An introduction to Clifford algebras and spinors

An introduction to Clifford algebras and spinors / Jayme Vaz, Jr. and Roldão da Rocha, Jr.

This book is unique compared to the existing literature. It is very didactical and accessible to both students and researchers, without neglecting the formal character and the deep algebraic completeness of the topic along with its physical applications.

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Bibliographic Details
Main Authors: Vaz Jr., Jayme (Author), Rocha Jr., Roldão da, 1976- (Author)
Format: eBook
Language:English
Published: New York, NY : Oxford University Press, 2016.
Subjects:
Clifford algebras.
MATHEMATICS > Algebra > Intermediate.
Clifford algebras
Online Access:Click for online access
Table of Contents:
  • Preface; Acknowledgements; Contents; 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, Algebra3.1 Definition of a Clifford Algebra; 3.2 Universal Clifford Algebra as a Quotient of the Tensor Algebra; 3.3 Some General Considerations; 3.4 From 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 Exercises5 Clifford Algebras, and Associated Groups; 5.1 Orthogonal Transformations and the Cartan-Dieudonné 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 Flagpole6.10 Weyl Spinors in Cl3,0; 6.11 Weyl Spinors in the Clifford Algebra Cl0,3 C"H H; 6.12 Spinor Transformations; 6.13 Spacetime Vectors as Paravectors of cl3,0 from Weyl Spinors; 6.14 Paravectors of Cl4,1 cl3,0 in via the Periodicity Theorem; 6.15 Twistors as Geometric Multivectors; 6.16 Spinor Classi cation 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 SpinorsA. 5 Covariant Dotted Spinors; A.6 Null Flags and Flagpoles; A.7 The Supersymmetry Algebra; Appendix B List of Symbols; References; Index.

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