Clifford Algebras: An Introduction

ISBN-13: 9781107096387 / Angielski / Twarda / 2011 / 210 str.

D. J. H. Garling

Opis

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."

Recenzje

'… it became clear that Garling has spotted a need for a particular type of book, and has delivered it extremely well. Of all the books written on the subject, Garling's is by some way the most compact and concise … this is a very good book which provides a balanced and concise introduction to the subject of Clifford algebras. Math students will find it ideal for quickly covering a range of algebraic properties, and physicists will find it a very handy source of reference for a variety of material.' Chris Doran, SIAM News

Spis treści

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.