Edth-a differential operator on the sphere
Edth-a differential operator on the sphere
复制标题
Edth-球面上的微分算子
DOI：
10.1017/s0305004100059971
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发表时间：
1982
影响因子：
0.8
通讯作者：
P. Tod
中科院分区：
文献类型：
--
作者：
M. Eastwood;P. Tod
导言。在(9)中，纽曼和彭罗斯引入了一种微分运算符，他们将其表示为Fin，音标Edth。这个运算符作用于两球面上的自旋加权函数或自旋和共形加权函数。通过球面的共形群与真非齐次洛伦兹群(11，4)的同构，证明它在相对论中是非常有用的。特别地，它可以被看作是SO(3)的适当表示的角动量降低算符，并且可以用来研究洛伦兹群(4)的表示。最近，Edth出现在Good Cut方程中，描述了渐近平坦的时空的纽曼ℋ空间(10)。这一发展与彭罗斯的旋风理论密切相关，特别是与渐近旋风理论(14)有关。
Introduction. In (9) Newman and Penrose introduced a differential operator which they denoted ð, the phonetic symbol edth. This operator acts on spin weighted, or spin and conformally weighted functions on the two-sphere. It turns out to be very useful in the theory of relativity via the isomorphism of the conformal group of the sphere and the proper inhomogeneous Lorentz group (11, 4). In particular, it can be viewed (2) as an angular momentum lowering operator for a suitable representation of SO(3) and can be used to investigate the representations of the Lorentz group (4). More recently, edth has appeared in the good cut equation describing Newman's ℋ-space for an asymptotically flat space-time (10). This development is closely related to Penrose's theory of twistors and, in particular, to asymptotic twistors (14).