Clifford Algebras and Spinors (London Mathematical Society Lecture Note Series, Series Number 286)

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. Pertti Lounesto. Previous Ed.: 1997. Includes Bibliographical References And Index. 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. Beginning chapters, suited for undergraduates, introduce vectors, complex numbers, and quaternions as background for material on Clifford algebras. Later chapters, also of interest physicists, treat the quantum mechanics of the electron, electromagnetism, and special relativity. Recent research on Clifford algebras is surveyed, and a new classification of spinors is introduced, based on bilinear covariants of physical observables. Scalar products of spinors are classified by involuntary anti-automorphisms of Clifford algebras. Brauer-Wall groups and Witt rings are discussed, and Cauchy's integral formula is generalized to higher dimensions. The author is affiliated with Helsinki Polytechnic Stadia. This is the second edition of Professor Lounesto's unique introduction to Clifford algebras and spinors. The author has added new material and exercises. This book will be of interest to physicists as well as mathematicians and gives the first comprehensive survey of recent research on Clifford algebras.