Your cart is empty.
  • Home

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

    By: Vaz Jr., Jayme [author.]Contributor(s): Rocha Jr., Roldão da, 1976- [author.]Material type: TextTextPublisher: Oxford, United Kingdom : Oxford University Press, 2016Copyright date: ©2016Edition: First editionDescription: xiv, 242 pages ; 26 cmContent type: text Media type: unmediated Carrier type: volumeISBN: 9780198782926; 0198782926Other title: Clifford algebras and spinorsSubject(s): Clifford algebras | Spinor analysis | Spinor analysis | Clifford algebras | Clifford-Algebra | SpinoranalysisDDC classification: 512/.57 LOC classification: QC20.7.C55 | V39 2016
    Contents:
    Preliminaries -- Vectors and Covectors -- The Tensor Product -- Tensor Algebra -- Exercises -- Exterior Algebra and Grassmann Algebra -- Permutations and the Alternator -- p-Vectors and p-Covectors -- The Exterior Product -- The Exterior Algebra (V) -- The Exterior Algebra as the Quotient of the Tensor Algebra -- The Contraction, or Interior Product -- Orientation, and Quasi-Hodge Isomorphisms -- The Regressive Product -- The Grassmann Algebra -- The Hodge Isomorphism -- Additional Readings -- Exercises -- Clifford, or Geometric, Algebra -- Definition of a Clifford Algebra -- Universal Clifford Algebra as a Quotient of the Tensor Algebra -- Some General Considerations -- Prom the Grassmann Algebra to the Clifford Algebra -- Grassmann Algebra versus Clifford Algebra -- Notation -- Additional Readings -- Exercises -- Classification and Representation of the Clifford Algebras -- Theorems on the Structure of Clifford Algebras -- The Classification of Clifford Algebras -- Idempotents and Representations -- Clifford Algebra Representations -- Additional Readings -- Exercises -- Clifford Algebras, and Associated Groups -- Orthogonal Transformations and the Cartan -- Dieudonne Theorem -- The Clifford -- Lipschitz Group -- The Pin Group and the Spin Group -- Conformal Transformations in Clifford Algebras -- Additional Readings -- Exercises -- Spinors -- The Babel of Spinors -- Algebraic Spinors -- Classical Spinors -- Spinor Operators -- A Comparison of the Different Definitions of Spinors -- The Inner Product in the Space of Algebraic Spinors -- The Triality Principle in the Clifford Algebraic Context -- Pure Spinors -- Dual Rotations, and the Penrose Flagpole -- Weyl Spinors in Cl3,0 -- Weyl Spinors in the Clifford Algebra Cl0,3 H H -- Spinor Transformations -- Spacetime Vectors as Paravectors of Cl3,0 from Weyl Spinors -- Paravectors of Cl4,1 in Cl3,0 via the Periodicity Theorem -- Twistors as Geometric Multivectors -- Spinor Classification According to Bilinear Covariants -- Additional Readings -- Exercises -- A The Standard Two-Component Spinor Formalism -- Weyl Spinors -- Contravariant Undotted Spinors -- Covariant Undotted Spinors -- Contravariant Dotted Spinors -- Covariant Dotted Spinors -- Null Flags and Flagpoles -- The Supersymmetry Algebra -- List of Symbols.
    Tags from this library: No tags from this library for this title. Log in to add tags.
        Average rating: 0.0 (0 votes)
    Item type Current library Call number Copy number Status Notes Date due Barcode
    Books Books Female Library
    		QC20.7.C55 .V39 2016 (Browse shelf (Opens below)) 1 Available STACKS 51952000329534
    Books Books Main Library
    		QC20.7.C55 .V39 2016 (Browse shelf (Opens below)) 1 Available STACKS 51952000329541

    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.

    1 2

    There are no comments on this title.

    to post a comment.