This book presents a systematic analysis of the formalism of quantum electrodynamics (QED) in strong external fields that give rise to an unstable vacuum and pair creation. The developed approach is applicable to any quantum field theory with unstable vacuum.

Klappentext

Intense external fields destabilize vacuum by introducing the creation of particle pairs. In this book the formalism of quantum electrodynamics (QED), using a special perturbation theory with matrix propagators, is systematically analyzed for such systems. The developed approach is, however, general for any quantum field with unstable vacuum. In addition to a description of the theory, the authors propose solutions for real pair-creating fields. They discuss the general form for the causal function and many other Green functions, as well as methods for finding them. Analogies for the optical theorem and rules for computing total probabilities are given, as are solutions for non-Abelian theories.

Inhalt
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.