The spinor and tensor fields with higher spin on spaces of constant curvature

Yasushi Homma, Takuma Tomihisa*

*この研究の対応する著者

研究成果: Article査読

抄録

In this article, we give all the Weitzenböck-type formulas among the geometric first-order differential operators on the spinor fields with spin j+ 1 / 2 over Riemannian spin manifolds of constant curvature. Then, we find an explicit factorization formula of the Laplace operator raised to the power j+ 1 and understand how the spinor fields with spin j+ 1 / 2 are related to the spinors with lower spin. As an application, we calculate the spectra of the operators on the standard sphere and clarify the relation among the spinors from the viewpoint of representation theory. Next we study the case of trace-free symmetric tensor fields with an application to Killing tensor fields. Lastly we discuss the spinor fields coupled with differential forms and give a kind of Hodge–de Rham decomposition on spaces of constant curvature.

本文言語English
ページ(範囲)829-861
ページ数33
ジャーナルAnnals of Global Analysis and Geometry
60
4
DOI
出版ステータスPublished - 2021 11月

ASJC Scopus subject areas

  • 分析
  • 政治学と国際関係論
  • 幾何学とトポロジー

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