Synopses & Reviews
This textbook bridges the gap between the level of introductory courses on mechanics and electrodynamics and the level of application in high energy physics and quantum field theory. After explaining the postulates that lead to the Lorentz transformation and after going through the main points special relativity has to make in classical mechanics and electrodynamics, the authors gradually lead the reader up to a more abstract point of view on relativistic symmetry - illustrated by physical examples - until finally motivating and developing Wigner's classification of the unitary irreducible representations of the inhomogeneous Lorentz group. Numerous historical and mathematical asides contribute to the conceptual clarification.
Review
"... I wish that many readers from the large English-speaking area ... will step on it and profit from an illuminating textbook which was reserved to German-language readers up to now." Wolfgang Hasse - General Relativity and Gravitation, vol. 34, 12/2002
Synopsis
Like many textbooks, the present one is the outgrowth of lecture courses, mainly given at the University of Vienna, Austria; on the occasion of the English edition, it may be mentioned that our first such lecture course was delivered by my late co- author, Roman U. Sexl, during the fall and winter term 1967-68 in the USA-more precisely, at the University of Georgia (Athens). Since then, Particle Physics has seen spectacular revolutions; but its relativistic symmetry has never been shaken. On the other hand, new technological developments have enabled applications like the GPS (Global Positioning System) that, in a sense, brought Relativity to the domain of everyday use. The purpose of the lecture courses, and thus of the book, is to fill a gap that the authors feel exists between the way Relativity is presented in introductory courses on mechanics and/or electrodynamics on the one hand and the way relativistic symmetry is presented in particle physics and field theory courses on the other. The reason for the gap is a natural one: too many other themes have to be addressed in the introductory courses, and too many applications are impatiently waiting for their presentation in the particle and field theory courses.
Synopsis
This textbook attempts to bridge the gap that exists between the two levels on which relativistic symmetry is usually presented the level of introductory courses on mechanics and electrodynamics and the level of application in high-energy physics and quantum field theory: in both cases, too many other topics are more important and hardly leave time for a deepening of the idea of relativistic symmetry. So after explaining the postulates that lead to the Lorentz transformation and after going through the main points special relativity has to make in classical mechanics and electrodynamics, the authors gradually lead the reader up to a more abstract point of view on relativistic symmetry always illustrating it by physical examples until finally motivating and developing Wigner's classification of the unitary irreducible representations of the inhomogeneous Lorentz group. Numerous historical and mathematical asides contribute to conceptual clarification.
Description
Includes bibliographical references (p. [373]-378) and indexes.
Table of Contents
The Lorentz Transformation.- Physical Interpretation.- Lorentz Group, Poincaré Group, and Minkowski Geometry.- Relativistic Mechanics.- Relativistic Electrodynamics.- The Lorentz Group and Some of Its Representations.- Representation Theory of the Rotation Group.- Representation Theory of the Lorentz Group.- Representation Theory of the Poincaré Group.- Conservation Laws in Relativistic Field Theory.- Appendices: Basic Concepts from Group Theory; Abstract Multilinear Algebra; Majorana Spinors, Charge Conjugation, and Time Reversal in Dirac Theory; Poincaré Covariance in Second Quantization