An Introduction to Clifford Algebras and Spinors
An in depth exploration of how Clifford algebras and spinors have been sparking collaboration and bridging the 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 points 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.
1132558501
An Introduction to Clifford Algebras and Spinors
An in depth exploration of how Clifford algebras and spinors have been sparking collaboration and bridging the 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 points 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.
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An Introduction to Clifford Algebras and Spinors

An Introduction to Clifford Algebras and Spinors

An Introduction to Clifford Algebras and Spinors

An Introduction to Clifford Algebras and Spinors

Overview

An in depth exploration of how Clifford algebras and spinors have been sparking collaboration and bridging the 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 points 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.

Product Details

ISBN-13: 9780198836285
Publisher: Oxford University Press
Publication date: 04/25/2019
Edition description: 2nd ed.
Pages: 256
Product dimensions: 9.70(w) x 6.80(h) x 0.70(d)

About the Author

Jayme Vaz, Jr., Professor of Mathematical Physics, University of Campinas, Brazil,Roldao da Rocha, Jr., Associate Professor, ABC Federal University, Brazil

Jayme Vaz, Jr.: B. Sc. (1987) and M. Sc. (1990) degrees in Physics from University of Sao Paulo (USP), Brazil, Ph.D. in Applied Mathematics (1993) and Habilitation in Mathematical Physics (1999) degrees from University of Campinas (Unicamp), Brazil. Since 1995, member of the academic staff of the Department of Applied Mathematics of the Institute of Mathematics, Statistics and Scientific Computations (IMECC) of Unicamp. Formerly director of IMECC (from 2006 to 2010). Research interests cover the area of Mathematical Physics, especially Clifford Algebras and their applications. Associate Editor of the journal Advances in Applied Clifford Algebras.

Roldao da Rocha, Jr.: Bachelor in Physics and Mathematics (1998), M.Sc. in Mathematics (2000) and Ph.D. in Physics (2005) at Campinas State University, Brazil. Post-Doctoral studies in the Theoretical Physics Institute, Sao Paulo, 2006-2007. Associate Professor at the Center of Mathematics of ABC Federal University, Brazil, wherein he has been working since 2007. In 2014 he spent the sabbatical year at the International School for Advanced Studied (SISSA), Trieste, Italy. Author of around 100 papers, on Mathematical-Physics, Gravity and Field Theory.

Table of Contents

1. Preliminaries2. Exterior Algebra and Grassmann Algebra3. Geometric or Clifford Algebra4. Classification and Representation of the Clifford Algebras5. Clifford Algebras and Associated Groups6. SpinorsAppendix. The Standard 2-Component Spinor Formalism
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