TY  - BOOK
AU  - Vaz Jr,Jayme
AU  - Rocha Jr,Roldão da
TI  - An introduction to Clifford algebras and spinors
SN  - 9780198782926
AV  - QC20.7.C55 V39 2016
U1  - 512/.57 23
PY  - 2016///
CY  - Oxford, United Kingdom
PB  - Oxford University Press
KW  - Clifford algebras
KW  - Spinor analysis
KW  - fast
KW  - Clifford-Algebra
KW  - gnd
KW  - Spinoranalysis
N1  - Includes bibliographical references (pages 231-237) and index; Machine generated contents note; 1; Preliminaries --; 1.1; Vectors and Covectors --; 1.2; The Tensor Product --; 1.3; Tensor Algebra --; 1.4; Exercises --; 2; Exterior Algebra and Grassmann Algebra --; 2.1; Permutations and the Alternator --; 2.2; p-Vectors and p-Covectors --; 2.3; The Exterior Product --; 2.4; The Exterior Algebra (V) --; 2.5; The Exterior Algebra as the Quotient of the Tensor Algebra --; 2.6; The Contraction, or Interior Product --; 2.7; Orientation, and Quasi-Hodge Isomorphisms --; 2.8; The Regressive Product --; 2.9; The Grassmann Algebra --; 2.10; The Hodge Isomorphism --; 2.11; Additional Readings --; 2.12; Exercises --; 3; Clifford, or Geometric, Algebra --; 3.1; Definition of a Clifford Algebra --; 3.2; Universal Clifford Algebra as a Quotient of the Tensor Algebra --; 3.3; Some General Considerations --; 3.4; Prom the Grassmann Algebra to the Clifford Algebra --; 3.5; Grassmann Algebra versus Clifford Algebra --; 3.6; Notation --; 3.7; Additional Readings --; 3.8; Exercises --; 4; Classification and Representation of the Clifford Algebras --; 4.1; Theorems on the Structure of Clifford Algebras --; 4.2; The Classification of Clifford Algebras --; 4.3; Idempotents and Representations --; 4.4; Clifford Algebra Representations --; 4.5; Additional Readings --; 4.6; Exercises --; 5; Clifford Algebras, and Associated Groups --; 5.1; Orthogonal Transformations and the Cartan -- Dieudonne Theorem --; 5.2; The Clifford -- Lipschitz Group --; 5.3; The Pin Group and the Spin Group --; 5.4; Conformal Transformations in Clifford Algebras --; 5.5; Additional Readings --; 5.6; Exercises --; 6; Spinors --; 6.1; The Babel of Spinors --; 6.2; Algebraic Spinors --; 6.3; Classical Spinors --; 6.4; Spinor Operators --; 6.5; A Comparison of the Different Definitions of Spinors --; 6.6; The Inner Product in the Space of Algebraic Spinors --; 6.7; The Triality Principle in the Clifford Algebraic Context --; 6.8; Pure Spinors --; 6.9; Dual Rotations, and the Penrose Flagpole --; 6.10; Weyl Spinors in Cl3,0 --; 6.11; Weyl Spinors in the Clifford Algebra Cl0,3 H H --; 6.12; Spinor Transformations --; 6.13; Spacetime Vectors as Paravectors of Cl3,0 from Weyl Spinors --; 6.14; Paravectors of Cl4,1 in Cl3,0 via the Periodicity Theorem --; 6.15; Twistors as Geometric Multivectors --; 6.16; Spinor Classification According to Bilinear Covariants --; 6.17; Additional Readings --; 6.18; Exercises --; Appendix; A The Standard Two-Component Spinor Formalism --; A.1; Weyl Spinors --; A.2; Contravariant Undotted Spinors --; A.3; Covariant Undotted Spinors --; A.4; Contravariant Dotted Spinors --; A.5; Covariant Dotted Spinors --; A.6; Null Flags and Flagpoles --; A.7; The Supersymmetry Algebra --; Appendix B; List of Symbols
ER  -