A CP5 Calculus for Space-Time Fields

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Hughston, L P and Hurd, T R. 1983. A CP5 Calculus for Space-Time Fields. Physics Reports, 100(5), pp. 273-326. ISSN 0370-1573 [Article]

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Official URL: https://doi.org/10.1016/0370-1573(83)90003-0

Abstract or Description

Compactified Minkowski space can be embedded in projective five-space CP 5 (homogeneous coordinates X i , i = 0, …, 5) as a four dimensional quadric hypersurface given by Ω ij X i X j = 0. Projective twistor space (homogeneous coordinates Z α , α = 0, …, 3) arises via the Klein representation as the space of two-planes lying on this quadric. These two facts of projective geometry form the basis for the construction of a global space-time calculus which makes use of the coordinates X i ↔X αβ (=-X βα ) to represent spinor and tensor fields in a manifestly conformally covariant form. This calculus can be regarded as a synthesis of work on conformal geometry by Veblen, Dirac, and others, with the theory of twistors developed by Penrose.

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Article

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https://doi.org/10.1016/0370-1573(83)90003-0