An Introduction to Clifford Algebras and Spinors

Abstract

AbstractThis book is unique in the literature on spinors and Clifford algebras in that it is accessible to both students and researchers while maintaining a formal approach to these subjects. Besides thoroughly introducing several aspects of Clifford algebras, it provides the geometrical aspects underlying the Clifford algebras, as well as their applications, particularly in physics. Previous books on spinors and Clifford algebras have either required the reader to have some prior expertise in these subjects, and thus were difficult to access, or did not provide a deep approach. In contrast, although this book is mathematically complete and precise, it demands little in the way of prerequisites—indeed, a course in linear algebra is the sole prerequisite. This book shows how spinors and Clifford algebras have fuelled interest in the no man’s land between physics and mathematics, an interest resulting from the growing awareness of the importance of algebraic and geometric properties in many physical phenomena. There is much common ground between Clifford algebras, including the geometry arising from those algebras, the classical groups, and the so-called spinors and their three definitions, including pure spinors and twistors, with their main point of contact being the representations of Clifford algebras and the periodicity theorems. Clifford algebras constitute a highly intuitive formalism and have an intimate relationship with quantum field theory; thus, this book will be useful for physicists as well as for mathematicians.