Relativistic Quantum Mechanics and Introduction to Field Theory

1. Front Matter

   Pages I-XII

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2. Relativistic Transformations. The Lorentz Group

   • Francisco J. Ynduráin

   Pages 1-22

3. The Klein-Gordon Equation. Relativistic Equation for Spinless Particles

   • Francisco J. Ynduráin

   Pages 23-34

4. Spin 1/2 Particles

   • Francisco J. Ynduráin

   Pages 35-66

5. Dirac Particle in a Potential

   • Francisco J. Ynduráin

   Pages 67-88

6. Massive Particles with Spin 1. Massless Spin 1 Particle: Photon Wave Functions. Particles with Higher Spins (3/2, 2, …)

   • Francisco J. Ynduráin

   Pages 89-107

7. General Description of Relativistic States

   • Francisco J. Ynduráin

   Pages 109-128

8. General Description of Relativistic Collisions: S Matrix, Cross-sections and Decay Rates. Partial Wave Analyses

   • Francisco J. Ynduráin

   Pages 129-158

9. Quantization of the Electromagnetic Field. Interaction of Radiation with Matter

   • Francisco J. Ynduráin

   Pages 159-188

10. Quantum Fields: Spin 0, 1/2, 1. Covariant Quantization of the Electromagnetic Field

    • Francisco J. Ynduráin

    Pages 189-228

11. Interactions in Quantum Field Theory. Nonrelativistic Limit. Reduction to Equivalent Potential

    • Francisco J. Ynduráin

    Pages 229-265

12. Relativistic Collisions in Field Theory. Feynman Rules. Decays

    • Francisco J. Ynduráin

    Pages 267-290

13. Relativistic Interactions with Classical Sources

    • Francisco J. Ynduráin

    Pages 291-308

14. Back Matter

    Pages 309-332

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A fully relativistic treatment of the quantum mechanics of particles requires the introduction of quantum field theory, that is to say, the quantum mechan­ ics of systems with an infinite number of degrees of freedom. This is because the relativistic equivalence of mass and energy plus the quantum possibility of fluctuations imply the existence of (real or virtual) creation and annihilation of particles in unlimited numbers. In spite of this, there exist processes, and energy ranges, where a treat­ ment in terms of ordinary quantum mechanical tools is appropriate, and the approximation of neglecting the full field-theoretic description is justified. Thus, one may use concepts such as potentials, and wave equations, clas­ sical fields and classical currents, etc. The present text is devoted precisely to the systematic discussion of these topics, to which we have added a gen­ eral description of one- and two-particle relativistic states, in particular for scattering processes. A field-theoretic approach may not be entirely avoided, and in fact an introduction to quantum field theory is presented in this text. However, field theory is not the object per se of this book; apart from a few examples, field theory is mainly employed to establish the connection with equivalent potentials, to study the classical limit of the emission of radiation or to discuss the propagation of a fermion in classical electromagnetic fields.

• Cross Section
• Potential
• S-Matrix
• Spin
• quantum field theory
• quantum mechanics
• relativistic Quantum Mechanics

• Departamento de Física Teórica, Universidad Autónoma de Madrid, Madrid, Spain

  Francisco J. Ynduráin

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