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
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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