The many faces of Maxwell, Dirac and Einstein equations: a Clifford bundle approach

Waldyr Alves Rodrigues Jr, Edmundo Capelas de Oliveira (auth.)3540712925, 9783540712923

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.

Table of contents :
Front Matter….Pages I-XIV
Introduction….Pages 1-17
Multiform and Extensor Calculus….Pages 19-60
The Hidden Geometrical Nature of Spinors….Pages 61-94
Some Differential Geometry….Pages 95-169
Some Issues in Relativistic Spacetime Theories….Pages 171-231
Clifford and Dirac-Hestenes Spinor Fields….Pages 233-267
Lagrangian Formalism in Minkowski Spacetime….Pages 269-292
Conservation Laws on Riemann-Cartan and Lorentzian Spacetimes….Pages 293-319
The DHE on a RCST and the Meaning of Active Local Lorentz Invariance….Pages 321-326
Gravitational Theory in Minkowski Spacetime….Pages 327-342
On the Many Faces of Einstein’s Equations….Pages 343-362
Maxwell, Dirac and Seiberg-Witten Equations….Pages 363-392
Superparticles and Superfields….Pages 393-405
Back Matter….Pages 407-445