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Mathematics - Analysis | The Many Faces of Maxwell, Dirac and Einstein Equations - A Clifford Bundle Approach

The Many Faces of Maxwell, Dirac and Einstein Equations

A Clifford Bundle Approach

Series: Lecture Notes in Physics, Vol. 722

Rodrigues, Waldyr A., de Oliveira, Edmundo C.

2007, XIV, 445 p.

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  • Comprehensive reference on differential geometry
  • Based upon the common mathematical features of Maxwell, Dirac and Einstein Equations
  • Calculation procedures are illustrated by many exercises solved in detail

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.

Content Level » Research

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

Related subjects » Analysis - Geometry & Topology - Theoretical, Mathematical & Computational Physics

Table of contents 

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.

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