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Quantum Mechanics in the Geometry of Space-Time

Elementary Theory

  • Book
  • © 2011

Overview

Authors:
  1. Roger Boudet

    1. Université de Provence, Bassan, France

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  • Represents the most complete treatment of relativistic quantum mechanics in terms of real spacetime algebra
  • Demonstrates practical advantages of STA theory
  • Shows how to incorporate electroweak theory and gives novel insight into calculation of the Lamb shift, one of the pivotal problems in relativistic quantum theory

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

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Table of contents (19 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Roger Boudet
    Pages 1-3

  3. The Real Geometrical Algebra or Space–Time Algebra. Comparison with the Language of the Complex Matrices and Spinors

    1. Front Matter

      Pages 5-5
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  4. The Real Geometrical Algebra or Space-Time Algebra. Comparison with the Language of the Complex Matrices and Spinors

    1. The Clifford Algebra Associated with the Minkowski Space–Time M

      • Roger Boudet
      Pages 7-11

    2. Comparison Between the Real and the Complex Language

      • Roger Boudet
      Pages 13-17

  5. 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

    1. Front Matter

      Pages 19-19
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    2. Geometrical Properties of the U(1) Gauge

      • Roger Boudet
      Pages 21-24

    3. Relation Between the U(1) Gauge, the Spin and the Energy of a Particle of Spin 1/2

      • Roger Boudet
      Pages 25-26

  6. Geometrical Properties of the Dirac Theory of the Electron

    1. Front Matter

      Pages 27-27
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    2. The Dirac Theory of the Electron in Real Language

      • Roger Boudet
      Pages 29-34

    3. The Invariant Form of the Dirac Equation and Invariant Properties of the Dirac Theory

      • Roger Boudet
      Pages 35-42

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

    1. Front Matter

      Pages 43-43
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  8. The SU(2) Gauge and the Yang-Mills Theory in Complex and Real Languages

    1. Geometrical Properties of the SU(2) Gauge and the Associated Momentum–Energy Tensor

      • Roger Boudet
      Pages 45-50

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

    1. Front Matter

      Pages 51-51
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  10. The SU(2) x U(1) Gauge in Complex and Real Languages

    1. Geometrical Properties of the SU(2)\(\times\)U(1) Gauge

      • Roger Boudet
      Pages 53-57

  11. The Glashow–Salam–Weinberg Electroweak Theory

    1. Front Matter

      Pages 59-59
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  12. The Glashow-Salam-Weinberg Electroweak Theory

    1. The Electroweak Theory in STA: Global Presentation

      • Roger Boudet
      Pages 61-66

    2. The Electroweak Theory in STA: Local Presentation

      • Roger Boudet
      Pages 67-72

  13. On a Change of SU(3) into Three SU(2) x U(1)

    1. Front Matter

      Pages 73-73
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  14. On a Change of SU(3) into Three SU(2) x U(1)

    1. On a Change of SU(3) into Three SU(2)\(\times \)U(1)

      • Roger Boudet
      Pages 75-79
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Keywords

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.

Reviews

From the reviews:

“This textbook addresses graduate students and researchers interested in quantum mechanics. … The author creates a very readable and well-accessible account of this new approach to quantum mechanics. … The basic endeavor of the book is a full translation of quantum mechanics into the real and invariant language of the Clifford algebra of space-time.” (Eckhard M. S. Hitzer, Mathematical Reviews, Issue 2012 m)

Authors and Affiliations

  • Université de Provence, Bassan, France

    Roger Boudet

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