Quantization of Geometry: A trial for the construction of non-commutative field theory

2015 Fiscal Year Final Research Report

• Project/Area Number: 25610015
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Tohoku University (2014-2015); Keio University (2013)
• Principal Investigator: MAEDA YOSHIAKI 東北大学, 知の創出センター, 特任教授(研究) (40101076)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 変形量子化 / 超弦理論 / ケーラー多様体 / 非可換ゲージ理論 / 量子場理論 / 素粒子物理学 / 国際交流ベルギー

Outline of Final Research Achievements

This study is a challenge for constructing a field theory from a non-commutative geometrical point of view. The original idea for this study is to use the deformation quantization, in particular, our advantage is to use the non-formal deformation quantization. By using this, we construct the non-commutative gauge theory on 4-manifolds. Other topic we have worked is to study infinite dimensional categories of deformation quantization via psued differential operators. In particular, we construct characteristic classes for loop space by using the regularization method. As an application, we showed the non-triviality of the fundamental group of the group of diffeomorphisms of 5 dimensional compact manifolds.

Free Research Field

微分幾何学