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.
Author(s): A.A. Wessol, D.M. Pirro
Series: London Mathematical Society Lecture Note Series
Edition: 2
Publisher: Cambridge University Press
Year: 2001
Language: English
Pages: 346
Contents......Page 5
Preface......Page 6
Mathematical Not
ation......Page 8
1.
Vectors and Linear Spaces......Page 9
2.
Complex Numbers......Page 26
3.
Bivectors and the Exterior Algebra......Page 40
4.
Pauli Spin Matrices and Spinors......Page 58
5. Quaternions
......Page 74
6.
The Fourth Dimension......Page 88
7.
The Cross Product......Page 100
8. Electromagnetism
......Page 108
9. Lorentz
Transformations......Page 126
10.
The Dirac Equation......Page 143
11.
Fierz Identities and Boomerangs......Page 160
12.
Flags, Poles and Dipoles......Page 169
13.
Tilt to the Opposite Metric......Page 182
14.
Definitions of the Clifford Algebra......Page 195
15.
Witt Rings and Brauer Groups......Page 203
16.
Matrix Representations and Periodicity of 8......Page 213
17.
Spin Groups and Spinor Spaces......Page 227
18.
Scalar Products of Spinors and the Chessboard......Page 239
19.
Mobius Transformations and Vahlen Matrices......Page 251
20.
Hypercomplex Analysis......Page 263
21.
Binary Index Sets and Walsh Functions......Page 286
22.
Chevalley 's Construction and Characteristic 2......Page 296
23.
Octonions and Triality......Page 308
A History of Clifford Algebras......Page 328
Selected Reading......Page 338
Index......Page 343
