The Many Faces of Maxwell, Dirac and Einstein Equations

This book is an exposition of the algebra and calculus of differentialforms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to aformulation of important concepts of differential geometry indispensable for anin-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 objectsof the same mathematical nature, namely sections of an appropriate Cliffordbundle. This approach reveals unity in diversity and suggests relationshipsthat are hidden in the standard formalisms and opens new paths for research.This thoroughly revised second edition also adds three new chapters: on the Cliffordbundle approach to the Riemannian or semi-Riemannian differential geometry ofbranes; on Komar currents in the context of the General Relativity theory; andan analysis of the similarities and main differences between Dirac, Majoranaand ELKO spinor fields.The exercises with solutions, thecomprehensive list of mathematical symbols, and the list of acronyms andabbreviations are provided for self-study for students as well as for classes.From the reviews of the firstedition:"The text is written in a veryreadable manner and is complemented with plenty of worked-out exercises whichare in the style of extended examples. ... their book could also serve as atextbook for graduate students in physics or mathematics." (AlbertoMolgado, Mathematical Reviews, 2008 k) von Rodrigues, Waldyr A. und Capelas de Oliveira, Edmundo