The Many Faces of Maxwell, Dirac and Einstein Equations

A Clifford Bundle Approach

Jr Rodrigues Waldyr A., Edmundo Capelas de Oliveira (Autoren)

Buch | Hardcover

XIV, 445 Seiten

2007 | 2007
Springer Berlin (Verlag)
978-3-540-71292-3 (ISBN)

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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.

Multiform and Extensor Calculus.- The Hidden Geometrical Nature of Spinors.- Some Differential Geometry.- Some Issues in Relativistic Spacetime Theories.- Clifford and Dirac-Hestenes Spinor Fields.- Lagrangian Formalism in Minkowski Spacetime.- Conservation Laws on Riemann-Cartan and Lorentzian Spacetimes.- The DHE on a RCST and the Meaning of Active Local Lorentz Invariance.- Gravitational Theory in Minkowski Spacetime.- On the Many Faces of Einstein's Equations.- Maxwell, Dirac and Seiberg-Witten Equations.- Superparticles and Superfields.

"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)

Reihe/Serie	Lecture Notes in Physics ; 722
Zusatzinfo	XIV, 445 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1810 g
Themenwelt	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
Schlagworte	Calculus • Clifford Bundle • Dirac-Hestenes Equation • EFE • Einstein equations • Gravity • Maxwell Equations • Minkowski space • RMS • Spin-Clifford Bundle
ISBN-10	3-540-71292-5 / 3540712925
ISBN-13	978-3-540-71292-3 / 9783540712923
Zustand	Neuware