We propose a direct derivation of the Lorentz generators for the four-potential of electrodynamics on the basis of Wigner's theorem. The derivation relies on a study of the behaviour of polarisation vectors under-space differentiation. The Coulomb and Lorenz gauges are discussed in that respect, and gauge invariance under Poincaré transformations is examined. The Poincaré generators given by Białynicki-Birula and Białynicka-Birula are found to correspond to the Coulomb gauge case.
![]() 0253-6102/71/4/403 Abstract
In these lectures I will follow for some part the book of Ryder 1. Other text books of Quantum Field Theory that are useful are given in refs 2-5. The notes contain all essential information, but are rather compact. Besides the books, there is also material available via the web pages of colleagues. Quantum Field Theory by Lewis H. Ryder, Cambridge University Press, 487 pages, Second Edition (1996). Ahluwalia (Los Alamos National Laboratory). The first edition of this book appeared in 1985. To my knowledge this was the the first book that presented a completely modern and logical development of quantum theory ofmatterandgaugefields.
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This book is a modern pedagogic introduction to the ideas and techniques of quantum field theory. After a brief overview of particle physics and a survey of relativistic wave equations and Lagrangian methods, the quantum theory of scalar and spinor fields, and then of gauge fields, is developed. The emphasis throughout is on functional methods, which have played a large part in modern field theory. The book concludes with a brief survey of ‘topological’ objects in field theory and, new to this edition, a chapter devoted to supersymmetry.
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March 2023
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