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

Yasushi Homma, Takuma Tomihisa*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Pages (from-to)829-861
Number of pages33
JournalAnnals of Global Analysis and Geometry
Volume60
Issue number4
DOIs
Publication statusPublished - 2021 Nov

Keywords

  • Generalized gradients
  • Harmonic analysis on spheres
  • Space of constant curvature
  • The (higher spin) Dirac
  • The Lichnerowicz Laplacian
  • Weitzenböck formulas

ASJC Scopus subject areas

  • Analysis
  • Political Science and International Relations
  • Geometry and Topology

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