Clifford algebras, built up from quadratic spaces, have applications in many areas of mathematics, as natural generalizations of complex numbers and the quaternions. They are famously used in proofs of the Atiyah-Singer index theorem, to provide double covers (spin groups) of the classical groups and to generalize the Hilbert transform. They also have their place in physics, setting the scene for Maxwell's equations in electromagnetic theory, for the spin of elementary particles and for the Dirac equation. This straightforward introduction to Clifford algebras makes the necessary algebraic background - including multilinear algebra, quadratic spaces and finite-dimensional real algebras - easily accessible to research students and final-year undergraduates. The author also introduces many applications in mathematics and physics, equipping the reader with Clifford algebras as a working tool in a variety of contexts.
Reihe
Sprache
Verlagsort
Zielgruppe
Illustrationen
ISBN-13
978-0-511-97299-7 (9780511972997)
Schweitzer Klassifikation
Autor*in
University of Cambridge
D. J. H. Garling is a Fellow of St John's College and Emeritus Reader in Mathematical Analysis at the University of Cambridge, in the Department of Pure Mathematics and Mathematical Statistics.
Introduction; Part I. The Algebraic Environment: 1. Groups and vector spaces; 2. Algebras, representations and modules; 3. Multilinear algebra; Part II. Quadratic Forms and Clifford Algebras: 4. Quadratic forms; 5. Clifford algebras; 6. Classifying Clifford algebras; 7. Representing Clifford algebras; 8. Spin; Part III. Some Applications: 9. Some applications to physics; 10. Clifford analyticity; 11. Representations of Spind and SO(d); 12. Some suggestions for further reading; Bibliography; Glossary; Index.
