Summary and Info
The differential geometric method has been one of the mostfundamental tools for theoretical physicists since its firstintroduction into special relativity (general relativity) by AlbertEinstein in 1905 (1915). Later it has been applied to many researchareas, such as fluid mechanics, elastomechanics, thermodynamics, solidstate physics, optics, electromagnetism, quantum field theory, etc. As a distinctive feature of traditional classical electrodynamics,this book rests on the metric-free integral formulation of theconservation laws of electrodynamics as represented by exteriordifferential forms. Therefore the book will be of great interest tograduate students and researchers in mathematics and theoreticalphysics who work in field theory and general relativity. The book consists of five parts; a short list of references and anauthor and a subject index are included. Every part ends with a listof references. The authors begin in Part A, as an introductorysection, with an elementary presentation of exterior differentialforms. The necessary geometric concepts, needed to formulateclassical electrodynamics and gravitational theory in the language ofdifferential forms, are explained in Part A and in Part C, too. Theaxioms of classical electrodynamics, the integral formulations ofelectric charge and magnetic flux conservation, are presented in PartB. Subsequently, the linear connection and the metric are introducedin Part C. The general framework is completed in Part D by a specificelectrodynamic spacetime relation and in Part E by applyingelectrodynamics to moving continua and to rotating and acceleratingobservers, for instance. Moreover, a computer algebra program is introduced in the book ina simple way, and some cartoon drawings will add to the tediousmathematics some humor. As to the exposition of the book, we areimpressed by illustrations and diagrams, which support our geometricalinsight. The mathematical abstraction and physical relevance aredisplayed neatly and appropriately. It is concise and comprehensiveas an introductory textbook for graduate students and a completereference book for researchers. Thus, there is no doubt that many specialists will be interestedin the book under review. The book proves to be a good scientificresource for university libraries as well as for graduate students andresearchers working in mathematical physics, field theory, and generalrelativity.
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