Quantum Mechanics in the Geometry of Space-Time

Elementary Theory

  • Roger Boudet

Part of the SpringerBriefs in Physics book series (SpringerBriefs in Physics)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Roger Boudet
    Pages 1-3
  3. The Real Geometrical Algebra or Space–Time Algebra. Comparison with the Language of the Complex Matrices and Spinors

  4. The U(1) Gauge in the Complex and Real Languages. Geometrical Properties and Relation with the Spin and the Energy of a Particle of Spin 1/2

  5. Geometrical Properties of the Dirac Theory of the Electron

  6. The SU(2) Gauge and the Yang–Mills Theory in Complex and Real Languages

  7. The SU(2) x U(1) Gauge in Complex and Real Languages

    1. Front Matter
      Pages 51-51
  8. The Glashow–Salam–Weinberg Electroweak Theory

    1. Front Matter
      Pages 59-59
  9. On a Change of SU(3) into Three SU(2) x U(1)

    1. Front Matter
      Pages 73-73
  10. Addendum

    1. Front Matter
      Pages 81-81
    2. Roger Boudet
      Pages 83-101
  11. Appendices

    1. Front Matter
      Pages 103-103
    2. Roger Boudet
      Pages 123-124
    3. Roger Boudet
      Pages 125-128
  12. Back Matter
    Pages 129-130

About this book


This book continues the fundamental work of Arnold Sommerfeld and David Hestenes formulating theoretical physics in terms of Minkowski space-time geometry. We see how the standard matrix version of the Dirac equation can be reformulated in terms of a real space-time algebra, thus revealing a geometric meaning for the “number i” in quantum mechanics. Next, it is examined in some detail how electroweak theory can be integrated into the Dirac theory and this way interpreted in terms of space-time geometry. Finally, some implications for quantum electrodynamics are considered.The presentation of real quantum electromagnetism is expressed in an addendum. The book covers both the use of the complex and the real languages and allows the reader acquainted with the first language to make a step by step translation to the second one.


Algebraic Languages Clifford Algebra Dirac Theory of the Electron Euclidean space Gauge and the Yang-Mills Theory Glashow-Salam-Weinberg Electroweak Theory Isospin Matrices Minkowski Space-Time Quantum Electromagnetism Quantum Field Theory Spin and the Energy of a Particle

Authors and affiliations

  • Roger Boudet
    • 1
  1. 1.Université de ProvenceBassanFrance

Bibliographic information

Industry Sectors
Energy, Utilities & Environment