Quantum Electrodynamics: With Unstable Vacuum

ISBN-13: 9783642842603 / Angielski / Miękka / 2011 / 288 str.

E. S. Fradkin; D. M. Gitman; S. M. Shvartsman

Opis

This book contains a systematic analysis of the formalisms of quantum electro dynamics in the presence of an intense external field able to create pairs from the vacuum, and thereby violate the stability of the latter. The approach developed is not specific to quantum electrodynamics, and can equally well be applied to any quantum field theory with an unstable vacuum. It should be noted that only macroscopic external fields are considered, whereas problems associated with the superstrong Coulomb (micro) field are not treated. As a rule, the discussion is confined to those details of the formalism and calculations that are specific to the instability property. For instance, renormalization is not discussed here since, in practical calculations, it is carried out according to standard methods. The presentation is based mainly on original research undertaken by the authors. Chapter 1 contains a general introduction to the problem. It also presents some standard information on quantum electrodynamics, which will be used later in the text. In addition, an interpretation of the concept of an external field is given, and the problems that arise when one tries to keep the interaction with the external field exactly are discussed. In Chapter 2, the perturbation expansion in powers of the radiative interac tion is developed for the matrix elements of transition processes, taking the arbitrary external field into account exactly."

Spis treści

1 Introduction.- 1.1 General Introduction and Definition of Notation.- 1.1.1 Chronological Review.- 1.1.2 Basic 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.- 2.1.1 Spinor Field.- 2.1.2 Scalar 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.- 4.1.1 Total Probability of Irradiation from the Vacuum Accompanied by Pair Creation.- 4.1.2 Differential Probability for Photon Irradiation from the Vacuum Accompanied by Pair Creation.- 4.1.3 Probability of Photon Irradiation from the Vacuum Accompanied by the Creation of a Single Pair.- 4.1.4 Total Probability of Irradiation from a One-Electron State Accompanied by Pair Creation.- 4.1.5 Differential Probability of a One-Photon Emission from a One-Electron State Accompanied by Pair Creation.- 4.1.6 Probability of One-Photon Emission from a One-Electron State Without Pair Creation.- 4.1.7 Radiative Processes with a Photon in the Initial State.- 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.- 4.4.1 Vacuum Decay Probability.- 4.4.2 Decay Probability of a One-Electron State.- 4.4.3 Decay Probability of a One-Photon State.- 5 Calculations of Zero-Order Processes in External Electromagnetic Fields.- 5.1 Processes in an Electric Field.- 5.1.1 Constant Electric Field.- 5.1.2 Alternating Electric Field.- 5.2 A Constant Field Combined with that of a Plane Wave.- 5.2.1 Solutions of the Klein-Gordon Equation.- 5.2.2 Solutions of the Dirac Equation.- 5.2.3 Calculation of Zero-Order Processes. Spinor QED.- 5.2.4 Calculation of Zero-Order Processes. Scalar QED.- 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.- 6.2.1 Constant Electric Field.- 6.2.2 A Constant Field Combined with that of a Plane Wave.- 6.2.3 Eigenfunction Method.- 6.3 Schwinger’s Proper-Time Method.- 6.4 Calculation of the Green’s Functions by the Functional Integration Method.- 6.4.1 Path Integral Representation of the Green’s Functions.- 6.4.2 Combination of a Constant Field with a Plane Wave.- 6.4.3 Stationary Phase Method.- 7 Calculations of Radiative Processes in External Electromagnetic Fields.- 7.1 Effective Action in the One-Loop Approximation.- 7.2 Vacuum Processes.- 7.2.1 Mean Current of Created Particles.- 7.2.2 Probability of Photon Emission from the Vacuum Accompanied by Pair Creation.- 7.2.3 Total Probability of Photon Emission from the Vacuum Accompanied by Pair Creation.- 7.2.4 Probability of a Photon Emission from the Vacuum Accompanied by the Creation of a Single Pair. Vacuum Decay Probability.- 7.3 Processes with an Electron in the Initial State. Mass Operator.- 7.3.1 Probability of Transition from a One-Electron State with the Emission of a Photon and the Creation of Pairs.- 7.3.2 Total Transition Probability from a One-Electron State with Photon Emission and Pair Creation.- 7.3.3 Probability of Photon Emission from a One-Electron State without Pair Creation. Decay Probability of a One-Electron State.- 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.