Format:
1 Online-Ressource (ix, 338 pages)
,
digital, PDF file(s).
Edition:
Second edition.
ISBN:
9780511526022
Series Statement:
London Mathematical Society lecture note series 286
Content:
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.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
,
Vectors and linear spaces -- Complex numbers -- Bivectors and the exterior algebras -- Pauli spin matrices and spinors -- Quaternions -- Fourth dimension -- Cross product -- Elecromagnetism -- Lorentz transformations -- Dirac equation -- Fierz identities and boomerangs -- Flags, poles and dipoles -- Tilt to the opposite metric -- Definitions of the clifford algebra -- Witt rings and brauer groups -- Matrix representations and periodicity of 8 -- Spin groups and spinor spaces -- Scalar products of spinors and the chessboard -- Möbius transformations and vahlen matrices -- Hypercomplex analysis -- Binary index sets and walsh functions -- Chevalley's construction and characteristic 2 -- Octonions and triality.
Additional Edition:
ISBN 9780521005517
Additional Edition:
ISBN 9780521005517
Additional Edition:
ISBN 9780521005517
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780521005517
Language:
English
DOI:
10.1017/CBO9780511526022
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