Quantum Electrodynamics

1 Introduction.- 1.1 General Introduction and Definition of Notation.- 1.2 Quantum Electrodynamics with an External Field.- 2 Scattering Processes in Which Interactions with the External Field are Taken into Account Exactly.- 2.1 The Quantized Charged Field in an External Electromagnetic Field.- 2.2 Perturbation Expansion in the Radiative Interaction in QED with an External Field.- 2.3 Green's Functions. The Generating Functional.- 2.4 Appendix. Extension of the Normal-Ordering Process to Theories with an Unstable Vacuum.- 3 Expectation Values.- 3.1 Green's Functions for the Calculation of Expectation Values.- 3.2 Perturbations in Powers of Radiative Interaction for Expectation Values.- 3.3 Equation for the Average Electromagnetic Field. Effective Action.- 3.4 Density Matrix of Particles Created by an External Field.- 4 Total Probabilities of Radiative Processes in an External Field.- 4.1 Total Irradiation Probability.- 4.2 Unitarity Relation and the Optical Theorem.- 4.3 Generating Functional for the Total Probabilities of Radiation Processes.- 4.4 Decay Probability of States.- 5 Calculations of Zero-Order Processes in External Electromagnetic Fields.- 5.1 Processes in an Electric Field.- 5.2 A Constant Field Combined with that of a Plane Wave.- 5.3 Creation of Particles from the Vacuum in Coherent States.- 5.4 Calculation of the Density Matrix for Particles Created in an External Field.- 6 Propagators of Particles in External Electromagnetic Fields.- 6.1 Introduction.- 6.2 Determination of Propagators by Summing Solutions of the Relativistic Wave Equations.- 6.3 Schwinger's Proper-Time Method.- 6.4 Calculation of the Green's Functions by the Functional Integration Method.- 7 Calculations of Radiative Processes in External Electromagnetic Fields.- 7.1 EffectiveAction in the One-Loop Approximation.- 7.2 Vacuum Processes.- 7.3 Processes with an Electron in the Initial State. Mass Operator.- 7.4 Radiative Processes with a Photon in the Initial State. Polarization Operator.- 8 Green's Function in Non-Abelian Theories.- 8.1 Introduction.- 8.2 Calculation of Green's Functions by the Functional Integration Method.- 8.3 Calculation of Green's Functions in an Abelian-like External Field.- References.