| preface 1 the geometry of world-vectors and spin-vectors 1.1 m inkowski 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 ofspinor 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 on a manifold 2.5 spinor algebra 3 spinors and worid-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 ofspinors 4.5 differentiation ofspinor components 4.6 the curvature spinors 4.7 spinor formulation of the einstein-cartan-sciama-kibble theory 4.8 the weyl tensor and the bei-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 |
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