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Table of contents

  1. Front Matter
    Pages I-XIV
  2. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 1-17
  3. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 19-60
  4. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 61-94
  5. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 95-169
  6. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 171-231
  7. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 233-267
  8. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 269-292
  9. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 293-319
  10. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 321-326
  11. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 327-342
  12. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 343-362
  13. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 363-392
  14. Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira
    Pages 393-405
  15. Back Matter
    Pages 407-445

About this book

Introduction

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.

Keywords

Clifford Bundle Dirac-Hestenes Equation EFE Einstein Equations Gravity Maxwell Equations Minkowski space RMS Spin-Clifford Bundle calculus

Authors and affiliations

  • Waldyr Alves RodriguesJr
    • 1
  • Edmundo Capelas de Oliveira
    • 1
  1. 1.Universidade Estadual Campinas, Instituto de Matemática Estatística e Computação CientíficaCampinasBrasil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-71293-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-540-71292-3
  • Online ISBN 978-3-540-71293-0
  • Series Print ISSN 0075-8450
  • Buy this book on publisher's site
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