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Clifford Algebras and Spinors

Clifford Algebras and Spinors

2nd Edition


Part of London Mathematical Society Lecture Note Series

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

£ 32.99

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About the Authors
  • 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.

    • Covers subject from basics up to recent research
    • Comprehensive bibliography for researchers
    • New material and exercises added
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    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

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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

    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

  • Author

    Pertti Lounesto, Helsinki Polytechnic

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