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The Many Faces of Maxwell, Dirac and Einstein Equations

A Clifford Bundle Approach

  • Waldyr A. Rodrigues, Jr
  • Edmundo Capelas de Oliveira

Part of the Lecture Notes in Physics book series (LNP, volume 922)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 1-19
  3. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 21-68
  4. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 69-105
  5. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 107-188
  6. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 189-224
  7. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 225-290
  8. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 291-329
  9. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 331-358
  10. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 359-393
  11. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 395-401
  12. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 403-427
  13. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 429-449
  14. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 451-483
  15. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 485-499
  16. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 501-516
  17. Waldyr A. Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 517-543
  18. Back Matter
    Pages 545-587

About this book

Introduction

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)

Keywords

Semi-Riemannian differential geometry of branes Clifford Bundle Formalism Dirac Hestenes Equation Maxwell Equations Minkowski space Spin-Clifford Bundle Clifford Products

Authors and affiliations

  • Waldyr A. Rodrigues, Jr
    • 1
  • Edmundo Capelas de Oliveira
    • 2
  1. 1.IMECCUniversidade Estadual de CampinasCampinasBrazil
  2. 2.IMECCUniversidade Estadual de CampinasCampinasBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-27637-3
  • Copyright Information Springer International Publishing Switzerland 2016
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-27636-6
  • Online ISBN 978-3-319-27637-3
  • Series Print ISSN 0075-8450
  • Series Online ISSN 1616-6361
  • Buy this book on publisher's site
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