TY  - BOOK
AU  - Lounesto,Pertti
TI  - Clifford algebras and spinors
T2  - London Mathematical Society lecture note series
SN  - 9780511526022 (ebook)
AV  - QA199 .L68 2001
U1  - 512/.57 21
PY  - 2001///
CY  - Cambridge
PB  - Cambridge University Press
KW  - Clifford algebras
KW  - Spinor analysis
N1  - Title from publisher's bibliographic system (viewed on 05 Oct 2015); Vectors and linear spaces --; Complex numbers --; Bivectors and the exterior algebras --; Pauli spin matrices and spinors --; Quaternions --; Fourth dimension --; Cross product --; Elecromagnetism --; Lorentz transformations --; 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 --; Möbius transformations and vahlen matrices --; Hypercomplex analysis --; Binary index sets and walsh functions --; Chevalley's construction and characteristic 2 --; Octonions and triality
N2  - 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
UR  - https://doi.org/10.1017/CBO9780511526022
ER  -