Spinors and space-time. Volume 1, Two-spinor calculus and relativistic fields /

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 h...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Penrose, Roger (Autor), Rindler, Wolfgang, 1924- (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge ; New York : Cambridge University Press, [1986]
Colección:Cambridge monographs on mathematical physics.
Temas:
Space and time.
Spinor analysis.
Analyse spinorielle.
SCIENCE > Energy.
SCIENCE > Mechanics > General.
SCIENCE > Physics > General.
Space and time
Spinor analysis
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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