Clifford Algebras and Spinors

This is the second edition of Professor Lounesto's unique introduction to Clifford algebras and spinors.

Pertti Lounesto (Author)

9780521005517, Cambridge University Press

Paperback, published 3 May 2001

352 pages, 35 b/w illus.
22.9 x 15.4 x 2.1 cm, 0.478 kg

'This book cannot be underestimated in its current influence.' B. Fauser, Zentralblatt für Mathematik

In this book, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. The initial chapters could be read by undergraduates; vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters will also interest physicists, and include treatments of the quantum mechanics of the electron, electromagnetism and special relativity with a flavour of Clifford algebras. This book also gives the first comprehensive survey of recent research on Clifford algebras. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing between the Weyl, Majorana and Dirac spinors. Scalar products of spinors are classified by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the analytic side, Brauer-Wall groups and Witt rings are discussed, and Caucy's integral formula is generalized to higher dimensions.

Preface
Mathematical notation
1. Vectors and linear spaces
2. Complex numbers
3. Bivectors and the exterior algebra
4. Pauli spin matrices and spinors
5. Quaternions
6. The fourth dimension
7. The cross product
8. Electromagnetism
9. Lorentz transformations
10. The Dirac equation
11. Fierz identities and boomerangs
12. Flags, poles and dipoles
13. Tilt to the opposite metric
14. Definitions of the Clifford algebra
15. Witt rings and Brauer groups
16. Matrix representations and periodicity of 8
17. Spin groups and spinor spaces
18. Scalar products of spinors and the chessboard
19. Möbius transformations and Vahlen matrices
20. Hypercomplex analysis
21. Binary index sets and Walsh functions
22. Chevalley's construction and characteristic 2
23. Octonions and triality
A history of Clifford algebras
Selected reading
Index.

Subject Areas: Physics [PH], Algebra [PBF]