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Clifford Algebras and Spinors


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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. Moebius 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.

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


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

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