包邮旋量与时空-第1卷

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