Quaternions, Clifford Algebras and Relativistic Physics

ISBN-13: 9783764377908 / Angielski / Miękka / 2007 / 180 str.

Patrick R. Girard

Opis

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.

Spis treści

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

Blurb

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.