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Synopsis
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.
Booknews
Details developments in complex general relativity and their application to classical and quantum gravity, focusing on the application of spinor calculus and fiber-bundle theory to complex general relativity. Treats complex manifolds, spinor techniques, conformal gravity, and complex space-time models with non-vanishing torsion, and discusses recent attempts by Penrose to define twistors as spin-3/2 charges in Ricci-flat space-time. Includes problems. For physicists, mathematicians, and graduate students. Annotation c. Book News, Inc., Portland, OR (booknews.com)