Relativistic Quantum Mechanics of Leptons and Fields, Softcover reprint of the original 1st ed. 1991
Fundamental Theories of Physics Series, Vol. 41

The material contained in this work concerns relativistic quantum mechanics, and as such pertains to classical fields. On the one hand it is meant to serve as a text on the subject, a desire stemming from the author's fruitless searches for an adequate, up-to-date reference when lecturing on these topics. At times the supplementary material was found to exceed by far that in the assigned text. On the other hand, there is some flavor of a monograph to what follows, most particularly in the later chapters, for a major goal is to demonstrate just how far we can advance our understanding of the behavior of stable particles and their interactions without introducing quantized fields. Those wishing to describe the world in this way may view the result as a point of departure, despite the fact that their wish remains unfulfilled. Confirmed quantum-field theorists, however, will doubtless view it as a summary of just why they feel compelled to quantize the fields. Approximately half the book is devoted to the single-particle Dirac equation and its solutions. A great deal of detail is provided in this respect, and the discus­ sion is reasonably comprehensive. The Dirac equation is extraordinarily important in its own right, particularly as a basis for quantum electrodynamics (QED), and is thus worthy of extensive study.

1 Nonrelativistic Quantum Mechanics.- A. Review of the Formalism.- B. Electromagnetic Fields and Spin.- C. The Two-Body Problem.- D. A Preliminary Next Step.- References.- 2 The Dirac Equation.- A. Spacetime Structure and Lorentz Transformations.- B. Dirac’s Way.- C. Zitterbewegung.- References.- 3 Electromagnetic Coupling.- A. External Electromagnetic Fields.- B. Discrete Symmetries.- References.- 4 Neutral Fermions and Bosons.- A. Neutral Fermions.- B. Theory of the Neutrino.- C. Boson Wave Equations.- References.- 5 Further Electromagnetic Interactions.- A. Electromagnetic Plane Waves.- B. Uniform Static Magnetic Field.- C. Other External-Field Problems.- D. Quasi-Static Particle-Particle Interactions.- References.- 6 Lagrangian Formulation and Green Functions.- A. Lagrangian Field Theory.- B. Boson Fields.- C. Propagator Theory.- D. Coulomb Green Functions.- References.- Chapter7 Quantum Theory of Radiation.- A. Quantum Field Theory.- B. Maxwell-Dirac Field Theory.- References.- Chapter8 The Two-Body Problem.- A. Equations of Motion.- B. Analysis of the Radial Equations.- C. Applications.- References.- Chapter9 Dirac Scattering Theory.- A. Nonrelativistic Review.- B. Two-Component Pauli Theory.- C. Relativistic Scattering.- D. Covariant Scattering Formalism.- References.- Chapter10 Quantum Electrodynamics.- Electromagnetic Field.- Dirac Field.- Uniform Magnetic Field.- Synchrotron Radiation.- Coulomb Field.- Vacuum Polarization.- Problems.- References.- Classical Theory of the Electron.