Development of spin geometry with the Rarita-Schwinger operators

2012 Fiscal Year Final Research Report

• Project/Area Number: 22740047
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Waseda University
• Principal Investigator: HOMMA Yasushi 早稲田大学, 理工学術院, 教授 (50329108)
• Project Period (FY): 2010 – 2012
• Keywords: 微分幾何学 / スピン幾何学 / ディラック作用素 / ラリタ・シュインガー作用素

Research Abstract

The Dirac operators and spinors are important geometrical tools to investigate differential manifolds. Such a filed in mathematics is called “spin geometry”. The purpose of this project is that we develop spin geometry with the Rarita-Schwinger operators instead of the Dirac operators. We have the following results:
(1) Some properties of spectra of the Rarita-Schwinger operator on the 3-dimHeisenberg manifold.
(2) Eta-functions and their special values for the Dirac operators on some 3-dimmanifolds (by joint work).
Besides, we found some ideas to develop spin geometry with the Rarita-Schwingeroperators.

Research Products

• [Presentation] ディラック作用素などの幾何学的一階微分作用素の話 (2012)
  • Author(s): 本間泰史
  • Organizer: 関東若手幾何セミナー
  • Place of Presentation: 首都大学東京
  • Year and Date: 2012-12-20
• [Presentation] The Rarita-Schwinger operator (spin 3/2 Dirac operator)について (2010)
  • Author(s): 本間泰史
  • Organizer: 幾何学阿蘇研究集会
  • Place of Presentation: 休暇村南阿蘇
  • Year and Date: 2010-08-31
• [Remarks] 研究集会「非可換幾何と数理物理2012」慶応大学2012年9月14、15日
• [Remarks] 研究集会「量子化の幾何学2011」早稲田大学2011年11月18、19日
• [Remarks] 研究集会「非可換幾何と数理物理2010」慶応大学2010年7月1、2日.