Clifford Algebras and Spinors
Clifford Algebras and Spinors
£44.99
GBPIn 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.
- Covers subject from basics up to recent research
- Comprehensive bibliography for researchers
- New material and exercises added
Reviews & endorsements
'The author gives a concise but thorough introduction to spinors and Clifford algebras extending from the very beginning to present research … A very recommendable book for everyone interested in this field.' G. Kowol, Monatschefte fur Mathematik
'This book sets standards in the field of quality and careful notation, especially in the relation of several kinds of spinors. It is highly recommended to teachers and researchers active in this field.' B. Fauser, Zentralblatt für Mathematik
'This book cannot be underestimated in its current influence.' B. Fauser, Zentralblatt für Mathematik
Product details
May 2001Paperback
9780521005517
352 pages
229 × 154 × 21 mm
0.478kg
35 b/w illus.
Available
Table of Contents
- 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.
