Complex General Relativity

Description:

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.

subjects: Quantum gravity,  General relativity (Physics),  Supersymmetry,  Partial Differential equations,  Mathematical physics,  Global differential geometry,  Mathematics,  Algebraic Geometry,  Physics,  Differential Geometry,  Geometry, algebraic,  Differential equations, partial,  Mathematical and Computational Physics,  Applications of Mathematics,  Relativité générale (Physique),  Gravité quantique,  Supersymétrie