Complex general relativity /

This book is written for theoretical and mathematical physicists and mat- maticians interested in recent developments in complex general relativity and their application to classical and quantum gravity. Calculations are presented by paying attention to those details normally omitted in research pap...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Esposito, Giampiero
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Dordrecht ; Boston : Kluwer Academic Publishers, ©1995.
Colección:Fundamental theories of physics ; v. 69.
Temas:
General relativity (Physics)
Quantum gravity.
Supersymmetry.
Relativité générale (Physique)
Gravité quantique.
Supersymétrie.
Quantum gravity
Supersymmetry
Andre fag (naturvidenskab og teknik) > Andre fag
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Table of Contents
  • PREFACE
  • PART I: SPINOR FORM OF GENERAL RELATIVITY
  • 1. INTRODUCTION TO COMPLEX SPACE-TIME
  • 1.1 From Lorentzian Space-Time to Complex Space-Time
  • 1.2 Complex Manifolds
  • 1.3 An Outline of This Work
  • 2. TWO-COMPONENT SPINOR CALCULUS
  • 2.1 Two-Component Spinor Calculus .
  • 2.2 Curvature in General Relativity
  • 2.3 Petrov Classification
  • 3. CONFORMAL GRAVITY.
  • 3.1 C-Spaces
  • 3.2 Einstein Spaces .
  • 3.3 Complex Space-Times
  • 3.4 Complex Einstein Spaces
  • 3.5 Conformal Infinity .
  • PART I I : HOLOMORPHIC IDEAS IN GENERAL RELATIVITY
  • 4. TWISTOR SPACES
  • 4.1 a-Planes in Minkowski Space-Time
  • 4.2 a-Surfaces and Twistor Geometry
  • 4.3 Geometrical Theory of Partial Differential Equations
  • 5. PENROSE TRANSFORM FOR GRAVITATION.
  • 5.1 Anti-Self-Dual Space-Times
  • 5.2 Beyond Anti-Self-Duality
  • 5.3 Twistors as Spin-3/2 Charges
  • PART I I I : TORSION AND SUPERSYMMETRY
  • 6. COMPLEX SPACE-TIMES WITH TORSION
  • 6.1 Introduction
  • 6.2 Frobenius' Theorem for Theories with Torsion
  • 6.3 Spinor Ricci Identities for Complex U4 Theory
  • 6.4 Integrability Condition for a -Surfaces
  • 6.5 Concluding Remarks
  • 7. S P IN-1/2 FIELDS IN RIEMANNIAN GEOMETRIES
  • 7.1 Dirac and Weyl Equations in Two-Component Spinor Form
  • 7.2 Boundary Terms for Massless Fermionic Fields
  • 7.3 Self-Adjointness of the Boundary-Value Problem
  • 7.4 Global Theory of the Dirac Operator
  • 8. SPIN-3/2 POTENTIALS
  • 8.1 Introduction
  • 8.2 Spin-Lowering Operators in Cosmology
  • 8.3 Spin-Raising Operators in Cosmology
  • 8.4 Dirac s spin 3/2 Potentials in Cosmology
  • 8.5 Boundary Conditions in Supergravity
  • 8.6 Rarita-Schwinger Potentials and Their Gauge Transformations
  • 8.7 Compatibility Conditions
  • 8.8 Admissible Background Four-Geometries
  • 8.9 Secondary Potentials in Curved Riemannian Backgrounds
  • 8.10 Results and Open Problems
  • P A R T I V :MATHEMATICAL FOUNDATIONS
  • 9 . UNDERLYING MATHEMATICAL STRUCTURES
  • 9.1 Introduction
  • 9.2 Local Twistors
  • 9.3 Global Null Twistors
  • 9.4 Hypersurface Twistors
  • 9.5 Asymptotic Twistors
  • 9.6 Penrose Transform
  • 9.7 Ambitwistor Correspondence
  • 9.8 Radon Transform
  • 9.9Massless Fields as Bundles
  • 9.10 Quantization of Field Theories
  • PROBLEMS FOR THE READER
  • APPENDIX A: Clifford Algebras
  • APPENDIX B: Rarita-Schwinger Equations
  • APPENDIX C: Fibre Bundles
  • APPENDIX D: Sheaf Theory
  • BIBLIOGRAPHY
  • SUBJECT INDEX.
  • Last Page.

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