This is the second edition of Professor Lounesto's unique introduction to Clifford algebras and spinors. The author has added new material and exercises. This book will be of interest to physicists as well as mathematicians and gives the first comprehensive survey of recent research on Clifford algebras.
This is the second edition of Professor Lounesto's unique introduction to Clifford algebras and spinors. The author has added new material and exercises. This book will be of interest to physicists as well as mathematicians and gives the first comprehensive survey of recent research on Clifford algebras.
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.
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.
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