.55. 245-268 (1991)

Osamu Suzuki：“超复杂结构、表面孤子方程和拟共形映射”Ann.Polo.Math.55 (1991)。

谷口彰男: "On the radii of starlikeness and convexity for certain multivalent functions" Proc.Inst.N.Scie.,Nihon Univ.26. 87-94 (1991)

Akio Taniguchi：“关于某些多价函数的星状半径和凸性”Proc.Inst.N.Scie.，Nihon Univ.26 (1991)。