The Many Faces of Maxwell Dirac and Einstein Equations

Author: Waldyr A. Rodrigues
Publisher: Springer Science & Business Media
ISBN: 3540712925
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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.

The Many Faces of Maxwell Dirac and Einstein Equations

Author: Waldyr A. Rodrigues, Jr
Publisher: Springer
ISBN: 3319276379
Format: PDF, Docs
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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)

Gravitation as a Plastic Distortion of the Lorentz Vacuum

Author: Virginia Velma Fernández
Publisher: Springer Science & Business Media
ISBN: 9783642135897
Format: PDF, Docs
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Addressing graduate students and researchers in theoretical physics and mathematics, this book presents a new formulation of the theory of gravity. In the new approach the gravitational field has the same ontology as the electromagnetic, strong, and weak fields. In other words it is a physical field living in Minkowski spacetime. Some necessary new mathematical concepts are introduced and carefully explained. Then they are used to describe the deformation of geometries, the key to describing the gravitational field as a plastic deformation of the Lorentz vacuum. It emerges after further analysis that the theory provides trustworthy energy-momentum and angular momentum conservation laws, a feature that is normally lacking in General Relativity.

An Introduction to Clifford Algebras and Spinors

Author: Vaz Jr.
Publisher: Oxford University Press
ISBN: 0191085782
Format: PDF, ePub
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This text explores how Clifford algebras and spinors have been sparking a collaboration and bridging a gap between Physics and Mathematics. This collaboration has been the consequence of a growing awareness of the importance of algebraic and geometric properties in many physical phenomena, and of the discovery of common ground through various touch points: relating Clifford algebras and the arising geometry to so-called spinors, and to their three definitions (both from the mathematical and physical viewpoint). The main point of contact are the representations of Clifford algebras and the periodicity theorems. Clifford algebras also constitute a highly intuitive formalism, having an intimate relationship to quantum field theory. The text strives to seamlessly combine these various viewpoints and is devoted to a wider audience of both physicists and mathematicians. Among the existing approaches to Clifford algebras and spinors this book is unique in that it provides a didactical presentation of the topic and is accessible to both students and researchers. It emphasizes the formal character and the deep algebraic and geometric completeness, and merges them with the physical applications. The style is clear and precise, but not pedantic. The sole pre-requisites is a course in Linear Algebra which most students of Physics, Mathematics or Engineering will have covered as part of their undergraduate studies.

Dirac Operatoren in der Riemannschen Geometrie

Author: Thomas Friedrich
Publisher: Springer-Verlag
ISBN: 3322803023
Format: PDF, Docs
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Dieses Buch entstand nach einer einsemestrigen Vorlesung an der Humboldt-Universität Berlin im Studienjahr 1996/ 97 und ist eine Einführung in die Theorie der Spinoren und Dirac-Operatoren über Riemannschen Mannigfaltigkeiten. Vom Leser werden nur die grundlegenden Kenntnisse der Algebra und Geometrie im Umfang von zwei bis drei Jahren eines Mathematik- oder Physikstudiums erwartet. Ein Anhang gibt eine Einführung in das aktuelle Gebiet der Seiberg-Witten-Theorie.

Kern und Teilchenphysik

Author: Claude Amsler
Publisher: vdf Hochschulverlag AG
ISBN: 3728136956
Format: PDF, ePub
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Dieses Buch bietet eine phänomenologische Einführung in die Welt der elementarsten Bausteine, die mit der Entdeckung der Radioaktivität im Jahre 1896 begann und bis zum kürzlich erfolgten Nachweis der Neutrino-Oszillationen reicht. Es richtet sich an Studierende der Physik, die die Grundlagen der Physik und Mathematik schon beherrschen. Der Stoff orientiert sich am Experiment, ist chronologisch aufgebaut und schlägt eine Brücke zwischen der Kern- und Teilchenphysik. Beschrieben werden die Methoden zur Herstellung von Teilchenstrahlen und zur Beobachtung von Teilchenreaktionen. Die bahnbrechenden Erkenntnisse werden anschaulich aus der Theorie hergeleitet und mit Messungen verglichen. Dieses Buch schliesst eine schon lange bestehende Lücke zwischen Kern- und Teilchenphysik und zwischen Experimenten und Theorie. Begriffe aus nieder- und hochenergetischen Bereichen der Teilchenphysik werden phänomenologisch hergeleitet und mit Messungen verglichen.

Attosecond Angular Streaking

Author: Petrissa Eckle
Publisher: Sudwestdeutscher Verlag Fur Hochschulschriften AG
ISBN: 9783838106854
Format: PDF, Docs
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In this thesis a new technique called 'attosecond angular streaking' (AAS) was applied for the first time. AAS allows to resolve ionization dynamics in the strong field regime with attosecond accuracy using only femtosecond pulses. In this regime, ionization mainly proceeds via tunneling through an energetically forbidden barrier. The process of tunneling is a fundamental and well-understood phenomenon in quantum mechanics. However, attempts to measure the 'tunneling time' have produced controversial results, partly due to the difficulty of defining a temporal operator in quantum mechanics, making it difficult to compare experiments. In this thesis, the question is addressed of whether the tunneling rate can adjust instantaneously to a changing barrier or if there is a delay between the field that defines the barrier and the corresponding tunneling ionization rate. It was found that indeed, no delay between the electric field and the corresponding tunneling rate exists within an experimental error limit of 12 attoseconds.