Introduces the application of two-component spinor calculus and fibre-bundle theory to complex general relativity. This volume presents a review of basic and important topics, such as two-component spinor calculus, conformal gravity, twistor spaces for Minkowski space-time and for curved space-time, and Penrose transform for gravitation.

This volume introduces the application of two-component spinor calculus and fibre-bundle theory to complex general relativity. A review of basic and important topics is presented, such as two-component spinor calculus, conformal gravity, twistor spaces for Minkowski space-time and for curved space-time, Penrose transform for gravitation, the global theory of the Dirac operator in Riemannian four-manifolds, various definitions of twistors in curved space-time and the recent attempt by Penrose to define twistors as spin-3/2 charges in Ricci-flat space-time.Original results include some geometrical properties of complex space-times with nonvanishing torsion, the Dirac operator with locally supersymmetric boundary conditions, the application of spin-lowering and spin-raising operators to elliptic boundary value problems, and the Dirac and Rarita - Schwinger forms of spin-3/2 potentials applied in real Riemannian four-manifolds with boundary. This book is written for students and research workers interested in classical gravity, quantum gravity and geometrical methods in field theory. It can also be recommended as a supplementary graduate textbook.

Part I: Spinor Form of General Relativity. 1. Introduction to Complex Space-Time. 2. Two-Component Spinor Calculus. 3. Conformal Gravity. Part II: Holomorphic Ideas in General Relativity. 4. Twistor Spaces. 5. Penrose Transform for Gravitation. Part III: Torsion and Supersymmetry. 6. Complex Space-Times with Torsion. 7. Spin-1/2 Fields in Riemannian Geometries. 8. Spin-1/2 Potentials. Part IV: Mathematical Foundations. 9. Underlying Mathematical Structures. Problems for the Reader. Appendix A: Clifford Algebras. Appendix B: Rarita-Schwinger Equations. Appendix C: Fibre Bundles. Appendix D: Sheaf Theory.