The Special Theory of Relativity

Based on a course taught at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view. It begins with the axioms for Minkowski space-time, and discusses the kinematics of Special Relativity in terms of Lorentz transformations. Extending the discussion to spinors, the author shows how a unimodular mapping of the spinor space can induce a proper Lorentz mapping on the Minkowski space. Relativistic mechanics is discussed from a Lagrangian point of view, and the book concludes with a development of relativistic (classical) field theory, including a proof of Noether's theorem and discussions of the Klein-Gordon, electromagnetic, and Dirac fields. The final chapter describes recent work on classical fields in an eight-dimensional covariant phase space.