Abstract
The Penrose transform has its origin in a contour integral formula established by R. Penrose; a holomorphic function with suitable singularities on the twistor space was used in the formula to produce a solution of the massless field equations (i.e. the Laplace and Dirac equations and similar equations for higher spins) on Minkowski space (see [61]). This procedure quickly developed into a full mathematical theory, where the Penrose transform is presented as a 1-1 map between holomorphic solutions of the massless field equation on a domain in the complexified Minkowski space and certain cohomology groups on the corresponding region in the twistor space (see [27]). A systematic description of the Penrose transform in this setting can be found in the book by Ward and Wells ([88]).
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© 1992 Springer Science+Business Media Dordrecht
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Delanghe, R., Sommen, F., Souček, V. (1992). Clifford analysis and the Penrose transform. In: Clifford Algebra and Spinor-Valued Functions. Mathematics and Its Applications, vol 53. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2922-0_6
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DOI: https://doi.org/10.1007/978-94-011-2922-0_6
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-5297-9
Online ISBN: 978-94-011-2922-0
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