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 - Tapa blanda

Sinopsis

Relativistic Symmetry Groups.- 1. Orthogonal and Conformal Groups.- 2. Asymptotically Simple Space-Times.- 3. The B.M.S. Group.- 4. Twistor Theory.- SL(2,C) Symmetry of the Gravitational Field.- 1. Spinor Representation of the Group SL(2,C).- 2. Connection between Spinors and Tensors.- 3. Maxwell, Weyl, and Riemann Spinors.- 4. Classification of Maxwell Spinor.- 5. Classification of Weyl Spinor.- 6. Isotopic Spin and Gauge Fields.- 7. Lorentz Invariance and the Gravitational Field.- 8. SL(2,C) Invariance and the Gravitational Field.- 9. Gravitational Field Equations.- Problems.- Coordinate Systems in Riemannian Space-Time: Classifications and Transformations; Generalization of the Poincaré Group.- 1. Introduction.- 2. Riemannian and Normal Coordinates.- 3. Transformations between Normal Coordinate Systems.- 4. Generalization of Inertial Frames to Curved Space-Time.- 5. Analytic Characterization of Geodesic Fermi Frames.- 6. Classifications of Coordinate Systems.- 7. The Principle of the Pre-Assigned Measurements.- 8. The Degree of Invariance of the Laws of Nature.- 9. Generalization of the Poincaré Group to Curved Space-Time; and Concluding Remarks.- Symmetric Spaces in Relativity and Quantum Theories.- 1. Introduction.- 2. Lie Transformation Groups, Lie Algebras, Covering and Pseudo-Orthogonal Groups.- I / Symmetric Spaces and Lie Triple Systems.- 3. Symmetric Spaces.- 4. Symmetric Spaces as Homogeneous Spaces of Groups.- 5. Lie Triple Systems as the Local Algebraic Structures of Symmetric Spaces.- 6. On Symmetric Spaces of Pseudo-Orthogonal Groups.- 7. Conformal Groups of Pseudo-Orthogonal Vector Spaces.- 8. Light Cones as Homogeneous but not Symmetric Spaces of the Pseudo-Orthogonal Groups.- 9. Applications in General Relativity.- II / Domains of Positivity and Formal Real Jordan Algebras.- 10. Domains of Positivity or Self-Dual Convex Cones.- 11. Jordan Algebras.- 12. The Relation between Domains of Positivity and Symmetric Spaces.- 13. The Jordan Algebra of Minkowski Space.- 14. The Jordan Algebra of Non-Relativistic Spin Observables.- III / Halfspaces of Jordan Algebras and Bounded Symmetric Domains.- 15. The Siegel Half Space.- 16. Halfspaces and Bounded Symmetric Domains.- 17. The Halfspace of Minkowski Space.- Boundary Values of Holomorphic Functions that Belong to Hilbert Spaces Carrying Analytic Representations of Semisimple Lie Groups.- 0. Preliminaries.- 1. The Discrete Series of SU(1,1).- 2. The Discrete Series of SU(2,2).- The Semisimp1e Subalgebras of the Algebra B3(SO(7)) and Their Inclusion Relations.- 1. Introduction.- 2. Classification Scheme.- 3. Actual Classification.- 4. Index of Embedding; Defining Matrix.- 5. Classification of Semisimple Subalgebras of B3.- External (Kinematical) and Internal (Dynamical) Conformal Symmetry and Discrete Mass Spectrum.- 1. Introduction.- 2. Conformal Transformations on External Co-ordinates.- 3. Conformal Transformations on Internal Co-ordinates.- 4. The Connection between the External and Internal Conformal Algebras. Discrete Mass Spectrum.- Non-Linear Problems in Transport Theory.- 1. A Non-Linear Transport Equation.- 2. General Properties of the Solution.- 3. Solution of the Milne Problem.- 4. Explicit Evaluation of the Milne Problem Solution.

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