The Many Faces of Maxwell, Dirac and Einstein Equations
A Clifford Bundle Approach
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Beschreibung
This book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-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 objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research.
This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields.
The exercises with solutions, the comprehensive list of mathematical symbols, and the list of acronyms and abbreviations are provided for self-study for students as well as for classes.
From the reviews of the first edition:
“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. ... their book could also serve as a textbook for graduate students in physics or mathematics." (Alberto Molgado, Mathematical Reviews, 2008 k)
This book is an exposition of the algebra and calculus of differential
forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a
formulation of important concepts of differential geometry indispensable for an
in-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 objects
of the same mathematical nature, namely sections of an appropriate Clifford
bundle. This approach reveals unity in diversity and suggests relationships
that are hidden in the standard formalisms and opens new paths for research.
This thoroughly revised second edition also adds three new chapters: on the Clifford
bundle approach to the Riemannian or semi-Riemannian differential geometry of
branes; on Komar currents in the context of the General Relativity theory; and
an analysis of the similarities and main differences between Dirac, Majorana
and ELKO spinor fields.
The exercises with solutions, the
comprehensive list of mathematical symbols, and the list of acronyms and
abbreviations are provided for self-study for students as well as for classes.
From the reviews of the first
edition:
“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. ... their book could also serve as a textbook for graduate students in physics or mathematics." (Alberto Molgado, Mathematical Reviews, 2008 k)
Comprehensive differential geometry reference work in its second, revised and expanded edition calculation procedures with many exercises and detailed solutions Provides lists of mathematical symbols, acronyms and abbreviations
Autor*in
Waldyr A. Rodrigues, Jr
Themen in »The Many Faces of Maxwell, Dirac and Einstein Equations«
Semi-Riemannian differential geometry of branes Clifford Bundle Formalism Dirac Hestenes Equation Maxwell Equations Minkowski space Spin-Clifford Bundle Clifford Products
Stimmen zu »The Many Faces of Maxwell, Dirac and Einstein Equations«
From the reviews of the 1st edition:
"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)
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