Synopsis:
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.
Book Description:
This is the second edition of a popular work offering 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. This edition has three new chapters, including material on conformal invariance and a history of Clifford algebras.
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