The Dirac Equation

1. Front Matter

   Pages I-XVII

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2. Free Particles

   • Bernd Thaller

   Pages 1-41

3. The Poincaré Group

   • Bernd Thaller

   Pages 42-80

4. Induced Representations

   • Bernd Thaller

   Pages 81-105

5. External Fields

   • Bernd Thaller

   Pages 106-137

6. Supersymmetry

   • Bernd Thaller

   Pages 138-175

7. The Nonrelativistic Limit

   • Bernd Thaller

   Pages 176-192

8. Special Systems

   • Bernd Thaller

   Pages 193-221

9. Scattering States

   • Bernd Thaller

   Pages 222-249

10. Solitons

    • Bernd Thaller

    Pages 250-273

11. Quantum Electrodynamics in External Fields

    • Bernd Thaller

    Pages 274-301

12. Back Matter

    Pages 302-357

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Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Its applications are so widespread that a description of all aspects cannot be done with sufficient depth within a single volume. In this book the emphasis is on the role of the Dirac equation in the relativistic quantum mechanics of spin-1/2 particles. We cover the range from the description of a single free particle to the external field problem in quantum electrodynamics. Relativistic quantum mechanics is the historical origin of the Dirac equation and has become a fixed part of the education of theoretical physicists. There are some famous textbooks covering this area. Since the appearance of these standard texts many books (both physical and mathematical) on the non­ relativistic Schrodinger equation have been published, but only very few on the Dirac equation. I wrote this book because I felt that a modern, comprehensive presentation of Dirac's electron theory satisfying some basic requirements of mathematical rigor was still missing.

• Coulomb and Magnetic Fields
• Dirac Equations
• Dirac Gleichung
• Dirac Operator
• Dirac equation
• Index Theory
• Nonrelativistic Quantum Electrodynamics
• Quantum mechanics
• Relativistic Quantum Mechanics
• Relativistische Quantenmechanik
• Spectral and Scattering Theory
• Spektra- und Streutheori

• Institut für Mathematik, Karl-Franzens-Universität Graz, Graz, Austria

  Bernd Thaller

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