TY - JOUR
T1 - The spinor and tensor fields with higher spin on spaces of constant curvature
AU - Homma, Yasushi
AU - Tomihisa, Takuma
N1 - Funding Information:
This work was partially supported by JSPS KAKENHI (Grant Number JP19K03480) and Waseda University Grant for Special Research Projects (Project number: 2020C-614). We thank the anonymous referee for helpful comments.
Publisher Copyright:
© 2021, The Author(s).
PY - 2021/11
Y1 - 2021/11
N2 - 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.
AB - 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.
KW - Generalized gradients
KW - Harmonic analysis on spheres
KW - Space of constant curvature
KW - The (higher spin) Dirac
KW - The Lichnerowicz Laplacian
KW - Weitzenböck formulas
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U2 - 10.1007/s10455-021-09791-4
DO - 10.1007/s10455-021-09791-4
M3 - Article
AN - SCOPUS:85111627908
SN - 0232-704X
VL - 60
SP - 829
EP - 861
JO - Annals of Global Analysis and Geometry
JF - Annals of Global Analysis and Geometry
IS - 4
ER -