Group Theory and General Relativity: Representations of the Lorentz Group and Their Applications to the Gravitational Field (McGraw-Hill Series in Electrical Engineering)

A study of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works on the use of group theory in general relativity theory. There are 12 chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups - particularly the Lorentz and the SL(2,C) groups - to the theory of general relativity. Each chapter is concluded with a set of problems. The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2,C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book. The entire work is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed. The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and should be of interest to theoretical physicists, general relativists and applied mathematicians. It should also be useful to graduate students and research workers in quantum field theory, general relativity and elementary particle theory.