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The Special Theory of Relativity

A Mathematical Exposition

  • Textbook
  • © 1993

Overview

Authors:
  1. Anadijiban Das

    1. Department of Mathematics and Statistics, Simon Fraser University, Burnaby, Canada

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Part of the book series: Universitext (UTX)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xii
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  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
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Keywords

About this book

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.

Authors and Affiliations

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

    Anadijiban Das

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