Overview
- Authors:
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Waldyr Alves Rodrigues
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Universidade Estadual Campinas, Instituto de Matemática Estatística e Computação Científica, Campinas, Brasil
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Edmundo Capelas Oliveira
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Universidade Estadual Campinas, Instituto de Matemática Estatística e Computação Científica, Campinas, Brasil
- Comprehensive reference on differential geometry
- Based upon the common mathematical features of Maxwell, Dirac and Einstein Equations
- Calculation procedures are illustrated by many exercises solved in detail
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Table of contents (13 chapters)
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 1-17
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 19-60
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 61-94
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 95-169
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 171-231
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 233-267
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 269-292
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 293-319
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 321-326
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 327-342
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 343-362
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 363-392
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- Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
Pages 393-405
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Back Matter
Pages 407-445
About this book
Maxwell, Dirac and Einstein’s equations are certainly among the most imp- tant equations of XXth century Physics and it is our intention in this book to 1 investigate some of the many faces of these equations and their relationship and to discuss some foundational issues involving some of the theories where they appear. To do that, let us brie?y recall some facts. Maxwell equations which date back to the XIXth century encodes all cl- sical electromagnetism, i. e. they describe the electromagnetic ?elds generated by charge distributions in arbitrary motion. Of course, when Maxwell f- mulated his theory the arena where physical phenomena were supposed to occur was a Newtonian spacetime, a structure containing a manifold which is 3 di?eomorphic to R×R , the ?rst factor describing Newtonian absolute time 2 [25] and the second factor the Euclidean space of our immediate perception . In his original approach Maxwell presented his equations as a system of eight linear ?rstorderpartialdi?erentialequations involvingthe components of the electricandmagnetic?elds[17]generatedbychargeandcurrentsdistributions 3 with prescribed motions in vacuum . It was only after Heaviside [12], Hertz and Gibbs that those equations were presented using vector calculus, which by the way, is the form they appear until today in elementary textbooks on Electrodynamics and Engineering Sciences. In the vector calculus formalism Maxwell equations are encoded in four equations involving the well known divergentandrotationaloperators.
Reviews
"The main intention of the present book is to familiarise the reader with the algebra and calculus within the Clifford bundle formalism … . The text is written in a very readable manner and is complemented with plenty of worked-out exercises which are in the style of extended examples. ... From my personal point of view, the authors elegantly succeed in their ambitions and, in my opinion, their book could also serve as a textbook for graduate students in physics or mathematics." (Alberto Molgado, Mathematical Reviews, 2008 k)
