Quaternions, Clifford Algebras and Relativistic Physics

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.

List of contents

Quaternions.- Rotation groups SO(4) and SO(3).- Complex quaternions.- Clifford algebra.- Symmetry groups.- Special relativity.- Classical electromagnetism.- General relativity.- Conclusion.

Summary

The use of Clifford algebras in mathematical physics and engineering has grown rapidly in recent years. Whereas other developments have privileged a geometric approach, this book uses an algebraic approach that can be introduced as a tensor product of quaternion algebras and provides a unified calculus for much of physics. It 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.

Product details

• Authors: Patrick R Girard, Patrick R. Girard
• Publisher: Birkhäuser
• Languages: English
• Product format: Paperback / Softback
• Released: 01.01.2007
• EAN: 9783764377908
• ISBN: 978-3-7643-7790-8
• No. of pages: 192
• Weight: 545 g
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; Algebra, Gravitation, A, Gravity, Group Theory, Physics, Mathematics and Statistics, Relativity physics, Mathematical physics, Topological Groups, Lie Groups, Rings (Algebra), Topological groups, Lie groups, Topological Groups and Lie Groups, Groups & group theory, Group Theory and Generalizations, Mathematical Methods in Physics, Associative rings, Associative Rings and Algebras, Classical and Quantum Gravity, Classical and Quantum Gravitation, Relativity Theory