The Special Theory of Relativity

1. Front Matter

   Pages i-xii

   PDF

2. Four-Dimensional Vector Spaces and Linear Mappings

   • Anadijiban Das

   Pages 1-19

3. Flat Minkowski Space-Time Manifold M4 and Tensor Fields

   • Anadijiban Das

   Pages 20-47

4. The Lorentz Transformation

   • Anadijiban Das

   Pages 48-71

5. Pauli Matrices, Spinors, Dirac Matrices, and Dirac Bispinors

   • Anadijiban Das

   Pages 72-88

6. The Special Relativistic Mechanics

   • Anadijiban Das

   Pages 89-119

7. The Special Relativistic Classical Field Theory

   • Anadijiban Das

   Pages 120-167

8. The Extended (or Covariant) Phase Space and Classical Fields

   • Anadijiban Das

   Pages 168-201

9. Back Matter

   Pages 202-215

   PDF

Based on courses taught at the University of Dublin, Carnegie Mellon University, and mostly at Simon Fraser University, this book presents the special theory of relativity from a mathematical point of view. It begins with the axioms of the Minkowski vector space and the flat spacetime manifold. Then it discusses the kinematics of special relativity in terms of Lorentz tranformations, and treats the group structure of Lorentz transformations. Extending the discussion to spinors, the author shows how a unimodular mapping of spinor (vector) space can induce a proper, orthochronous Lorentz mapping on the Minkowski vector space. The second part begins with a discussion of relativistic particle mechanics from both the Lagrangian and Hamiltonian points of view. The book then turns to the relativistic (classical) field theory, including a proof of Noether's theorem and discussions of the Klein-Gordon, electromagnetic, Dirac, and non-abelian gauge fields. The final chapter deals with recent work on classical fields in an eight-dimensional covariant phase space.

• Lorentz group
• Lorentz transformation
• Minkowski space
• RMS
• Relativity
• Special relativity
• special theory of relativity

• Department of Mathematics and Statistics, Simon Fraser University, Burnaby, Canada

  Anadijiban Das