Study on Renormalization as Invariant Theory under Infinite-dimensional Groups

2016 Fiscal Year Final Research Report

• Project/Area Number: 26610022
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Kyoto University
• Principal Investigator: UMEDA Toru 京都大学, 理学研究科, 准教授 (00176728)
• Research Collaborator: NOUMI Masatoshi 神戸大学, 大学院理学研究科, 教授 (80164672)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: Capelli 型恒等式 / Bell 多項式 / 普遍包絡環

Outline of Final Research Achievements

For the renormalization from the invariant-theoretic point of view, we studied some basic facts on the Capelli identities, Bell polynomials and differential　operator of infinite variables, and universal enveloping algebras.These are necessary for the study of the infinite dimensional group of general coordinate transformation, and for its invariants. Their importance is that they are related both group theoretic and combinatorial points of view. In particular, the study on the Bell polynomials using the differential operators of infinite variables are similar to classical invariant theoy in the sense of the featuring "ground form". This will be useful in the calculation of non-commuting variables like in the universal enveloping algebras.

Free Research Field

不変式論