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Clifford Algebras and Spinors

Clifford Algebras and Spinors

2nd Edition

$130.00 (C)

Part of London Mathematical Society Lecture Note Series

  • Date Published: May 2001
  • availability: Available
  • format: Paperback
  • isbn: 9780521005517

$ 130.00 (C)
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  • This second edition of a popular and unique introduction to Clifford algebras and spinors has three new chapters. The beginning chapters cover the basics: vectors, complex numbers and quaternions are introduced with an eye on Clifford algebras. The next chapters, which will also interest physicists, include treatments of the quantum mechanics of the electron, electromagnetism and special relativity. A new classification of spinors is introduced, based on bilinear covariants of physical observables. This reveals a new class of spinors, residing among the Weyl, Majorana and Dirac spinors. Scalar products of spinors are categorized by involutory anti-automorphisms of Clifford algebras. This leads to the chessboard of automorphism groups of scalar products of spinors. On the algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy'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
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    Reviews & endorsements

    "This is certainly one of the best and most useful books written about Clifford algebras and spinors." Mathematical Reviews

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    Product details

    • Edition: 2nd Edition
    • Date Published: May 2001
    • format: Paperback
    • isbn: 9780521005517
    • length: 352 pages
    • dimensions: 229 x 154 x 21 mm
    • weight: 0.478kg
    • contains: 35 b/w illus.
    • availability: 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.

  • Author

    Pertti Lounesto, Helsinki Polytechnic

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