Relativistic Quantum Mechanics of Leptons and Fields

ISBN-13: 9789401054584 / Angielski / Miękka / 2012 / 438 str.

Jr. Walter T. Grandy

Opis

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."

Spis treści

1 Nonrelativistic Quantum Mechanics.- A. Review of the Formalism.- Space-Time Symmetries.- The Spinor Representation.- B. Electromagnetic Fields and Spin.- Inclusion of the Spin.- Uniform Magnetic Field.- C. The Two-Body Problem.- D. A Preliminary Next Step.- Problems.- References.- 2 The Dirac Equation.- A. Spacetime Structure and Lorentz Transformations.- The Homogeneous Lorentz Group.- Spinors Revisited.- B. Dirac’s Way.- Properties of the Dirac Matrices.- Relativistic Covariance.- Free-Particle Solutions.- Negative-Energy States.- Observables and Wavepackets.- C. Zitterbewegung.- Problems.- References.- 3 Electromagnetic Coupling.- A. External Electromagnetic Fields.- Nonrelativistic Limit.- Central Fields.- The Coulomb Field.- Continuous Spectrum.- Strong Fields.- Electromagnetic Structure.- B. Discrete Symmetries.- Space Reflection (Parity).- Time Reversal.- Charge Conjugation.- Symmetry Breaking.- Problems.- References.- 4 Neutral Fermions and Bosons.- A. Neutral Fermions.- Massless Particles.- B. Theory of the Neutrino.- The Weyl Theory.- The Four-Component Neutrino.- Lepton Families.- C. Boson Wave Equations.- Spin-0 Bosons.- Spin-1 Bosons.- The Photon.- Problems.- References.- 5 Further Electromagnetic Interactions.- A. Electromagnetic Plane Waves.- B. Uniform Static Magnetic Field.- The Heisenberg Equations and Spin.- Stationary States.- Inclusion of the Anomalous Moment.- C. Other External-Field Problems.- Linear Potentials.- Crossed Electric and Magnetic Fields.- Summary of Further Results.- D. Quasi-Static Particle-Particle Interactions.- Anomalous Moment in a Coulomb Field.- Charged Magnetic Dipole Field.- The General Eigenvalue Problem.- Relativistic Wave Equations.- Problems.- References.- 6 Lagrangian Formulation and Green Functions.- A. Lagrangian Field Theory.- The Electromagnetic Field.- B. Boson Fields.- Electromagnetic Field.- C. Propagator Theory.- The Relativistic Propagator.- D. Coulomb Green Functions.- Summary.- Free-Particle Reduction.- Problems.- References.- Chapter7 Quantum Theory of Radiation.- A. Quantum Field Theory.- Quantum Electrodynamical Results—A Survey.- Critique.- B. Maxwell-Dirac Field Theory.- Free Fields.- Interacting Fields.- Critique.- Problems.- References.- Chapter8 The Two-Body Problem.- A. Equations of Motion.- Self-Energy and Radiative Effects.- Relative and Center-of-Mass Motions.- Angular-Radial Separation.- Radial Equations.- B. Analysis of the Radial Equations.- Perturbation Theory.- C. Applications.- Hydrogen.- Muonium.- Positronium.- The Annihilation Contribution.- Problems.- References.- Chapter9 Dirac Scattering Theory.- A. Nonrelativistic Review.- The Two-Body Problem.- Spherical Symmetry.- B. Two-Component Pauli Theory.- Spin-1/2—Spin-0.- Spin-1/2—Spin-1/2.- Particle Beams.- Helicity Formulation.- C. Relativistic Scattering.- Coulomb Scattering of Electrons.- Polarization of Dirac Particles.- D. Covariant Scattering Formalism.- Spin-1/2—Spin-0.- Spin-1/2—Spin-1/2.- Problems.- References.- Chapter10 Quantum Electrodynamics.- Electromagnetic Field.- Dirac Field.- A. Schwinger’s Synthesis.- B. Selected Applications.- Uniform Magnetic Field.- Synchrotron Radiation.- Coulomb Field.- Vacuum Polarization.- Problems.- References.- Classical Theory of the Electron.