Overview
- Comprehensive differential geometry reference
- work in its second, revised and expanded edition
- calculation procedures with many exercises and detailed solutions
- Provides lists of mathematical symbols, acronyms and abbreviations
Part of the book series: Lecture Notes in Physics (LNP, volume 922)
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Table of contents (16 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
From the reviews of the first
edition:
“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. ... their book could also serve as a textbook for graduate students in physics or mathematics." (Alberto Molgado, Mathematical Reviews, 2008 k)
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)
Authors and Affiliations
About the authors
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.Bibliographic Information
Book Title: The Many Faces of Maxwell, Dirac and Einstein Equations
Book Subtitle: A Clifford Bundle Approach
Authors: Waldyr A. Rodrigues, Jr, Edmundo Capelas de Oliveira
Series Title: Lecture Notes in Physics
DOI: https://doi.org/10.1007/978-3-319-27637-3
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-27636-6Published: 27 April 2016
eBook ISBN: 978-3-319-27637-3Published: 26 April 2016
Series ISSN: 0075-8450
Series E-ISSN: 1616-6361
Edition Number: 2
Number of Pages: XVI, 587
Number of Illustrations: 14 b/w illustrations
Topics: Classical and Quantum Gravitation, Relativity Theory, Mathematical Applications in the Physical Sciences, Differential Geometry