Clifford Algebras & Spinors

Pertti Lounesto - Collection London Mathematical Society Student Texts

338 pages, parution le 27/09/2004 (2^eme édition)

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Résumé

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.

Sommaire

Vectors and linear spaces
Complex numbers
Bivectors and the exterior algebra
Pauli spin matrices and spinors
Quaternions
The fourth dimension
The cross product
Electromagnetism
Lorentz transformations
The 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
Mobius transformations and Vahlen matrices
Hypercomplex analysis
Binary index sets and Walsh functions
Chevalley's construction and characteristic 2
Octonions and triality
A history of Clifford algebras
Selected reading

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Pertti Lounesto
Collection	London Mathematical Society Student Texts
Parution	27/09/2004
Édition	2^eme édition
Nb. de pages	338
Format	15 x 22,5
Couverture	Broché
Poids	472g
Intérieur	Noir et Blanc
EAN13	9780521005517
ISBN13	978-0-521-00551-7