Spinors and space-time. Volume 1, Two-spinor calculus and relativistic fields / Roger Penrose, Wolfgang Rindler.

"Reprinted with corrections 1986"--Title page verso

Includes bibliographical references (pages 435-443) and index.

This volume introduces and systematically develops the calculus of 2-spinors. This is the first detailed exposition of this technique which leads not only to a deeper understanding of the structure of space-time, but also provides shortcuts to some very tedious calculations. Many results are given here for the first time.

Cover -- Half-title -- Title -- Copyright -- Contents -- Preface -- 1 The geometry of world-vectors and spin-vectors -- 1.1 Minkowski vector space -- 1.2 Null directions and spin transformations -- 1.3 Some properties of Lorentz transformations -- 1.4 Null flags and spin-vectors -- 1.5 Spinorial objects and spin structure -- 1.6 The geometry of spinor operations -- 2 Abstract indices and spinor algebra -- 2.1 Motivation for abstract-index approach -- 2.2 The abstract-index formalism for tensor algebra -- 2.3 Bases.

2.4 The total reflexivity of 6* on a manifold -- 2.5 Spinor algebra -- 3 Spinors and world-tensors -- 3.1 World-tensors as spinors -- 3.2 Null flags and complex null vectors -- 3.3 Symmetry operations -- 3.4 Tensor representation of spinor operations -- 3.5 Simple propositions about tensors and spinors at a point -- 3.6 Lorentz transformations -- 4 Differentiation and curvature -- 4.1 Manifolds -- 4.2 Covariant derivative -- 4.3 Connection-independent derivatives -- 4.4 Differentiation of spinors -- 4.5 Differentiation of spinor components.

4.6 The curvature spinors -- 4.7 Spinor formulation of the Einstein-Cartan-Sciama-Kibble theory -- 4.8 The Weyl tensor and the Bel-Robinson tensor -- 4.9 Spinor form of commutators -- 4.10 Spinor form of the Bianchi identity -- 4.11 Curvature spinors and spin-coefficients -- 4.12 Compacted spin-coefficient formalism -- 4.13 Cartan's method -- 4.14 Applications to 2-surfaces -- 4.15 Spin-weighted spherical harmonics -- 5 Fields in space-time -- 5.1 The electromagnetic field and its derivative operator.

5.2 Einstein-Maxwell equations in spinor form -- 5.3 The Rainich conditions -- 5.4 Vector bundles -- 5.5 Yang-Mills fields -- 5.6 Conformal rescalings -- 5.7 Massless fields -- 5.8 Consistency conditions -- 5.9 Conformal invariance of various field quantities -- 5.10 Exact sets of fields -- 5.11 Initial data on a light cone -- 5.12 Explicit field integrals -- Appendix: diagrammatic notation -- References -- Subject and author index -- Index of symbols.

Online resource; title from digital title page (viewed on December 13, 2019).

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