Overview

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.

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9780198782926

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Reviews

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 d *

An Introduction to Clifford Algebras and Spinors, by Jayme Vaz Jr. and Roldao da Rocha Jr. is a thoughtful exposition of the main results of the theory of Clifford algebras and spinors. It 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). Indeed, the concept of operator spinor is very important since besides revealing naturally the true geometrical nature of the concept it also clarifies that contrary to what is usually stated in the literature it is not the case that spinors are mathematical objects more fundamental than tensors. Indeed spinors can be written as some well-defined equivalence classes of non-homogeneous multivectors in appropriate Clifford algebras. 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

Author Information

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.

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