Lecture Notes in Physics

The Many Faces of Maxwell, Dirac and Einstein Equations

A Clifford Bundle Approach

Authors: Rodrigues, Jr, Waldyr A., Capelas de Oliveira, Edmundo

  • 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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Softcover $159.00
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  • ISBN 978-3-642-09038-7
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About this book

This book is a thoughtful exposition of the algebra and calculus of differential forms, the Clifford and Spin-Clifford bundles formalisms with emphasis in calculation procedures, and vistas to a formulation of some important concepts of differential geometry necessary for a deep understanding of spacetime physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, are shown to have representatives as objects of the same mathematical nature, i.e. as sections of an appropriate Clifford bundle. This approach reveals unity in the diversity and also the many faces of the equations satisfied by those fields. Moreover, it suggests relationships which are hidden in the standard formalisms and new paths for research. Some foundational issues of relativistic field theories, in particular the one concerning the conditions for the existence of the conservation laws of energy-momentum and angular momentum in spacetime theories and many misconceptions concerning this issue is analyzed in details.

The book will be useful as reference book for researchers and advanced students of theoretical physics and mathematics. Calculation procedures are illustrated by many exercises solved in detail, using the "tricks of the trade". Furthermore the readers will appreciate the comprehensive list of mathematical symbols as well as a list of acronyms and abbreviations.

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)


Buy this book

Softcover $159.00
price for USA
  • ISBN 978-3-642-09038-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Many Faces of Maxwell, Dirac and Einstein Equations
Book Subtitle
A Clifford Bundle Approach
Authors
Series Title
Lecture Notes in Physics
Series Volume
722
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
Softcover ISBN
978-3-642-09038-7
Series ISSN
0075-8450
Edition Number
1
Number of Pages
XIV, 445
Topics