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An Introduction to Clifford Algebras and Spinors


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Table of Contents

1: Preliminaries
2: Exterior Algebra and Grassmann Algebra
3: Geometric or Clifford Algebra
4: Classification and Representation of the Clifford Algebras
5: Clifford Algebras and Associated Groups
6: Spinors
Appendix: The Standard 2-Component Spinor Formalism

About the Author

Jayme Vaz, Jr.: B. Sc. (1987) and M. Sc. (1990) degrees in Physics from University of São 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. Roldão 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, São 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.


This book wonderfully captures the essence of progress in the study of Clifford algebras and spinors. Throughout the text, from the word go, the reader finds various worked examples to help understand the ideas presented.
*Johar Ashfaque, IMA Book Reviews*

The authors approach is very clear and elementary despite the formal and rather heavy algebraic aspects involved. The numerous concrete examples given to illustrate each new notion are valuable for a better understanding of the subject and are helpful for potential applications in different fields.
*Oussama Hijazi, Acta Crystallographica A*

An Introduction to Clifford Algebras and Spinors is really an essential book to any student that wants to understand and grasp the several different (but under certain conditions equivalent) concepts of spinors appearing in the literature (algebraic, classical and operator spinors).
*Waldyr A. Rodrigues Jr., Institute of Mathematics, Statistics and Scientific Computation, State University of Campinas, Brazil*

This is a textbook that was missing until now. It presents the topic of spinors from many different viewpoints which are presently used in the literature and clarifies the connections among them. One is surprised by the vastness and fertility of this subject, and, at the same time, realizes that it provides the appropriate equipment to tackle fundamental themes such as Dirac and the second quantization of spinors.
*Loriano Bonora, Theoretical Particle Physics, SISSA, Italy*

The approach undertaken by the authors is very clear and friendly to the readers, because formal developments are nearly always accompanied by illustrative examples. This is a great merit of the book.
*Matej Pavsic, Jozef Stefan Institute*

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