论文标题
在恒定曲率的空间上，旋转器和张量场具有较高的自旋磁场
The spinor and tensor fields with higher spin on spaces of constant curvature
论文作者
论文摘要
在本文中，我们在旋转曲线的Riemannian Spin歧管上旋转$ J+1/2 $的几何差异算子之间给出了所有Weitzenböck-type公式。然后，我们找到了提高到功率$ j+1 $的拉普拉斯操作员的明确分解公式，并了解旋转$ j+1/2 $的旋转磁场与较低旋转的旋转器有关。作为应用程序，我们从表示理论的角度来计算算子在标准球上的光谱，并阐明纺纱器之间的关系。接下来，我们研究了无微量的对称张量场，并应用于杀死张量场的应用。最后，我们讨论了旋转磁场，再加上差异形式，并在恒定曲率的空间上给出了一种hodge-de rham分解。
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.
