Book: 2nd edition of The Many Faces of Maxwell, Dirac and Einstein Equations by Rodrigues, Jr. & Capelas de Oliveira

The Many Faces of Maxwell, Dirac and Einstein Equations — A Clifford Bundle Approach
Rodrigues, Jr, Waldyr A., Capelas de Oliveira, Edmundo

Bibliographic Information

Series Title Lecture Notes in Physics
Series Volume 922
Copyright 2016
Publisher Springer International Publishing
Copyright Holder Springer International Publishing Switzerland
eBook ISBN 978-3-319-27637-3
DOI 10.1007/978-3-319-27637-3
Softcover ISBN 978-3-319-27636-6
Series ISSN 0075-8450
Edition Number 2
Number of Pages XVI, 587
Number of Illustrations and Tables 14 b/w illustrations

This book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics.
The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research.
This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields.
The exercises with solutions, the comprehensive list of mathematical symbols, and the list of acronyms and abbreviations are provided for self-study for students as well as for classes.

Waldyr Alves Rodrigues Jr, full professor of Mathematical Physics, at the State University of Campinas, São Paulo, Brazil, received his BSc from the University of São Paulo, and his PhD from the University of Torino, Italy. He has held various positions at Brazilian and European universities, one of them being director of the Institute of Mathematics, Statistics and Scientific Computation, State University of Campinas (IMECC-UNICAMP) from 1994 to1998. He has more than 40 years of teaching experience in more than 70 courses at graduate and post-graduate levels. As a researcher he received many grants, and various prizes – especially in 2012 he won the Paul Sabatier honor medal in 2012 for his contributions to applications of Clifford algebras to mathematical physics. He is the editor-in-chief of the journal “Advances in Applied Clifford Algebras”.

Edmundo Capelas de Oliveira is a member of the Mathematical Physics Group at the State University of Campinas, Sao Paulo, Brazil. He received his PhD in Physics in 1982, and became a full professor in Applied Mathematics in 2015. His research topics involve projective relativity, differential equations, complex analysis and fractional calculus. He is author of several successful  textbooks (in Portuguese), teaches undergraduate as well as graduate courses, and held positions as Library Coordinator, Graduate Studies Coordinator of the Department and Associate Director of the Institute.

From the reviews of the 1st edition:
“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)

Source: Email from Waldyr Alves Rodrigues Jr, 17 June 2016 (,


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