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This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. The choice of material presented has evolved from graduate lectures given in London and Oxford and the authors have aimed to retain the informal tone of those lectures. The book will provide graduate students with an introduction to the literature of twistor theory, presupposing some knowledge of special relativity and differential geometry. It would also be of use for a short course on space-time structure independently of twistor theory. The physicist could be introduced gently to some of the mathematics which has proved useful in these areas, and the mathematician could be shown where sheaf cohomology and complex manifold theory can be used in physics.

Twistor theory. --- Twistors --- Congruences (Geometry) --- Field theory (Physics) --- Space and time --- Twistor theory --- Torseurs, théorie des

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Twistor theory --- 514.8 --- Geometric study of objects of mechanics and physics --- Twistor theory. --- 514.8 Geometric study of objects of mechanics and physics --- Twistors --- Congruences (Geometry) --- Field theory (Physics) --- Space and time --- Space-time model --- Special relativity

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Differential geometry. Global analysis --- Harmonic maps. --- Twistor theory. --- Symmetric spaces. --- Manifolds (Mathematics) --- Applications harmoniques --- Torseurs, théorie des --- Espaces symétriques --- Variétés (Mathématiques) --- 51 --- Mathematics --- 51 Mathematics --- Cartes harmoniques --- Espaces symetriques --- Harmonic maps --- Harmonische kaarten --- Menigvuldigheden (Wiskunde) --- Symmetric spaces --- Symmetrische ruimten --- Torseurs [Théorie des ] --- Torsievectortheorie --- Twistor theory --- Varietes (Mathematiques) --- Torseurs, théorie des --- Espaces symétriques --- Variétés (Mathématiques)

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Twistor theory --- 514.8 --- Twistors --- Congruences (Geometry) --- Field theory (Physics) --- Space and time --- 514.8 Geometric study of objects of mechanics and physics --- Geometric study of objects of mechanics and physics --- Mathematical physics

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Scattering amplitudes are fundamental and rich observables in quantum field theory. Based on the observation that, for massless particles of spin-one or more, scattering amplitudes are much simpler than expected from traditional Feynman diagram techniques, the broad aim of this work is to understand and exploit this hidden structure. It uses methods from twistor theory to provide new insights into the correspondence between scattering amplitudes in supersymmetric Yang-Mills theory and null polygonal Wilson loops. By additionally exploiting the symmetries of the problem, the author succeeds in developing new ways of computing scattering amplitudes.

Geometry, Algebraic. --- Particles (Nuclear physics) --- Twistor theory. --- Twistors --- Elementary particles (Physics) --- High energy physics --- Nuclear particles --- Nucleons --- Algebraic geometry --- Physics. --- Mathematical physics. --- Quantum field theory. --- String theory. --- Elementary particles (Physics). --- Quantum Field Theories, String Theory. --- Mathematical Physics. --- Elementary Particles, Quantum Field Theory. --- Mathematical Applications in the Physical Sciences. --- Congruences (Geometry) --- Field theory (Physics) --- Space and time --- Nuclear physics --- Geometry --- Quantum theory. --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics --- Mechanics --- Thermodynamics --- Physical mathematics --- Models, String --- String theory --- Nuclear reactions --- Relativistic quantum field theory --- Quantum theory --- Relativity (Physics) --- Mathematics