Basics of Quantum Electrodynamics

By (author) Merches, Ioan; By (author) Tatomir, Dorian; By (author) Lupu, Roxana E.

Quantum electrodynamics (QED) is the branch of relativistic quantum field theory that deals specifically with the interactions between charged particles. It is widely used to solve problems in many areas of physics, such as elementary particles, atomic and molecular systems, and solid state physics. This accessible text, Basics of Quantum Electrodynamics, supplies a solid foundation in this dynamic area of physics, making a direct connection to the concepts of quantum mechanics familiar to the advanced undergraduate student. Chapters cover the general theory of free fields and the quantization of the scalar, electromagnetic, and spinorial fields, which prepares readers for understanding field interactions. The authors describe the general theory of field interactions, introducing the scattering matrix and the Feynman-Dyson graphs. They then discuss divergence-free second-order processes, such as Compton and Moller scattering, followed by divergent second-order processes, which cover vacuum polarization and mass and charge renormalization. Providing a modern, informative textbook, this volume illustrates the intimate connection between quantum mechanics and QED in two basic steps: the quantization of free fields, followed by the theory of their interactions. The text contains solved problems to facilitate the application of the theory, as well as a useful appendix on the theory of distributions. The step-by-step description of the quantization of various fields and the clear presentation of the most important interaction processes in QED make this textbook a useful guide for those studying physics at both the graduate and undergraduate level, as well as a reference for teachers and researchers in the field.

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  • General Field Theory Basic field equations Infinitesimal Lorentz Transformation Transformation of the quantities U(r) in particular cases Invariance of the Lagrangian density under infinitesimal Lorentz transformation The energy-momentum tensor of a field The angular momentum tensor of a field Symmetry transformations Phase transformations General Problems of Field Quantization Necessity of field quantization Commutation and anti-commutation relations. Emission and absorption operators Commutation relations and the Bose-Einstein statistics Anti-commutation relations and the Fermi-Dirac statistics Alternative methods of field quantization Notations and units in QFT The Quantization of the Scalar Field The Lagrangian formalism Momentum representation Momentum, energy and charge of the complex scalar field in momentum representation Commutators of the free scalar field Products of operators Vacuum states. The Fock representation Wick's theorems The Quantization of the Electromagnetic Field Lagrangian formalism Momentum representation Momentum, energy and spin of the electromagnetic field in momentum representation Commutators of the free electromagnetic field The indefinite metric formalism The Lorentz-Fermi condition The Quantization of the Spinorial Field The Dirac equation and the algebra of gamma matrices Lagrangian formalism The free particle in the Dirac theory Energy, momentum, charge and spin of the free spinorial field in momentum representation Anti-commutators of the free spinorial field Products of spinorial operators General Problems of Field Interactions Generalities The S-matrix Choice of the interaction Lagrangian density The Feynman-Dyson diagrams Examples of Feynman-Dyson diagrams Transition probability Scattering cross section Non-Divergent Second-Order Processes Transition probability for Compton scattering Differential cross section for Compton scattering Electron-positron annihilation Transition probability for Moller scattering Moller scattering cross section Photon-photon scattering with electron-positron pair production Electron-positron scattering Divergent Second-Order Processes Self-energy diagram of the electron Self-energy diagram of the photon. The vacuum polarization Mass and charge renormalization Appendix. Distributions Unidimensional delta function Various representations of the delta function Some functions related to delta Functions Dm+ and Dmae' Functions Dm and Dm Functions D0, D0, D0+, D0ae' Functions S, S, S+, Sae' Retarded and advanced functions Causal functions Problems with Solutions References Subject Index

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書名 Basics of Quantum Electrodynamics
著作者等 Lupu, Roxana E.
Tatomir, Dorian
Merches, Ioan
出版元 Taylor & Francis Inc
刊行年月 2013.01.31
ページ数 352p
ISBN 9781466580381
言語 英語
出版国 アメリカ合衆国