Clifford Algebras and Spinors

Here, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. This will interest physicists as well as mathematicians, and includes treatments of the quantum mechanics of the electron, electromagnetism and special relativity with Clifford algebras.

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In this book, Professor Lounesto offers a unique introduction to Clifford algebras and spinors. The beginning 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. A new classification of spinors is introduced, one 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 algebraic side, Brauer/Wall groups and Witt rings are discussed, and on the analytic, Cauchy's integral formula is generalised to higher dimensions.