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Book synopsis

This book is a comprehensive reference on differential geometry. It shows that Maxwell, Dirac and Einstein fields, which were originally considered objects of a very different mathematical nature, have representatives as objects of the same mathematical nature. The book also analyzes some foundational issues of relativistic field theories. All calculation procedures are illustrated by many exercises that are 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.

Book details

Book category Knihy po anglicky Mathematics & science Mathematics Geometry

• Full title: Many Faces of Maxwell, Dirac and Einstein Equations
• Subtitle: A Clifford Bundle Approach
• Author: Waldyr A. Rodrigues, Edmundo C. de Oliveira
• Language: English
• Binding: Paperback
• Number of pages: 445
• EAN: 9783642090387
• ISBN: 3642090389
• ID: 01653979
• Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
• Weight: 698 g
• Dimensions: 154 × 235 × 32 mm
• Date of publishing: 24. November 2010

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