Quantum Electrodynamics: with Unstable Vacuum (Springer Series in Nuclear and Particle Physics)

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

ISBN 10: 3642842607 / ISBN 13: 9783642842603

Editore: Springer, 2011

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Codice articolo ABLIING23Mar3113020237647

Dati bibliografici

• Titolo: Quantum Electrodynamics: with Unstable Vacuum (Springer Series in Nuclear and Particle Physics)
• Editore: Springer
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 3642842607
• ISBN 13: 9783642842603
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

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.