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Edth-a differential operator on the sphere

Published online by Cambridge University Press:  24 October 2008

Michael Eastwood  and
Paul Tod
Michael Eastwood
Affiliation:
Institute for Advanced Study, Princeton
Paul Tod
Affiliation:
Mathematical Institute, Oxford University
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Extract

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).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 92 , Issue 2 , September 1982 , pp. 317 - 330
Copyright
Copyright © Cambridge Philosophical Society 1982

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References

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