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Clifford Algebras and Spinorsby: Pertti Lounesto
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AbstractThis second edition of a popular and unique introduction to Clifford algebrasand spinors has three new chapters. The beginning chapters cover the basics:vectors, complex numbers and quaternions are introduced with an eye onClifford algebras. The next chapters, which will also interest physicists,include treatments of the quantum mechanics of the electron, electromagnetismand special relativity. A new classification of spinors is introduced, basedon bilinear covariants of physical observables. This reveals a new class ofspinors, residing among the Weyl, Majorana and Dirac spinors. Scalar productsof spinors are categorized by involutory anti-automorphisms of Cliffordalgebras. This leads to the chessboard of automorphism groups of scalarproducts of spinors. On the algebraic side, Brauer/Wall groups and Witt ringsare discussed, and on the analytic, Cauchy's integral formula is generalizedto higher dimensions.
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