Journal ArticleDOI
The twistor programme
TLDR
The twistor formalism as discussed by the authors provides a new approach to the description of basic physics, where 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.About:
This article is published in Reports on Mathematical Physics.The article was published on 1977-08-01. It has received 249 citations till now. The article focuses on the topics: Twistor space & Twistor theory.read more
Citations
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Journal ArticleDOI
Loop Quantum Gravity
TL;DR: A general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity is provided, and a guide to the relevant literature is provided.
Journal ArticleDOI
Instantons and algebraic geometry
Michael Atiyah,R. S. Ward +1 more
TL;DR: In this paper, it was shown that SU(2) Yang-Mills fields in Euclidean 4-space correspond, via the Penrose twistor transform, to algebraic bundles on the complex projective 3-space.
Book
Geometry of Yang-Mills fields
TL;DR: The major breakthrough came with the observation by Ward that the complex methods developed by Penrose in his 'twistor programme' were ideally suited to the study of the Yang-Mills equations.
Journal ArticleDOI
Cohomology and massless fields
TL;DR: In this paper, an integral-geometric transform is used to transform complex-analytic data on twistor space to solutions of the linear massless free-field equations, including Maxwell's source-free equations, the wave equation, the Dirac-Weyl neutrino equations, and the linearized (weakfield limit of) Einstein's vacuum equations.
Journal ArticleDOI
Superstrings and supermembranes in the doubly supersymmetric geometrical approach
TL;DR: In this article, a generalization of the geometrical approach to describing extended objects for studying the doubly supersymmetric twistor-like formulation of super p -branes is presented.
References
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Book
Analytic functions of several complex variables
Robert C. Gunning,Hugo Rossi +1 more
TL;DR: The theory of analytic functions of several complex variables enjoyed a period of remarkable development in the middle part of the twentieth century after initial successes by Poincare and others in the late 19th and early 20th centuries, the theory encountered obstacles that prevented it from growing quickly into an analogue of the theory for functions of one complex variable as discussed by the authors.
Book
Analytic functions of several complex variables
Carl Ludwig Siegel,P. T. Bateman +1 more
TL;DR: In this article, the authors discuss the properties of holomorphic functions of complex vectors in more detail, including their properties with respect to their properties in the context of complex vector models.
Book
Differential analysis on complex manifolds
TL;DR: In this paper, the authors present an introduction to the basics of analysis and geometry on compact complex manifolds and provide tools which are the building blocks of many mathematical developments over the past 30 years.
Journal ArticleDOI
Nonlinear gravitons and curved twistor theory
TL;DR: In this paper, a new approach to the quantization of general relativity is suggested in which a state consisting of just one graviton can be described, but in a way which involves both the curvature and nonlinearities of Einstein's theory.
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Twistor theory: An approach to the quantisation of fields and space-time
R. Penrose,Malcolm MacCallum +1 more
TL;DR: Twistor theory as mentioned in this paper is a new approach, starting with conformally-invariant concepts, to the synthesis of quantum theory and relativity, and it is represented here in two-component spinor terms.