Description: 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 / softback, published 3 May 2001 352 pages 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]
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BIC Subject Area 1: Physics [PH]
BIC Subject Area 2: Algebra [PBF]
Number of Pages: 352 Pages
Publication Name: Clifford Algebras and Spinors
Language: English
Publisher: Cambridge University Press
Item Height: 229 mm
Subject: Mathematics
Publication Year: 2001
Type: Textbook
Item Weight: 478 g
Author: Pertti Lounesto
Item Width: 154 mm
Series: London Mathematical Society Lecture Note Series
Format: Paperback
