# The twistor programme

@article{Penrose1977TheTP, title={The twistor programme}, author={R. Penrose}, journal={Reports on Mathematical Physics}, year={1977}, volume={12}, pages={65-76} }

Abstract The formalism of twistors provides a new approach to the description of basic physics. The points of Minkowski space-time are represented by 2-dimensional linear subspaces of a complex 4-dimensional vector space (flat twistor space) on which a Hermitian form of signature ++-- is defined. Free massless fields can be represented in terms of the sheaf cohomology of portions of this space. Twistor space (or a suitable part of it) can be expressed in two different ways as a complex… Expand

#### 200 Citations

Scattering theory and the geometry of multitwistor spaces

- Mathematics
- 1983

Existing results which show the zero rest mass field equations to be encoded in the geometry of projective twistor space are extended, and it is shown that the geometries of spaces of more than one… Expand

A CP5 calculus for space-time fields

- Physics
- 1983

Abstract 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.… Expand

Gauged twistor formulation of a massive spinning particle in four dimensions

- Physics, Mathematics
- 2015

We present a gauged twistor model of a free massive spinning particle in four-dimensional Minkowski space. This model is governed by an action, referred to here as the gauged generalized Shirafuji… Expand

Cohomology and massless fields

- Physics
- 1981

The geometry of twistors was first introduced in Penrose [28]. Since that time it has played a significant role in solutions of various problems in mathemetical physics of both a linear and nonlinear… Expand

G-structures of twistor type and their twistor spaces

- Mathematics
- 1993

Abstract The notion of a group of twistor type is defined as a linear group G whose Lie algebra has an element J with J =–1. The twistor space Z of a G -structure with a connection on a manifold M is… Expand

Instantons in six dimensions and twistors

- Physics
- 2014

Abstract Recently, conformal field theories in six dimensions were discussed from the twistorial point of view. In particular, it was demonstrated that the twistor transform between chiral… Expand

Twistor formulation of a massive particle with rigidity

- Physics, Mathematics
- 2018

Abstract A massive rigid particle model in ( 3 + 1 ) dimensions is reformulated in terms of twistors. Beginning with a first-order Lagrangian, we establish a twistor representation of the Lagrangian… Expand

Twistor Cosmology and Quantum Space‐Time

- Physics
- 2005

The purpose of this paper is to present a model of a ‘quantum space‐time’ in which the global symmetries of space‐time are unified in a coherent manner with the internal symmetries associated with… Expand

Twistor transform in d dimensions and a unifying role for twistors

- Physics
- 2006

Twistors in four dimensions d=4 have provided a convenient description of massless particles with any spin, and this led to remarkable computational techniques in Yang-Mills field theory. Recently it… Expand

THE TWISTOR SPACES OF A PARA-QUATERNIONIC KÄHLER MANIFOLD

- Mathematics
- 2008

We develop the twistor theory of G-structures for which the (linear) Lie algebra of the structure group contains an involution, instead of a c omplex structure. The twistor space Z of such a… Expand

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AbstractThe formalism of twistors [the ‘spinors’ for the group O(2,4)] is employed to give a concise expression for the solution of the zero rest-mass field equations, for each spin (s=0, 1/2, 1,… Expand

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