The Many Faces of Maxwell, Dirac and Einstein Equations

1. Front Matter

   Pages I-XIV

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2. Introduction

   • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

   Pages 1-17

3. Multiform and Extensor Calculus

   • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

   Pages 19-60

4. The Hidden Geometrical Nature of Spinors

   • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

   Pages 61-94

5. Some Differential Geometry

   • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

   Pages 95-169

6. Some Issues in Relativistic Spacetime Theories

   • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

   Pages 171-231

7. Clifford and Dirac-Hestenes Spinor Fields

   • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

   Pages 233-267

8. Lagrangian Formalism in Minkowski Spacetime

   • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

   Pages 269-292

9. Conservation Laws on Riemann-Cartan and Lorentzian Spacetimes

   • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

   Pages 293-319

10. The DHE on a RCST and the Meaning of Active Local Lorentz Invariance

    • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

    Pages 321-326

11. Gravitational Theory in Minkowski Spacetime

    • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

    Pages 327-342

12. On the Many Faces of Einstein’s Equations

    • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

    Pages 343-362

13. Maxwell, Dirac and Seiberg-Witten Equations

    • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

    Pages 363-392

14. Superparticles and Superfields

    • Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira

    Pages 393-405

15. Back Matter

    Pages 407-445

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Maxwell, Dirac and Einstein’s equations are certainly among the most imp- tant equations of XXth century Physics and it is our intention in this book to 1 investigate some of the many faces of these equations and their relationship and to discuss some foundational issues involving some of the theories where they appear. To do that, let us brie?y recall some facts. Maxwell equations which date back to the XIXth century encodes all cl- sical electromagnetism, i. e. they describe the electromagnetic ?elds generated by charge distributions in arbitrary motion. Of course, when Maxwell f- mulated his theory the arena where physical phenomena were supposed to occur was a Newtonian spacetime, a structure containing a manifold which is 3 di?eomorphic to R×R , the ?rst factor describing Newtonian absolute time 2 [25] and the second factor the Euclidean space of our immediate perception . In his original approach Maxwell presented his equations as a system of eight linear ?rstorderpartialdi?erentialequations involvingthe components of the electricandmagnetic?elds[17]generatedbychargeandcurrentsdistributions 3 with prescribed motions in vacuum . It was only after Heaviside [12], Hertz and Gibbs that those equations were presented using vector calculus, which by the way, is the form they appear until today in elementary textbooks on Electrodynamics and Engineering Sciences. In the vector calculus formalism Maxwell equations are encoded in four equations involving the well known divergentandrotationaloperators.

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

"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)

• Universidade Estadual Campinas, Instituto de Matemática Estatística e Computação Científica, Campinas, Brasil

  Waldyr Alves Rodrigues, Edmundo Capelas Oliveira

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