Quaternions, Clifford Algebras and Relativistic Physics
Girard, Patrick R.
Quaternions, Clifford Algebras and Relativistic Physics [electronic resource] / by Patrick R. Girard. - XII, 180 p. 2 illus. online resource.
Quaternions -- Rotation groups SO(4) and SO(3) -- Complex quaternions -- Clifford algebra -- Symmetry groups -- Special relativity -- Classical electromagnetism -- General relativity -- Conclusion.
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.
9783764377915
10.1007/978-3-7643-7791-5 doi
Mathematics.
Algebra.
Associative rings.
Rings (Algebra).
Group theory.
Topological groups.
Lie groups.
Physics.
Gravitation.
Mathematics.
Algebra.
Classical and Quantum Gravitation, Relativity Theory.
Associative Rings and Algebras.
Group Theory and Generalizations.
Topological Groups, Lie Groups.
Mathematical Methods in Physics.
QA150-272
512
Quaternions, Clifford Algebras and Relativistic Physics [electronic resource] / by Patrick R. Girard. - XII, 180 p. 2 illus. online resource.
Quaternions -- Rotation groups SO(4) and SO(3) -- Complex quaternions -- Clifford algebra -- Symmetry groups -- Special relativity -- Classical electromagnetism -- General relativity -- Conclusion.
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.
9783764377915
10.1007/978-3-7643-7791-5 doi
Mathematics.
Algebra.
Associative rings.
Rings (Algebra).
Group theory.
Topological groups.
Lie groups.
Physics.
Gravitation.
Mathematics.
Algebra.
Classical and Quantum Gravitation, Relativity Theory.
Associative Rings and Algebras.
Group Theory and Generalizations.
Topological Groups, Lie Groups.
Mathematical Methods in Physics.
QA150-272
512