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OverviewIntense 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. This monograph on elementary particle physics, electrodynamics, quantized fields, quantum mechanics, fields and particles, nuclear physics, mathematical physics is intended for postgraduates, researchers and students. Full Product DetailsAuthor: E. S. Fradkin , Dmitri M. Guitman , S. M. Shvartsman , S.M. Shvartsman (Tomsk State Pedagogical Institute, USSR)Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K Weight: 0.595kg ISBN: 9783540529354ISBN 10: 3540529357 Pages: 297 Publication Date: 27 August 1991 Audience: College/higher education , Professional and scholarly , Undergraduate , Postgraduate, Research & Scholarly Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of Contents1 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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