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Quaternions, Clifford Algebras and Relativistic Physics [electronic resource] /by Patrick R. Girard.

by Girard, Patrick R [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookPublisher: Basel : Birkhäuser Basel, 2007.Description: XII, 179 p. 2 figs. online resource.ISBN: 9783764377915.Subject(s): Mathematics | Algebra | Group theory | Topological Groups | Mathematical physics | Relativity (Physics) | Mathematics | Algebra | Associative Rings and Algebras | Group Theory and Generalizations | Topological Groups, Lie Groups | Mathematical Methods in Physics | Relativity and CosmologyDDC classification: 512 Online resources: Click here to access online
Contents:
Foreword -- Introduction -- 1. Quaternions -- 2. Rotation Groups SO(3) and SO(4) -- 3. Complex Quaternions -- 4. Clifford Algebras -- 5. Symmetry Groups -- 6. Special Relativity -- 7. Classical Electromagnetism -- 8. General Relativity -- Conclusion -- Solutions to Exercises -- Appendices -- Bibliography.
In: Springer eBooksSummary: The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have priviledged a geometric approach, the author uses an algebraic approach which can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. The book proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism and general relativity. The volume is intended for students, researchers and instructors in physics, applied mathematics and engineering interested in this new quaternionic Clifford calculus.
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Foreword -- Introduction -- 1. Quaternions -- 2. Rotation Groups SO(3) and SO(4) -- 3. Complex Quaternions -- 4. Clifford Algebras -- 5. Symmetry Groups -- 6. Special Relativity -- 7. Classical Electromagnetism -- 8. General Relativity -- Conclusion -- Solutions to Exercises -- Appendices -- Bibliography.

The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have priviledged a geometric approach, the author uses an algebraic approach which can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. The book proposes a pedagogical introduction to this new calculus, based on quaternions, with applications mainly in special relativity, classical electromagnetism and general relativity. The volume is intended for students, researchers and instructors in physics, applied mathematics and engineering interested in this new quaternionic Clifford calculus.

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