Group Theory In Non-linear Problems: Lectures Presented At The Nato Advanced Study Institute On Mathematical Physics, Held In Istanbul, Turkey, August 7-18, 1972 (nato Science Series C)

This is the second volume of a series of books in various aspects of Mathematical Physics. Mathematical Physics has made great strides in recent years, and is rapidly becoming an important dis­ cipline in its own right. The fact that physical ideas can help create new mathematical theories, and rigorous mathematical theo­ rems can help to push the limits of physical theories and solve problems is generally acknowledged. We believe that continuous con­ tacts between mathematicians and physicists and the resulting dialogue and the cross fertilization of ideas is a good thing. This series of studies is published with this goal in mind. The present volume contains contributions which were original­ ly presented at the Second NATO Advanced Study Institute on Mathe­ matical Physics held in Istanbul in the Summer of 1972. The main theme was the application of group theoretical methods in general relativity and in particle physics. Modern group theory, in par­ ticular, the theory of unitary irreducibl~ infinite-dimensional representations of Lie groups is being increasingly important in the formulation and solution of dynamical problems in various bran­ ches of physics. There is moreover a general trend of approchement of the methods of general relativity and elementary particle physics. We hope it will be useful to present these investigations to a larger audience. Front Matter....Pages I-VII Relativistic Symmetry Groups....Pages 1-58 SL(2, C) Symmetry of the Gravitational Field....Pages 59-110 Coordinate Systems in Riemannian Space-Time: Classifications and Transformations; Generalization of the Poincaré Group....Pages 111-141 Symmetric Spaces in Relativity and Quantum Theories....Pages 143-184 Boundary Values of Holomorphic Functions that Belong to Hilbert Spaces Carrying Analytic Representations of Semisimple Lie Groups....Pages 185-229 The Semisimple Subalgebras of the Algebra B 3 (SO(7)) and their Inclusion Relations....Pages 231-246 External (Kinematical) and Internal (Dynamical) Conformal Symmetry and Discrete Mass Spectrum....Pages 249-259 Non-Linear Problems in Transport Theory....Pages 261-281 Lectures presented at the NATO Advanced Study Institute, Istanbul, Turkey, August 7-18, 1972